Real-time estimation of aeroelastic flutter

Abstract

A system including an excitation pod coupled to distal end of an aircraft wing and a shaker assembly including a linear guide, a moving mass movable along the linear guide, an excitation actuator structured to move the moving mass, and an inertial measurement unit. An accelerometer array is configured to be coupled to the aircraft wing and the system includes one or more processing circuits comprising one or more memory devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide a predetermined excitation force, receive information from the accelerometer array and the inertial measurement unit, and determine a frequency response function as a measure of a flutter boundary of the aircraft wing based on the received information.

Description

REAL-TIME ESTIMATION OF AEROELASTIC FLUTTERCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 503,783, filed on May 23, 2023, the entire contents of which are incorporated herein by reference.GOVERNMENT LICENSES RIGHTS

[0002] This invention was made with government support under grant / contract number 15-C- UAS-OSU-A awarded by the Federal Aviation Administration. The government has certain rights in the invention.BACKGROUND

[0003] This disclosure relates to aircraft wing flutter. More specifically, this disclosure relates to systems, devices, and methods for determining a parametric flutter boundary.SUMMARY

[0004] In some aspects, the techniques described herein relate to a system for determining a parametric flutter margin including: an excitation pod including a housing structured to be coupled to distal end of an aircraft wing, and a shaker assembly including a linear guide coupled to the housing, a moving mass movable along the linear guide, an excitation actuator structured to move the moving mass, and an inertial measurement unit; an accelerometer array configured to be coupled to the aircraft wing; and one or more processing circuits including one or more memory devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide a predetermined excitation force parallel to the linear guide, receive information from the accelerometer array and the inertial measurement unit in response to providing the predetermined excitation force, and determine a frequency response function as a measure of a flutter boundary of the aircraft wing based on the received information.

[0005] In some aspects, the techniques described herein relate to a system, wherein the excitation pod further includes a static mass spaced apart from the moving mass.

[0006] In some aspects, the techniques described herein relate to a system, wherein a stabilization mass is defined by a ratio between the static mass and the moving mass.

[0007] In some aspects, the techniques described herein relate to a system, wherein the shaker assembly is positioned forward of an elastic axis of the aircraft wing.

[0008] In some aspects, the techniques described herein relate to a system, wherein at least one of the one or more processing circuits is positioned within the excitation pod.

[0009] In some aspects, the techniques described herein relate to a system, wherein the excitation actuator is a voice coil motor.

[0010] In some aspects, the techniques described herein relate to a system, further including a calibration fixture having a clamp sized to hold the shaker assembly, the clamp coupled to a load cell.

[0011] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to calibrate the shaker assembly using the calibration fixture.

[0012] In some aspects, the techniques described herein relate to a system, further including a ground vibration testing system configured to rigidly hold the aircraft wing.

[0013] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide the predetermined excitation force parallel to the linear guide while the aircraft wing is rigidly held by the ground vibration testing system, and determine a pre-flight frequency response function.

[0014] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to determine finite element analysis model tuning parameters including stiffness and damping characteristics based on results of a ground vibration test.

[0015] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed bythe one or more processors, cause the one or more processors to determine a finite element analysis frequency response function based on the tuned finite element analysis model.

[0016] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide the predetermined excitation force parallel to the linear guide while the aircraft wing is in flight, and determine an in-flight frequency response function.

[0017] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: determine a pre-flight frequency response function, determine a finite element analysis frequency response function, and determine an in-flight frequency response function.

[0018] In some aspects, the techniques described herein relate to a system, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to generate a report including the pre-flight frequency response function, the finite element analysis frequency response function, and the in-flight frequency response function.

[0019] In some aspects, the techniques described herein relate to an excitation pod including: a tubular housing structured to be coupled to a distal end of an aircraft wing; and a shaker assembly including a moving mass, an excitation actuator structured to move the moving mass, and an inertial measurement unit, wherein the shaker assembly is positioned within the tubular housing forward of a elastic axis of the aircraft wing.

[0020] In some aspects, the techniques described herein relate to an excitation pod, wherein the excitation actuator is a voice coil motor.

[0021] In some aspects, the techniques described herein relate to an excitation pod, further including one or more processing circuits including one or more memory devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to determine a frequency response function as a measure of a flutter boundary of the aircraft wing.

[0022] In some aspects, the techniques described herein relate to a method including: controlling operation of an excitation actuator to impart a predetermined excitation force via an excitation pod coupled to a distal end of an aircraft wing while the aircraft is in flight; and determine an in-flight frequency response function as a measure of flutter boundary based information received from an accelerometer array coupled to the aircraft wing and an inertial measurement device within the excitation pod.

[0023] In some aspects, the techniques described herein relate to a method, further including: coupling the aircraft wing to a ground vibration testing system; receiving pre-flight information from the accelerometer array and the inertial measurement device within the excitation pod during a ground vibration test; determining a pre-flight frequency response function based on the preflight information; and outputting the pre-flight frequency response function and the in-flight frequency response function.

[0024] This summary is illustrative only and is not intended to be in any way limiting. Other aspects, features, and advantages of the devices or processes described herein will become apparent in the detailed description set forth herein, taken in conjunction with the accompanying figures, wherein like reference numerals refer to like elements.BRIEF DESCRIPTION OF DRAWINGS

[0025] The device is explained in even greater detail in the following drawings. The drawings are merely exemplary and certain features may be used singularly or in combination with other features. The drawings are not necessarily drawn to scale.

[0026] FIG. 1 is a schematic view of an aircraft including excitation pods, according to some implementations.

[0027] FIG. 2 is a schematic view of the excitation pod of FIG. 1, according to some implementations.

[0028] FIG. 3 is a perspective view of a shaker assembly of the excitation pod of FIG. 2, according to some implementations.

[0029] FIG. 4 is a schematic representation of a wing of the aircraft of FIG. 1 mounted in a ground vibration testing system, according to some implementations.

[0030] FIG. 5 is a schematic representation of the controller of the aircraft of FIG. 1, according to some implementations.

