A broadband vibration absorber with dual-mode coupling and a design method thereof

Abstract

The present invention belongs to the technical field of mechanical vibration reduction, and discloses a broadband vibration absorber with dual-mode coupling and a design method thereof, wherein the broadband vibration absorber comprises a base, a guide column is arranged on the top surface of the base, a main system to be absorbed is slidably mounted on the guide column, a spring is arranged on the guide column sleeve, and the spring is located between the main system to be absorbed and the base, two fixed plates are arranged on the top surface of the main system to be absorbed, and a slide groove arranged in the vertical direction is arranged above the two fixed plates, a hinge support is arranged on the top surface of the main system to be absorbed, and the hinge support is located between the two fixed plates, and a smooth ball joint is arranged at the hinge support, and a vibration absorbing beam is connected to the top surface of the smooth ball joint, a cylindrical pin is fixed above the vibration absorbing beam, and the two ends of the cylindrical pin are located in the two slide grooves, and the vibration absorbing beam is connected to a hollow rod arranged in the horizontal direction, and both ends of the hollow rod are provided with a mass ball. The beneficial effects of the present invention are as follows: the amplitude overflow effect generated by single-mode vibration absorption can be effectively suppressed, and the integrated and compact design of dual-mode vibration absorption is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical vibration reduction, and in particular to a broadband vibration absorber with dual-mode coupling and a design method thereof. Background Art

[0002] In aviation transport equipment, the operation of mechanical systems will generate a large amount of vibration, which not only affects driving safety and comfort, but also easily leads to structural vibration fatigue failure, bringing severe challenges to the safe service of equipment. Dynamic vibration absorption technology can effectively absorb vibration energy at a certain resonant frequency, reduce vibration amplitude, extend the service life of mechanical systems, and thus reduce maintenance costs and operating costs. Therefore, it has been widely used. However, the mechanical systems in the transport equipment cabin are often subject to multi-source loads and are prone to low-bandwidth forced vibrations. Therefore, it is necessary to develop technologies and devices that can effectively absorb vibrations in multiple modes or wider frequency bands.

[0003] The vibration absorption band of traditional linear dynamic vibration absorbers is narrow, and new resonance peaks will be generated on both sides of the vibration absorption band, making it difficult to achieve full-band vibration reduction in the field of aviation equipment under lightweight conditions. Nonlinear vibration absorption is an effective way to achieve broadband vibration absorption and reduce amplitude overflow. Self-parameter resonance is a modal coupling nonlinear mechanism with square nonlinear characteristics, and thus has saturation and penetration characteristics. The modal coupling of the forced resonance mode of the main system to be absorbed and the parametric resonance mode of the vibration absorbing beam can cause the main mechanical system to produce saturation, that is, the amplitude of the main system to be absorbed will not increase with the increase of the excitation amplitude. This mechanism can achieve broadband vibration absorption and reduce the amplitude overflow on both sides of the vibration absorption band. However, due to the nonlinear hysteresis effect, although the amplitude overflow amplitude is reduced, the overflow band is widened. If an integrated vibration absorption structure that uses multi-frequency self-parameter resonance to achieve modal coupling vibration absorption can be designed, it is of great significance to develop a multi-modal collaborative vibration absorber design method for broadband vibration absorption in the full band and reduce amplitude overflow.

[0004] Therefore, it is necessary to provide a broadband vibration absorber with dual modal coupling and a design method thereof, which can be used for broadband vibration reduction of mechanical systems in aircraft and other aviation transportation equipment, so as to overcome the defects of traditional vibration absorbers with narrow operating frequency band, high overflow amplitude and wide overflow frequency band. Summary of the invention

[0005] The present invention discloses a broadband vibration absorber with dual-mode coupling and a design method thereof, and specifically relates to a broadband vibration absorber with dual-mode coupling self-parametric resonance of bending-torsion coupling and a design method thereof, which can be used for broadband vibration reduction of mechanical systems in aviation equipment such as aircraft, and can effectively solve the technical problems involved in the background technology.