[0031] FIG. 6 is a flow diagram of a method of determining a parametric flutter margin, according to some implementations.DETAILED DESCRIPTION

[0032] Following below are more detailed descriptions of concepts related to, and implementations of, methods, apparatuses, and systems for determining a parametric flutter margin. The figures illustrate exemplary implementations in detail and the present disclosure is not limited to the details or methodology set forth in the description or illustrated in the figures. The terminology used herein is for the purpose of description only and should not be regarded as limiting.

[0033] Referring to the figures generally, the various implementations disclosed herein relate to systems, apparatuses, and methods for determining a parametric flutter margin 11 by utilizing a excitation pod mounted on an aircraft wing. The excitation pod includes a shaker assembly having a moving mass actuatable by an excitation actuator, an inertial measurement unit, and a control system. The parametric flutter margin is determined by conducting a ground vibration test with the aircraft wing fixed in place at a proximal wing end and the excitation pod positioned at a distal end of the aircraft wing. Predetermined excitation forces are applied to the wing by the excitation pod, and vibration information is collected. A finite element analysis model of the aircraft wing is created tuned based on the vibration information. A digital parametric flutter margin is then determined digitally using the finite element analysis model. The aircraft wing is then mounted to an aircraft, and an experimental parametric flutter margin is determined in flight tests using the excitation pod. The digital parametric flutter margin is then compared to the experimental parametric flutter margin, and a report is generated. The excitation pod allows for accurate digital and experimental determinization of the parametric flutter margin and improves the ability of accurate testing for unmanned aircraft and other aircraft.

[0034] Of the numerous setbacks that may occur during the certification process of an aircraft, the onset of unexpected aeroelastic flutter may be the most catastrophic. Aeroelastic flutter occurs when unsteady aerodynamic and structural forces couple in an unstable manner, resulting in unbounded oscillations of an aircraft’s structure. In cases where corrective action is not taken inan appropriate amount of time, these unstable structural modes may lead to severe damage to the vehicle, loss of aircraft, or loss of life.

[0035] For new or modified aircraft to pass certification requirements, flight testing must be accomplished that demonstrates freedom from flutter, proper damping margins, and non-rapid reduction of damping over the proposed flight envelope. Past flight-testing campaigns have verified compliance with these requirements by subjecting the aircraft to higher dynamic pressures until flutter onset is perceived to be imminent. Multiple data reduction techniques have been proposed and utilized over the past 90 years to predict an aircraft’s flutter onset speed from collected flight-test data. Specifically, flight-test engineers have relied on methods such as damping extrapolation, Zimmerman-Weissenburger flutter margin, envelope functions, Nissim- Gilyard method, and Autoregressive Moving Average (ARMA) models to predict flutter-prone flight conditions from subcritical test points. Unfortunately, all the listed methods may require an aircraft to operate at dynamic pressures dangerously close to flutter onset to collect data related to flutter margins. Consequently, any uncertainty in the predictive models, atmospheric turbulence, or deviation from the targeted flight conditions may result in inadvertently adding energy to the aircraft’s structure and exciting an unstable aeroelastic response. As a result, these methods cannot be safely applied at the flutter onset velocity and are extrapolative in nature. With the growing desire to certify Unmanned Aerial Vehicles (UAVs) and Urban Air Mobility (UAM) vehicles with unique configurations for commercial operations, safe and accurate flight-test methodologies that positively identify flutter margins without exposing the vehicle to flutter are needed.

[0036] The Parametric Flutter Margin (PFM) method allows data to be collected at flight conditions exceeding the nominal aircraft’s flutter boundary through the addition of a stabilizing mass ahead of the elastic axis of the lifting surface. Simulation techniques can be utilized to compute the flutter onset condition of a simple three-degree-of-freedom airfoil and generic transport aircraft model. These numerical simulations show that the flutter boundary calculated via the PFM method and classical flutter analysis techniques, such as the p-k method (NASTRAN) and g-method (ZAERO), agreed within 0.7%. This indicates that the PFM method can be used for frequency-based analysis of an aeroelastic system at the flutter onset speed of the unmodified wing without the need for extrapolation to higher velocities.

[0037] The PFM method has been successfully applied to several experiments conducted within a controlled wind tunnel environment. A small stabilizing mass can be added to the wing tip’s leading edge, and an impedance head can be utilized to provide an excitation force to the structure.The computed Frequency Response Functions (FRFs) indicated that the nominal wing section’s flutter boundary identified via the PFM method and by traditional flutter testing techniques was within 6%. Furthermore, this experiment demonstrated that the addition of a stabilizing mass element ahead of the elastic axis of the wing structure, required for PFM in flight-test, increased the dynamic pressure needed to excite aeroelastic instabilities. In some implementations, a flexible half-wing model with a tip store containing a stabilizing mass element positioned well ahead of the wing’s leading edge can be tested. In this experiment, a known excitation force can be applied to the wing by abruptly cutting a pre-loaded tension chord attached to the stabilizing mass element. Again, the PFM method can be applied and can identify the nominal wing’s flutter onset condition without relying on conventional aeroelastic models. Additionally, aeroelastic testing can be performed with half of a flying wing UAV in a subsonic low turbulence wind tunnel to investigate the applicability of a self-contained electro-mechanical shaker pod for use in combination with the PFM method.

[0038] This work extends the wind tunnel demonstrations of the PFM methodology to a flighttest, using a highly instrumented flexible wing vehicle developed specifically for this purpose. As a result of operating outside of a controlled wind tunnel environment, complexities related to rigid- body flight dynamics and atmospheric turbulence effects must be considered. This disclosure includes a pre-flight Ground Vibration Test (GVT) of an isolated flexible wing to characterize its modal response fortuning of a FEAmodel. This FEAmodel was used to generate body-free flutter predictions and was compared to an initial round of flight testing. This disclosure includes applying the PFM method to an aircraft in free flight.

[0039] As shown in FIG. 1, a flight test vehicle 10 includes a fuselage 14, a tail 18, and two wings 22. Each wing 22 includes an excitation pod 26, and an accelerometer array 30. In some implementations, the flight test vehicle 10 is a fixed-wing small-scale unmanned aerial vehicle (UAV) operating in a free-flight environment. In some implementations, the flight test vehicle 10 is a traditional fixed-gear, tail-dragger monoplane featuring a high-mounted wing and conventional empennage. An exemplary fuselage 14 was constructed with birch plywood covered with an UltraKote polymer skin. Foam cores covered with fiberglass composite skin were utilized to build both horizontal and vertical stabilizers. To mitigate engine vibrations, an electric propulsion system consisting of an E-flite Power 160 brushless motor, Castle Creation Edge High Voltage 80 Amp Electronic Speed Controller, two Zippy 5S 8000 mAh Lithium-Polymer batteries, and an APC 19x 12e propeller was selected to power the flight test vehicle 10. A Castle CreationCC Battery Eliminating Circuit 2.0 was used to supply power from the propulsion system to five HiTec HS-645MG servos responsible for deflecting aerodynamic control surfaces. The servos were actuated by a Pixhawk 4 autopilot system, which served as the guidance, navigation, and control flight computer for the flight test vehicle 10. Additional geometric and performance specifications of the flight-test vehicle are listed in Table 1.

[0040] Table 1 shows the geometric and performance specifications of the exemplary flight-test vehicle 10.

[0041] The exemplary flight test vehicle’s 10 flexible wings 22 were 3.4 m long. The straight, untapered rectangular wing used an SD-7043 airfoil and had an aspect ratio of 10. Additionally, a 2° dihedral angle was incorporated to improve lateral-directional handling qualities. The wing’s 22 structure consisted of 3D printed Nylon 12 airfoil sections joined together along a 6061- aluminum front and rear spar. Due to the allowable printing volume of the SLS machine, each wing half 22 included eight individual airfoil sections approximately 0.15 m in length. The front and rear spars spanned the entire length of the wing 22 and have a 25.4 mm x 25.4 mm hollow square cross-section and 19.1 mm diameter hollow circular geometry, respectively. Furthermore, the left-wing and right-wing halves 22 mount to the fuselage 14 via a stainless-steel central wing box.

[0042] The exemplary wing 22 was equipped with the accelerometer array 30, including sixteen ADX333 3-axis accelerometers distributed equally along the front and rear aluminum spars. The spatial distribution of the accelerometers is offset by 0.2 m between the left-wing and right-wing halves 22 to reduce the possibility of locating a sensor at a structural node.

[0043] As shown in FIG. 2, each excitation pod 26 includes a shaker assembly 34 and a controller38. In some implementations, the excitation pod 26 is constructed as a fiberglass tube. In someimplementations, the excitation pod 26 is a 0.61 m x 0.07 m cylindrical fiberglass tube mounted to each wingtip of the flexible wing 22. The shaker assembly 34 can be positioned at discrete locations inside the excitation pod 26 ahead of an elastic axis of the wing 22, which positively augments the aeroelastic system’s stability. Consequently, the shaker assembly 34 can provide both the stabilizing element and mechanism for generating the exciting force required for the determination of the parametric flutter margin. In some implementations, the excitation pod 26 further includes an additional static mass 40 (e.g., 100 gm) located at the rear of excitation pod 26, added to reduce the nominal flutter velocity.

[0044] As shown in FIG. 3, the shaker assembly 34 includes a housing 42 sized to be received within the excitation pod 26, a guide rail 46 secured to the housing 42, a guide shaft 48 secured to the housing 42, a moving mass 48 constrained by the guide rail 46 and the guide shaft 48, an excitation actuator in the form of a voice coil motor 54, and an inertial measurement unit 58.

[0045] In some implementations, an 82-gram moving mass 50 is driven by a linear voice coil 54 and transverses a 60 mm magnetic guide shaft 48 such that the resultant force acts perpendicular to a local chord line. In some implementations, the guide rail 46 is eliminated. In some implementations, the guide shaft 48 is eliminated. In some implementations, the inertial measurement unit 58 includes a small MPU-9250 Inertial Measurement Unit (IMU) attached to the moving mass 50 such that the induced force applied to the wing 22 structure can be computed via Newton’s laws of motion, F=mmvamv. In some implementations, the inertial measurement unit 58 includes a closed-loop position controller that incorporates feedback from a Hall effect sensor and is utilized to track desired sinusoidal motion with input frequencies up to 20 Hz. The exemplary inertial measurement unit 58 can be equipped with an additional MPU-9250 such that the flexible wing 22 structural dynamic response can be measured. Experimental data associated with both the excitation pod 26 and the accelerometer array 30 are communicated to the controller 38 and information can be stored (e.g., stored on a local micro-SD card at a sampling rate of 200 Hz). Other masses may be added to the excitation pod 26 to reduce the nominal flutter velocity into the flight test vehicle 10 achievable flight envelope for research purposes.

[0046] As shown in FIG. 4, a ground vibration testing system 60 includes a rigid structure to which the wing 22 can be mounted. In some implementations, the wing 22 is rigidly mounted to an optical table. By rigidly mounting the wing 22 to a significantly more massive base, the measured acceleration response data can be directly attributed to the structural dynamics of the wing 22. In some implementations, the ground vibration testing system 60 includes a calibrationfixture having a shaker assemble clamp connected to a load cell. The calibration fixture is used to measure and calibrate a force output of the shaker assembly 34. In some implementations, the calibration fixture includes a Polylactic Acid (PLA) 3D-printed clamp, and a base mounted 2-axis Futek MBA500 load cell rated for a maximum applied force and torque of 222 N and 5.65 Nm, respectively. In some implementations, the Futek load cell is connected to a custom signal conditioner and sampled at 4 kHz using a National Instrument’s USB-6009 DAQ.Controller Architecture

[0047] Referring now to FIG. 5, a schematic diagram of the controller 38 is shown according to an example implementation. As shown in FIG. 5, the controller 38 includes a processing circuit 62 having a processor 66 and a memory device 70, a control system 74 having a pre-flight circuit 78, an FEA model circuit 82, an excitation circuit 86, a data collection circuit 90, and a frequency response function circuit 94, and a communications interface 98. Generally, the controller 38 is structured to communicate with and control the accelerometer array 30, the voice coil motor 54, the inertial measurement unit 58, and the ground vibration testing system 60 to implement a method of determining the parametric flutter margin.