[0006] To achieve the above object, the technical solution of the present invention is:

[0007] A broadband vibration absorber with dual-mode coupling comprises a base, the top surface of the base is provided with a guide column, a main vibration-absorbed system is slidably mounted on the guide column, the guide column sleeve is provided with a spring, the spring is located between the main vibration-absorbed system and the base, the top surface of the main vibration-absorbed system is provided with two fixed plates arranged relatively at intervals, a slide groove arranged in a vertical direction is provided above the two fixed plates, a hinge support is provided on the top surface of the main vibration-absorbed system, the hinge support is located between the two fixed plates, a smooth ball joint is provided at the hinge support, a vibration-absorbing beam is connected to the top surface of the smooth ball joint, a cylindrical pin is fixed above the vibration-absorbing beam, two ends of the cylindrical pin are located in the two slide grooves, the vibration-absorbing beam is connected to a hollow rod arranged in a horizontal direction, and mass balls are provided at both ends of the hollow rod.

[0008] As a preferred improvement of the present invention: the number of the guide columns is 4 and they are evenly distributed around the base.

[0009] As a preferred improvement of the present invention: the vibration-absorbed main system is provided with reinforcing ribs, and the reinforcing ribs are connected to the fixing plate.

[0010] As a preferred improvement of the present invention: the hollow rod is located at the midpoint of the vibration absorbing beam, and the distances from the two mass balls to the vibration absorbing beam are the same.

[0011] As a preferred improvement of the present invention: the top surface of the hinge support is recessed downward to form a rotation space, and a hinge support cover is fixed to the top surface of the hinge support via a hinge support screw, and the hinge support cover limits the smooth ball hinge to the rotation space.

[0012] As a preferred improvement of the present invention: a boss is provided on the top surface of the vibration-absorbed main system, and the guide column passes through the boss.

[0013] As a preferred improvement of the present invention: the outer diameter of the hollow rod does not exceed the width of the vibration absorbing beam, the length of the hollow rod does not exceed 3 / 5 of the height of the vibration absorbing beam, and the diameter of the mass ball is less than twice the outer diameter of the hollow rod.

[0014] A design method for a broadband vibration absorber with dual-mode coupling comprises the following steps:

[0015] S1. Perform vibration test on the base to obtain the excitation frequency and excitation amplitude provided by the base to the main vibration absorption system, and calculate the natural frequency ω of the main vibration absorption system nm and the damping ratio of the spring ζ3;

[0016] S2. Derive the dynamic control equations of the vibration absorption system;

[0017] Firstly, the displacement field model of the vibration absorbing beam is established;

[0018] (1)

[0019] in: , , It is the relative displacement of any point on the vibration absorbing beam in the x, y, and z directions with the main vibration absorbing system as the reference system. and denote the mid-plane displacements corresponding to x=0 and z=0, respectively; v and w denote the longitudinal and transverse displacements of the central axis on the mid-plane; t denotes time; φ denotes the cross-sectional angle related only to the y-direction position; is the sector coordinate;

[0020] Using the von Karman nonlinear geometric relationship, the positive strain in the y direction is obtained , shear strain in xy direction , shear strain in yz direction and ,

[0021] (2)

[0022] Where: Subscript Respectively represent the first and second order partial derivatives of the coordinate y;

[0023] (3)

[0024] Where: yy represents the normal stress in the y direction, represents the shear stress in the yz direction, b represents the width of the vibration absorbing beam, h represents the thickness of the vibration absorbing beam, E represents the Young's modulus of the vibration absorbing beam, G represents the shear modulus, Ix and Iz are the moments of inertia of the cross section on the x and z axes respectively, is the sector moment of inertia of the cross section, J is the polar moment of inertia of the centroid of the cross section;

[0025] (4);

[0026] The control equations for the coupling of the bending mode and torsional mode of the vibration absorbing beam expressed by internal force and the mode of the main vibration absorbing system are obtained.