[0048] Generally, the method of determining the parametric flutter margin is configured for use on an aeroelastic system and can be modified in a prescribed manner such that the nominal system’s flutter onset condition is artificially increased by the addition of a stabilizing mass and a hypothetical single-input-single-output (SISO) feedback system. A known excitation force is applied coincidentally to the stabilizing mass’s position, and the resulting structural dynamics are measured to compute frequency response functions. The phase cross-over frequency and corresponding gain margin can be recorded for increasing dynamic pressures to obtain a gain margin versus velocity curve. Of particular interest is the velocity corresponding to a gain margin of 0 dB, which can indicate the nominal (unmodified) aeroelastic system’s flutter boundary. Due to the addition of the stabilizing element, parametric flutter margin testing can be conducted at airspeeds exceeding the unmodified vehicle’s flutter speed, allowing for positive identification of the flutter boundary in a safe manner.

[0049] The application of the method of determining the parametric flutter margin to experimental data can be demonstrated using the augmented aeroelastic system modeled by Eq. 1 in the frequency domain.

[0050] In Eq. 1, A represents the nominal system’s generalized mass, stiffness, damping, and unsteady aerodynamic terms, Bf dictates the modal distribution of the excitation input, Cf is the row-output vector, Uf corresponds to the excitation input, yf is associated with the resulting output, and a> signifies frequency. Pf is associated with the stabilizing mass, assumed to affect flutter only in the z-direction, normal to the wing’s planform.

[0051] The stabilization parameter is defined as the ratio between the shaker assembly’s static mass, mst, and moving mass, rrtmv. Consequently, the aeroelastic system previously described in Eq. 1 can be expressed in terms of the moving mass’s acceleration, amv, and static mass’s acceleration, ast. This representation is presented below in Eq. 2, where 0eis defined as the modal displacement vector in the z-direction at the moving mass’s point of action.

[0052] A salient feature of the method of determining the parametric flutter margin is the inclusion of a stabilizing element such that flight conditions exceeding the nominal flutter boundary can be safely explored. Additionally, the aeroelastic system’s dynamic response to an applied excitation can be accurately measured such that frequency response functions can be identified.

[0053] In one configuration, the circuits of the control system 74 are in the form of machine or computer-readable media that is executable by a processor, such as processor 66. As described herein, the machine-readable media facilitates the performance of certain operations to enable the reception and transmission of data. For example, the machine-readable media may provide an instruction (e.g., command, etc.) to acquire data. In this regard, the machine-readable media may include programmable logic that defines the frequency of acquisition of the data (or, transmission of the data). The computer readable media may include code written in any programming language. The computer readable program code may be executed on one processor, multiple co located processors, multiple remote processors, or any combination of local and remote processors. Remote processors may be connected to each other through any type of network (e.g., CAN bus,etc.). In particular, the pre-flight circuit 78 and the FEA model circuit 82 can be located remotely from the excitation pod 26.

[0054] In another configuration, the circuits of the control system 74 are implemented as hardware units, such as electronic control units. As such, the circuits of the control system 74 may be implemented as one or more circuitry components including, but not limited to, processing circuitry, network interfaces, peripheral devices, input devices, output devices, sensors, etc. In some implementations, the circuits of the control system 74 may take the form of one or more analog circuits, electronic circuits (e.g., integrated circuits (IC), discrete circuits, system on a chip (SOCs) circuits, microcontrollers, etc.), telecommunication circuits, hybrid circuits, and any other type of “circuit.” In this regard, the circuits of the control system 74 may include any type of component for accomplishing or facilitating achievement of the operations described herein. For example, a circuit as described herein may include one or more transistors, logic gates (e.g., NAND, AND, NOR, OR, XOR, NOT, XNOR, etc.), resistors, multiplexers, registers, capacitors, inductors, diodes, wiring, and so on). The circuits of the control system 74 may also include programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like. The circuits of the control system 74 may include one or more memory devices for storing instructions that are executable by the processor(s) of the circuits of the control system 74. The one or more memory devices and processor(s) may have the same definition as provided below with respect to the memory device 70 and processor 66. In some hardware unit configurations, the circuits of the control system 74 may be geographically dispersed throughout separate locations. Alternatively and as shown, the circuits of the control system 74 may be implemented in or within a single unit / housing, which is shown as the controller 38.

[0055] In the example shown, the controller 38 includes the processing circuit 62 having the processor 66 and the memory device 70. The processing circuit 62 may be structured or configured to execute or implement the instructions, commands, and / or control processes described herein with respect to the circuits of the control system 74. The depicted configuration represents the circuits of the control system 74 as machine or computer-readable media. However, as mentioned above, this illustration is not meant to be limiting as the present disclosure contemplates other implementations where the circuits of the control system 74, or at least one circuit of the circuits of the control system 74, is configured as a hardware unit. All such combinations and variations are intended to fall within the scope of the present disclosure.

[0056] The hardware and data processing components used to implement the various processes, operations, illustrative logics, logical blocks, modules and circuits described in connection with the implementations disclosed herein (e.g., the processor 66) may be implemented or performed with a general purpose single- or multi-chip processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, or, any conventional processor, or state machine. A processor also may be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some implementations, the one or more processors may be shared by multiple circuits (e.g., the circuits of the control system 74 may comprise or otherwise share the same processor which, in some example implementations, may execute instructions stored, or otherwise accessed, via different areas of memory). Alternatively or additionally, the one or more processors may be structured to perform or otherwise execute certain operations independent of one or more co-processors. In other example implementations, two or more processors may be coupled via a bus to enable independent, parallel, pipelined, or multi -threaded instruction execution. All such variations are intended to fall within the scope of the present disclosure.

[0057] The memory device 70 (e.g., memory, memory unit, storage device) may include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage) for storing data and / or computer code for completing or facilitating the various processes, layers and modules described in the present disclosure. The memory device 70 may be communicably connected to the processor 66 to provide computer code or instructions to the processor 66 for executing at least some of the processes described herein. Moreover, the memory device 70 may be or include tangible, non-transient volatile memory or non-volatile memory. Accordingly, the memory device 70 may include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described herein.

[0058] The pre-flight circuit 78 is structured to control the voice coil motor 54 and the ground vibration testing system 60, and utilize information received from the accelerometer array 30 and the voice coil motor 54 to conduct pre-flight ground vibration testing. A method of determiningthe parametric flutter margin can require precise knowledge of the external force applied to the wing 22 to positively identify a flutter boundary of the flight test vehicle 10. Consequently, the ground vibration testing system 60 is used to verify that the force generated by the shaker assembly 34 can be applied to the wing 22 with minimal attenuation and phase lag. The pre-flight circuit 78 controls testing during pre-flight and collects information regarding the dynamic response of the wing 22 while connected to the ground vibration testing system 60.

[0059] When the shaker assembly 34 is secured to the calibration fixture of the ground vibration testing system 60, Eq. 3 can be used to calculate the external force, Fex, generated by the shaker assembly 34 in terms of the moving mass 50 and the corresponding vertical acceleration component. Since the moving mass 50 is constrained to translate in a direction perpendicular to the local chord line, it is assumed that both the acceleration and excitation forces act along the same local z-axis.

[0060] The transfer function described by Eq. 4 can be used to determine the gain and phaseshift characteristics of the external forcing function of the excitation pod 26.

[0061] In Eq. 4, F ex denotes the force generated by the moving mass while Fex,m represents the applied force as directly measured by the load cell of the calibration fixture of the ground vibration testing system 60.

[0062] The resulting transfer function can be depicted in a Bode plot. The exemplary experimental data used to identify the frequency response function can be collected by performing a frequency sweep over the excitation pod’s operational frequency range of 2- 20 Hz. In some implementations, the shaker assembly 34 has a mean gain value of 1.03 ±0.05 and a mean phaseshift angle of 0.8°±2.1° across the excitation pod’s operational frequency range.

[0063] Although the method of determining the parametric flutter margin is not model -based, the flight-testing procedures are aided by knowledge of the anticipated flutter mechanism as estimated from an approximate FEA model (discussed in more detail below with respect to the FEA modelcircuit 82). To enable the FEA model circuit 82 to calibrate the FEA model of the flexible wing’s structure, ground vibration tests are conducted before flight tests. Ground vibration tests are conducted such that frequency response functions can be identified through measured acceleration data and compared to the computational model. Significant variations between the experimental and computational frequency response functions were addressed by tuning the FEA model’s mass, stiffness, and damping properties. By validating the model’s structural dynamic response at zero airspeed, better estimates of the projected flutter onset speed can be determined. This, in turn, will be used to establish the flight conditions targeted during the flight-testing campaign and validate the results of the method of determining the parametric flutter margin.

[0064] As described above, the method of determining the parametric flutter margin requires precise knowledge of the aeroelastic system’s dynamic response at the same location as the applied excitation force. Since the inertial measurement unit 58 of the shaker assembly 34 is positioned well behind the moving mass 50, a transformation is required to estimate a response of the wing 22 at a centroid of the shaker assembly 34. By utilizing accelerometer and gyroscope measurements from onboard sensors of the controller 38 in combination with rigid-body dynamics, an acceleration vector of the static mass, ast, can be estimated by Eq. 5. In Eq. 5, aCb corresponds to the control board’s rectilinear acceleration vector; X is the displacement vector between the control board’s IMU and static mass’s centroid; pCb, qCb, and rCb represent the control board’s body axis roll, pitch, and yaw angular velocities, respectively; and p'cb, qCb, and r'cb are associated with the control board’s body axis roll, pitch, and yaw angular accelerations, respectively.

[0065] The transfer function described in Eq. 6 is used to define the frequency response function associated with the ground vibration testing campaign. In Eq. 6, the static mass’s vertical acceleration component, ast,z, is computed by Eq. 5, and the moving mass’s vertical acceleration, amv,z, is directly measured by the shaker assembly’s MPU-9250 IMU. It should be noted that a negative sign is included to account for the reaction force generated from the moving mass onto the wing’s structure.

[0066] The frequency response functions of the isolated flexible wing can be shown in Bode plots. Experimental information was used to show both the left-wing and right-wing halves’ transfer functions defined in Eq. 6. The frequency response functions were identified by performing a 2 - 20 Hz frequency sweep with the excitation pod system. It should be noted that left- and right-wing ground vibration trials can performed separately to mitigate coupled dynamics and better isolate each wing half’s frequency response characteristics.

[0067] In the experimental information, distinct gain peaks were observed at input frequencies of 3.7 Hz and 3.8 Hz and correspond to the natural frequencies of the left- and right-wing's first bending modes. The associated phase angles also indicate a change of 180° in the vicinity of the gain peaks. These experimental results closely match the estimated bending frequency predicted by the FEA model. Additional peaks in the gain at higher input frequencies of 17.6 Hz and 17.0 Hz are also present for the left- and right-wings and correspond to the first torsional mode. Lastly, a phase angle change of 180° can be observed at an input frequency of approximately 8 Hz for both wings without a corresponding gain peak. Spectral data from the x-axis acceleration indicates a slight peak at 8.5 Hz, corresponding to a weak fore-aft mode. It should be noted that the corresponding FEA model did not predict this in-plane mode. When comparing the two experimental frequency response functions, the identified bending and torsional modes have slightly different natural frequencies and corresponding gain values between the left and right wings. Although both wings were built utilizing the same construction techniques, it is possible that the stiffness, damping, and mass attributes of each wing differed due to slight variations in material properties associated with the spar structure and 3D-printed airfoil sections.

[0068] The FEA model circuit 82 is structured to generate and update a finite element analysis (FEA) model of the wing 22 and / or the flight test vehicle 10 in view of information gathered by the pre-flight circuit 78.

[0069] In some implementations, the FEA model includes estimates of the clamped wing’s eight lowest-frequency modes tabulated with the respective mode descriptions and natural frequencies. The FEA model of the flexible wing attached to a rigid base simulates the wing 22 fixed to the ground vibration testing system 60 described above. This wing configuration is referred to as “Basic” below. The flexible wing’s FEA model is based on the corresponding CAD drawing andincorporates material properties associated with the physical system’s components. During experimentation, the 3D printed wing sections were modeled with Nylon 12 material, and 6061 aluminum was used for both wing spars. The experimental FEA model was based on 2479 grid points. There are three couples of wing modes in the bending, torsion, and fore-aft directions. It may be observed that the symmetric frequencies are practically identical to the anti-symmetric ones, indicating that FEA wings are practically identical and that the frequencies reflect those of separate clamped wings. In some implementations, the FEA model includes a NASTRAN finite- element model in FEMAP. A detailed NASTRAN FEA model developed from the flight-test vehicle’s CAD drawings with 9,162 grid points and more than 50,000 degrees of freedom (DOF) was used to estimate the free-flight frequency response of the vehicle.