[0027] (5)

[0028] in: represents the first-order derivative of displacement with respect to time, represents the second-order derivative of each displacement with respect to time; v m represents the displacement of the main system being absorbed, represents the base excitation displacement, l represents the length of the vibration absorbing beam, Represents the density of the vibration absorbing beam, m b is the mass of the vibration absorbing beam, , m d is the mass of the additional rubber mass ball, c, c 01 、c 02 They represent the damping coefficients of the supporting spring of the main vibration-absorbing system and the bending and torsional modes of the vibration-absorbing beam respectively;

[0029] (6)

[0030] Where: represents the Dirac function, R d is the distance from the center of mass of a single rubber mass ball to the midpoint of the vibration absorbing beam;

[0031] Using the above nonlinear geometric relationship (2) and the internal force equation (3) expressed in terms of displacement, and introducing the inextensibility condition,

[0032] (7)

[0033] The control equation expressed in terms of displacement is obtained:

[0034] (8)

[0035] Bending displacement w and torsional displacement of the vibration absorbing beam Represented by separating variables in time and space domains;

[0036] (9)

[0037] Where: , , ;

[0038] Substituting equation (9) into equation (8) we get the residual equations of the bending and torsion modes. Performing Galerkin truncation on the bending and torsion equations we get the following equations:

[0039] (10);

[0040] Using the first-order Galerkin cutoff, the time domain control equations for the coupling between the bending mode and torsional mode of the vibration absorbing beam and the main vibration absorbing system can be obtained:

[0041] (11)

[0042] Where w1 and w2 represent the first-order modal displacement of the midpoint of the bending mode of the vibration absorbing beam and the first-order modal displacement of the lower boundary of the torsion mode of the vibration absorbing beam, respectively. q 、m 01 、m 02represents the generalized mass parameter of the main vibration-absorbing system and the bending and torsional modes of the vibration-absorbing beam; k, k ij Represents the stiffness coefficient of each subsystem, where ij represents 01, 11, 21, 22, 31, 32, 02, 12, 23, 33; The coefficients representing the nonlinear inertia generated by the bending and torsional modes of the beam;

[0043] S3: the natural frequency of the vibration-absorbed system measured in step S1 and damping ratio , using the control equation formula of the vibration-absorbing system obtained in step S2, determine the parameters of the vibration-absorbing system, then derive the first-order bending and torsional natural frequency formulas of the vibration-absorbing beam according to the control equation, design the sizes of the two according to the self-parameter resonance mode coupling conditions, select the material of the vibration-absorbing beam, test the first-order bending and torsional vibration damping ratios, and inversely calculate the parameter values ​​related to the stiffness and damping of the vibration-absorbing beam;

[0044] S4. Use the incremental harmonic balance method to solve the time domain control equations (11) of the coupling between the bending mode and torsional mode of the vibration absorbing beam and the main vibration absorbing system, and then adjust the size m of the rubber mass ball with different d and relative to the midpoint position R of the vibration absorbing beam d , obtain the system self-parametric resonance stable boundary spectrum;

[0045] S5. Design and adjust the size of the mass ball so that the bending modal natural frequency of the vibration absorbing beam is close to half of the natural frequency of the main system being absorbed, but less than 1 / 100; adjust the position of the mass ball so that the torsional natural frequency is greater than half of the natural frequency of the main system being absorbed, and the excitation amplitude at the intersection of the stable boundary of the torsional self-parameter resonance and the stable boundary of the bending self-parameter resonance is within the range of plus or minus 1 / 10 of the actual excitation amplitude; select the size and position of the mass ball corresponding to the stable boundary that meets the above conditions as the final design parameters of the vibration absorber;

[0046] S6. Calculate the frequency response curve and transmissibility of the main system to be absorbed by numerical integration method, and confirm the vibration absorption performance of the vibration absorber by judging the magnitude of the transmissibility and the frequency band where the transmissibility is less than 1.