[0070] The FEA model is used to calculate the frequency response functions of ast to a unitamplitude force in the z-direction. Three changes were made to compare the results with those of the ground vibration testing discussed above conducted via the pre-flight circuit 78. The first was multiplication of the frequency response function by -amvCist / = -82 / 67 to obtain the transfer function of Eq. 6. The second was performing the response calculations with the damping coefficients $=0.04 around 4 Hz and $=0.06 around 17 Hz to approximate the damping coefficients deduced from the width of the peak shape of the right-wing. The third change was removing the moving mass, mmv=82 gm, from the modal properties because this mass generates the external excitation. The resulting frequency response function indicates peaks at 4.3 Hz and 17 Hz with amplitudes and widths similar to those of the right-wing. The tuned model aligns well with the experimental data, even for the left wing, where a slight model asymmetry is indicated.

[0071] Normal modal analysis was carried out for the full vehicle with the excitation pods located at each of the aircraft’s wingtips. Six rigid-body modes and 14 low-frequency elastic modes were used for preliminary flutter analyses of this configuration. This FEA model was used to estimate the flexible wing’s symmetric and anti-symmetric modes’ aeroelastic frequencies for the true airspeed cases conducted in the flight testing, which are tabulated below in Table 2.

[0072] The excitation circuit 86 is structured to control the shaker assembly 34 including the voice coil motor 54 to instigate flutter and conduct in-flight testing.

[0073] Following the completion of the ground vibration testing, flight testing was conducted using the flight test vehicle 10. The flight tests discussed below were performed to estimate frequency response functions at different airspeeds and identify trends relating to the flexiblewing’s structural modes at increasing dynamic pressures. These experimental results are then compared to those identified by the tuned FEA model.

[0074] Unlike the ground vibration testing, which calculated the frequency response function of each wing half in isolation, the flight-test results rely on decomposing the flexible wing’s structural response into separate symmetric and anti-symmetric frequency response functions. The input and output acceleration measurements are modified by incorporating both symmetric, uSym, and anti-symmetric, uasym, components (Eq. 7 and Eq. 8). Equations 7 and 8 are expressed in terms of the moving mass’s vertical acceleration signals as directly measured by the IMUs attached to the left and right shaker assemblies.

[0075] Similarly to Eq. 7 and Eq. 8, the flexible wing’s symmetric response signal, ysym, and anti-symmetric response signal, yaSym, are calculated via Eq. 9 and Eq. 10, respectively. In Eq. 9 and Eq. 10, ast,zLand ast,zRdenote the static mass’s vertical acceleration components as calculated by Eq. 5 for both the left- and right-wings.q. )

[0076] The transfer functions presented below in Eq. 11 and Eq. 12 were numerically evaluated via MATLAB’s tfestimate function to calculate the flexible wing’s symmetric and anti-symmetric frequency response functions.

[0077] It should be noted that the forcing functions applied to the wing’s structure during the flight test were generated simultaneously by both the left- and right-wings’ excitation pods 26. Both excitation pods 26 performed a frequency sweep between 2 - 20 Hz over a 30-second test window. The frequency sweeps were approximately time-aligned as both the left- and right-shaker assemblies 34 follow a pre-programmed command signal that varies the input frequency as a function of elapsed time. During the frequency sweeps, the flight-test vehicle 10 maintained a steady, level, unaccelerated flight condition to mitigate the effects of unsteady loading on the airframe.

[0078] The data collection circuit 90 is structured to collect information from the pre-flight circuit 78, the FEA model circuit 82, and the excitation circuit 86. In some implementations, all excitation and response data were processed through a bandpass filter with a passband of 2 - 22 Hz in order to attenuate both rigid-body dynamics and higher frequency noise exceeding the excitation pods’ operational frequency range.

[0079] The frequency response function circuit 94 is structured to communicate with the preflight circuit 78 to determine pre-flight frequency response functions, communicate with the FEA model circuit 82 to determine FEA frequency response functions, and communicate with the excitation circuit 86 to determine in-flight frequency response functions.

[0080] Experimentally, symmetric frequency response functions for TAS conditions of 26.7 ms- 1, 31.8 ms-1, and 35.2 ms-1 were determined. The low-frequency range of the frequency response functions was noisy, but peak amplitudes are observed at input frequencies of 3.7 Hz, 4.5 Hz, and 4.6 Hz for each of the tested airspeeds. Comparing the phase behavior with the pre-flgiht results indicates these natural frequencies corresponding to the wing’s first symmetric bending mode. Additional peak amplitudes associated with the first symmetric torsional mode were observed at higher frequencies of 16.2 Hz for each explored flight condition. Although the first symmetric bending mode’s natural frequency increases with airspeed, the natural frequency of the first symmetric torsional mode remains constant. A phase angle shift was observed at input frequencies around 7 Hz for each of the test conditions explored. Similar to the pre-flight frequency response functions, the gain subplot did not indicate a corresponding gain peak. Given the similarities between the flight test and pre-flight frequency response functions, this phase angle shift likelyrepresents an in-plane structural mode that does not have a significant impact on the flutter mechanism.

[0081] Experimentally, the anti-symmetric frequency response functions from the same flight tests showed that gain peaks occured at input frequencies of 16.1 Hz, 15.6 Hz, and 15.9 Hz, corresponding to the first anti-symmetric torsional mode’s aeroelastic frequencies. Results for the symmetric and anti-symmetric natural frequencies are listed below in Table 2 for direct comparison to predicted FEA frequency response functions results.