[0047] As a preferred improvement of the present invention: the step S3 specifically includes the following process:

[0048] Due to the natural frequency , while M q is known, Has been measured, then the stiffness k can be calculated, because , then the damping coefficient c can be calculated;

[0049] Secondly, according to equation (11), the general formula of the bending and torsional natural frequencies of the vibration absorbing beam can be obtained, and the relationship between the first-order bending and torsional natural frequencies of the vibration absorbing beam and the mass and position of the attached ball can be obtained:

[0050] (13)

[0051] in: and represents the first-order bending and torsional natural frequencies of the vibration absorbing beam;

[0052] According to the natural frequency of the main system being absorbed The first-order bending natural frequency of the vibration absorbing beam is determined by half of and the first-order torsional natural frequency The initial value of is selected, and the vibration absorber material is selected, and the optional range is steel and alloy; then the length l, width b and height h of the vibration absorbing beam of the series that meets the above natural frequency conditions are obtained by using the above formula (13), and then I can be obtained x ,I z ,I ω , J, determine the mass m of the additional mass ball that satisfies the first-order bending and torsional natural frequency conditions of the above vibration-absorbing beam d and the distance Rd from the ball to the midpoint of the beam;

[0053] Define the ratio of the total mass M0 of the main vibration-absorbing system, the fixed plate, and the hinge support to the mass of the additional vibration-absorbing beam , must meet , select the parameters of the vibration absorbing beam that meet this condition;

[0054] According to the parameters obtained in this step, materials are selected and processed into vibration-absorbing beams. The displacement time history curve of the attenuated vibration is tested by the tapping method, and the bending and torsional damping ratios of the vibration-absorbing beam are measured. ,because , we can calculate c 01 , c 02 .

[0055] As a preferred improvement of the present invention: in step S6, the numerical integration method includes the Runge-Kutta method and the Newmark method.

[0056] The beneficial effects of the present invention are as follows:

[0057] It can achieve a wider vibration absorption band than existing linear vibration absorbers and single-mode nonlinear vibration absorbers, can effectively suppress the amplitude overflow effect caused by single-mode vibration absorption, and realize the integrated and compact design of dual-mode vibration absorption. It also uses the stable boundary of self-parameter resonance to realize the rapid design of vibration absorber parameters, avoid repeated iterative cycles, and improve design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0059] Figure 1 It is a schematic diagram of the structure of the dual self-parameter resonant vibration absorber of the present invention;

[0060] Figure 2 It is a ball hinge constraint structure of the lower end portion of the dual self-parameter resonance vibration absorbing beam in the present invention;

[0061] Figure 3 It is a restraining structure of the upper end part of the double self-parameter resonance vibration absorbing beam in the present invention;

[0062] Figure 4 It is a mechanical diagram of the vibration absorbing beam in the present invention;

[0063] Figure 5 It is a schematic diagram of the vibration absorbing beam design method in the present invention;

[0064] Figure 6 is an amplitude-frequency response diagram of the main vibration-absorbed system of the vibration absorber of the present invention;

[0065] Figure 7 It is the displacement time history curve of the main vibration-absorbed system of the vibration absorber of the present invention when the excitation frequency is 54.8 Hz;

[0066] Figure 8 It is the Poincare mapping curve of the main vibration-absorbed system of the vibration absorber of the present invention when the excitation frequency is 54.8 Hz.