[0082] Compared to the symmetric modes, the anti-symmetric gain and phase subplots have substantially higher noise. This behavior can be explained by referencing Eq. 8, which computes the anti-symmetric input function, uasym, in terms of the difference between the left- and rightmoving mass measured acceleration signals. As previously mentioned, both excitation pods were approximately time aligned throughout the execution of the flight test. Consequently, the left- and right-moving mass’ measured acceleration signals were nearly identical in the time domain, resulting in a significantly attenuated anti-symmetric forcing function. Since the resultant antisymmetric response signal was comprised of a diluted component associated with the excitation pods’ applied force, the frequency response functions were dominated by external anti-symmetric accelerations from atmospheric turbulence or aircraft rigid-body dynamics. As a result, the uncertainty associated with the anti-symmetric frequency response functions, as estimated by flight-test data, are significantly higher than their symmetric counterparts. Even so, the measured gains are small when the phase angles are close to zero, implying being far from the nominal system’s flutter speed.

[0083] Table 2 Identified aeroelastic frequencies from FEA model and flight tests.

[0084] Numerical flutter results, used for the test design and for comparisons with the test results, are presented in this section. The FEA model was used for calculating the six rigid-bodymodes and 19 low-frequency elastic modes of the Basic configuration considered in flutter analyses using the ZAERO and DynResp codes. The variations of damping coefficients and aeroelastic frequencies with velocity were calculated by ZAERO. Flutter occurs when a damping branch crosses the zero line. The lowest anti-symmetric and symmetric flutter velocities, with the associated flutter frequency and shape, are compared in Table 3 to those obtained with the shaker masses removed (nominal configuration). The shaker’s mass increases the flutter velocity to 7% beyond that of the nominal configuration, which makes the PFM flutter test safer. However, the predicted flutter velocities are well beyond the flight-test vehicle’s performance envelope.

[0085] Table 3 Flutter parameters of Basic (with moving mass) and nominal (without moving mass) configurations.

[0086] Simulations of the flutter tests were performed using the method of determining the parametric flutter margin in the DynResp code, with the shaker’s mass removed to obtain the nominal configuration and with Pf = 67 gm at the shaker’s point of action used as the flutter parameter. Two simulations were performed, a symmetric and an anti-symmetric, for the transfer functions of Eq. 11 and 12, respectively. Bode plots were generated for the three flight-test velocities, and for several velocities between 60 and 72 ms-1 around the anticipated flutter onset condition. The resulting flutter velocities are slightly higher than the nominal model results of Table 3 because the ZAERO calculations were performed with modal structural damping of g = 0.02, while the presented DynResp results are with the GVT-based increased damping values. This work presented the first flight-test evaluation of the PFM method for safe flutter testing. A detailed series of experiments were conducted to characterize the excitation pods that provide the necessary input force for the PFM method. By characterizing the shaker assemblies used to excite the wing’selastic modes, it was shown that the excitation force can be resolved with minimal attenuation and phase lag. An initial GVT study of the flexible wing rigidly mounted in isolation was conducted to tune an FEA model. After adjusting the model’s mass, stiffness, and damping characteristics, the computationally estimated natural frequencies closely aligned with those identified experimentally within 16%. Lastly, an initial demonstration of the PFM method and excitation pods was performed in the free-flight environment. Through this flight testing, the symmetric bending and torsional natural frequencies identified via the PFM method agreed within 1.95 Hz and 0.4 Hz of the FEA predictions, respectively. Additionally, the experimental results indicated a predicted shift in the flexible wing’s first symmetric bending and first antisymmetric torsional aeroelastic frequencies with increased airspeed. Flight-test data also revealed challenges with recovering anti-symmetric modal characteristics due to the approximately time-aligned excitation functions. The results of the abbreviated free-flight testing indicate initial promise in applying the PFM method to flutter flight-testing campaigns.

[0087] While various circuits with particular functionality are shown in FIG. 5, it should be understood that the controller 38 may include any number of circuits for completing the functions described herein. For example, the activities and functionalities of the circuits of the control system 74 may be combined in multiple circuits or as a single circuit. Additional circuits with additional functionality may also be included. Further, the controller 38 may further control other activity beyond the scope of the present disclosure. In some implementations, the circuits described herein may include one or more processing circuits comprising one or more memory devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to perform the operations performed herein and described with reference to circuits.

[0088] As mentioned above and in one configuration, the “circuits” may be implemented in machine-readable medium for execution by various types of processors, such as the processor 66 of FIG. 5. An identified circuit of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions, which may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified circuit need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the circuit and achieve the stated purpose for the circuit. Indeed, a circuit of computer readable program code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among differentprograms, and across several memory devices. Similarly, operational data may be identified and illustrated herein within circuits, and may be implemented in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.

[0089] While the term “processor” is briefly defined above, the term “processor” and “processing circuit” are meant to be broadly interpreted. In this regard and as mentioned above, the “processor” may be implemented as one or more general-purpose processors, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), digital signal processors (DSPs), or other suitable electronic data processing components structured to execute instructions provided by memory. The one or more processors may take the form of a single core processor, multi -core processor (e.g., a dual core processor, triple core processor, quad core processor, etc.), microprocessor, etc. In some implementations, the one or more processors may be external to the apparatus, for example the one or more processors may be a remote processor (e.g., a cloud based processor). Alternatively or additionally, the one or more processors may be internal and / or local to the apparatus. In this regard, a given circuit or components thereof may be disposed locally (e.g., as part of a local server, a local computing system, etc.) or remotely (e.g., as part of a remote server such as a cloud based server). To that end, a “circuit” as described herein may include components that are distributed across one or more locations.

[0090] Implementations within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.

[0091] As shown in FIG. 6, a method of determining a parametric flutter margin 100 includes calibrating a shaker assembly 34 at step 104, conducting a ground vibration test of a wing 22 including an excitation pod 26 using a ground vibration testing system 60 at step 108, determining a pre-flight frequency response function based on the results of the ground vibration test at step 110, generating an FEA model based on the results of the ground vibration test at step 112, determining a FEA frequency response function using the generated EA model at step 114, controlling shaker assembly 34 during a flight test at step 116, determining an in-flight frequency response function based on information received during the flight test at step 118, and comparing the pre-flight frequency response function, the FEA frequency response function and the in-flight frequency response function in step 120. The method 100 can also include generating a report comparing and / or validating the frequency response functions at step 122.Conclusion

[0092] For purposes of this description, certain advantages and novel features of the aspects and configurations of this disclosure are described herein. The described methods, systems, and apparatus should not be construed as limiting in any way. Instead, the present disclosure is directed toward all novel and nonobvious features and aspects of the various disclosed aspects, alone and in various combinations and sub-combinations with one another. The disclosed methods, systems, and apparatus are not limited to any specific aspect, feature, or combination thereof, nor do the disclosed methods, systems, and apparatus require that any one or more specific advantages be present or problems be solved.

[0093] Although the figures and description may illustrate a specific order of method steps, the order of such steps may differ from what is depicted and described, unless specified differently above. Also, two or more steps may be performed concurrently or with partial concurrence, unless specified differently above. Such variation may depend, for example, on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations of the described methods could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps, and decision steps.

[0094] Features disclosed in this specification (including any accompanying claims, abstract, and drawings), and / or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and / or steps are mutuallyexclusive. The claimed features extend to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract, and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0095] As used in the specification and the appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another aspect includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about”, it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. The terms “about” and “approximately” are defined as being “close to” as understood by one of ordinary skill in the art. In one non-limiting aspect the terms are defined to be within 10%. In another non-limiting aspect, the terms are defined to be within 5%. In still another non-limiting aspect, the terms are defined to be within 1%.

[0096] The terms “coupled”, “connected”, and the like as used herein mean the joining of two members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another. If “coupled” or variations thereof are modified by an additional term (e.g., directly coupled), the generic definition of “coupled” provided above is modified by the plain language meaning of the additional term (e.g., “directly coupled” means the joining of two members without any separate intervening member), resulting in a narrower definition than the generic definition of “coupled” provided above. Such coupling may be mechanical, electrical, or fluidic. For example, circuit A communicably “coupled” to circuit B may signify that the circuit A communicates directly with circuit B (i.e., no intermediary) or communicates indirectly with circuit B (e.g., through one or more intermediaries).

[0097] Certain terminology is used in the following description for convenience only and is not limiting. The words “right”, “left”, “lower”, and “upper” designate direction in the drawings to which reference is made. The words “inner” and “outer” refer to directions toward and away from, respectively, the geometric center of the described feature or device. The words “distal” and“proximal” refer to directions taken in context of the item described and, with regard to the instruments herein described, are typically based on the perspective of the practitioner using such instrument, with “proximal” indicating a position closer to the practitioner and “distal” indicating a position further from the practitioner. The terminology includes the above-listed words, derivatives thereof, and words of similar import.

[0098] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises”, means “including but not limited to”, and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal aspect. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0099] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description but is not intended to be exhaustive or limited to the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the present disclosure.

Claims

What is claimed is:

1. A system for determining a parametric flutter margin comprising: an excitation pod including a housing structured to be coupled to distal end of an aircraft wing, and a shaker assembly including a linear guide coupled to the housing, a moving mass movable along the linear guide, an excitation actuator structured to move the moving mass, and an inertial measurement unit; an accelerometer array configured to be coupled to the aircraft wing; and one or more processing circuits comprising one or more memory devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide a predetermined excitation force parallel to the linear guide, receive information from the accelerometer array and the inertial measurement unit in response to providing the predetermined excitation force, and determine a frequency response function as a measure of a flutter boundary of the aircraft wing based on the received information.

2. The system of claim 1, wherein the excitation pod further includes a static mass spaced apart from the moving mass.

3. The system of claim 2, wherein a stabilization mass is defined by a ratio between the static mass and the moving mass.

4. The system of claim 1, wherein the shaker assembly is positioned forward of an elastic axis of the aircraft wing.

5. The system of claim 1, wherein at least one of the one or more processing circuits is positioned within the excitation pod.

6. The system of claim 1, wherein the excitation actuator is a voice coil motor.

7. The system of claim 1, further comprising a calibration fixture having a clamp sized to hold the shaker assembly, the clamp coupled to a load cell.

8. The system of claim 7, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to calibrate the shaker assembly using the calibration fixture.

9. The system of claim 1, further comprising a ground vibration testing system configured to rigidly hold the aircraft wing.

10. The system of claim 9, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide the predetermined excitation force parallel to the linear guide while the aircraft wing is rigidly held by the ground vibration testing system, and determine a pre-flight frequency response function.

11. The system of claim 1, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to determine finite element analysis model tuning parameters including stiffness and damping characteristics based on results of a ground vibration test.

12. The system of claim 11, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to determine a finite element analysis frequency response function based on the tuned finite element analysis model.

13. The system of claim 1, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: control operation of the excitation actuator to provide the predetermined excitation force parallel to the linear guide while the aircraft wing is in flight, anddetermine an in-flight frequency response function.

14. The system of claim 1, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to: determine a pre-flight frequency response function, determine a finite element analysis frequency response function, and determine an in-flight frequency response function.

15. The system of claim 14, wherein the one or more memory devices are further configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to generate a report including the pre-flight frequency response function, the finite element analysis frequency response function, and the in-flight frequency response function.

16. An excitation pod comprising: a tubular housing structured to be coupled to a distal end of an aircraft wing; and a shaker assembly including a moving mass, an excitation actuator structured to move the moving mass, and an inertial measurement unit, wherein the shaker assembly is positioned within the tubular housing forward of a elastic axis of the aircraft wing.

17. The excitation pod of claim 16, wherein the excitation actuator is a voice coil motor.

18. The excitation pod of claim 16, further comprising one or more processing circuits comprising one or more memory devices coupled to one or more processors, the one or more memory devices configured to store instructions thereon that, when executed by the one or more processors, cause the one or more processors to determine a frequency response function as a measure of a flutter boundary of the aircraft wing.

19. A method compri sing : controlling operation of an excitation actuator to impart a predetermined excitation force via an excitation pod coupled to a distal end of an aircraft wing while the aircraft is in flight; and determine an in-flight frequency response function as a measure of flutter boundary based information received from an accelerometer array coupled to the aircraft wing and an inertial measurement device within the excitation pod.

20. The method of claim 19, further comprising: coupling the aircraft wing to a ground vibration testing system; receiving pre-flight information from the accelerometer array and the inertial measurement device within the excitation pod during a ground vibration test; determining a pre-flight frequency response function based on the pre-flight information; and outputting the pre-flight frequency response function and the in-flight frequency response function.

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