[0067] In the figure: 1-slide groove, 2-hollow rod, 3-mass ball, 4-guide column, 5-vibration absorbed main system, 6-spring, 7-base, 8-boss, 9-reinforcement rib, 10-hinge support screw, 11-hinge support cover, 12-hinge support, 13-smooth ball hinge, 14-vibration absorbing beam, 15-fixing plate, 16-cylindrical pin. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0069] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0070] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0071] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0072] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0073] See also Figure 1As shown, the present invention provides a wide-band vibration absorber with dual-mode coupling. The main system 5 to be damped is placed on a base 7 through four springs 6. The base 7 is fixed on the actual equipment cabin and provides displacement excitation to the main structure through the springs 6 and damping. There are four circular-section guide columns 4 on the base 7, and four holes with the same aperture as the guide columns 4 are provided on the main system 5 to be absorbed. The holes are clearance-matched so that the main system to be absorbed can only vibrate up and down. There are two fixed plates 15 on both sides of the main system to be absorbed, each supported by a reinforcing rib 9. Two grooves 1 are left above the two fixed plates. The main system to be absorbed is supported by an elastic beam-type vibration absorbing structure, and its main structure includes: an elastic beam with an equal-section having a smooth ball joint 13 fixed at the lower end, and two hollow rods 2 are attached at the midpoint of the beam, and rubber balls are inserted into the rods. A smooth ball joint is fixed at the lower end of the elastic beam, and the ball joint is restricted in the hinge support 12 on the main system to be absorbed and can only rotate. The material of the ball joint has high strength, high hardness and good wear resistance, and the options include: hard alloy, ceramic, martensitic stainless steel, etc. There is a rigid cylindrical pin (cylindrical pin 16) on the top of the vibration absorbing beam, so that the pin slides up and down in the slide groove 1 of the fixed plate 15 on both sides of the beam. Its outer diameter is consistent with the gap width, and the gap fit is also adopted. The material of the additional vibration absorbing beam and the cylindrical pin on the top should not be easy to plastically deform, and the options include: ceramic, glass, stainless steel, etc.

[0074] Two hollow rods are attached on both sides of the midpoint of the beam, and the cross-sectional shapes can be selected from: round, square, triangle, etc. The relative position of the hollow rod to the beam is at the midpoint, and a processing deviation of 1 / 100 is allowed, otherwise the torsional mode of the beam will not be horizontal, and a new mode will be introduced to the vibration-absorbing beam. The hollow rod should be made of lightweight rigid materials, and the optional range is: titanium alloy, foam aluminum, honeycomb structure material, polycarbonate material. The maximum cross-sectional diameter (outer diameter) of the rod shall not exceed the width of the vibration-absorbing beam, the wall thickness shall be 1 / 30-1 / 3 of the outer diameter of the rod, and the maximum length shall not exceed 3 / 5 of the length of the beam. Removable rubber mass balls 3 are inserted at both ends of the rod so that their position can be adjusted and the mass balls can be kept stationary during vibration. The diameter of the mass balls shall not exceed one times the outer diameter of the hollow rod. By adjusting the position and size of the mass balls, the bending and torsional natural frequencies of the vibration-absorbing beam can be adjusted.

[0075] The vibration absorbing beam with dual mode coupling has the following characteristics: the bending mode boundary condition can be simplified to two simple supports, where the upper end is a movable boundary and the lower end is immovable. For the torsion mode, the upper end is a fixed constraint, while the lower end can be freely twisted. The vibration absorbing beam has two vibration absorbing modes, namely the bending self-parameter resonance mode and the torsion self-parameter resonance mode. The above boundary constraint characteristics can obtain the following boundary conditions: for the upper end of the beam, the lateral displacement is 0, the bending moment is 0, the axial internal force is 0, and the rotation angle is 0; the lower end of the beam has a lateral displacement of 0, a bending moment of 0, and a torque of 0. Such boundary constraints make the bending and torsion natural frequencies of the vibration absorbing beam closest and easier to adjust to the same. By attaching a rubber mass ball to the lightweight rod, the bending natural frequency of the beam is reduced to a certain extent, and the torsion natural frequency can be greatly reduced until the bending and torsion natural frequencies are equal to half of the natural frequency of the main system to be absorbed. When the bending and torsional natural frequencies are both half of the natural frequency of the main vibration-absorbing system, the forced resonance of the main vibration-absorbing system will excite the bending self-parameter resonance and torsional self-parameter resonance of the vibration-absorbing beam through modal coupling, and the vibration-absorbing beam will undergo bending and torsional coupled vibrations, and the vibration energy will also be absorbed from the main vibration-absorbing system to the bending and torsional modes of the vibration-absorbing beam. On the contrary, the vibration of the main vibration-absorbing system is suppressed. By staggered tuning of the bending and torsional natural frequencies, the vibration-absorbing frequency band can be widened and the amplitude overflow phenomenon on both sides of the vibration-absorbing frequency band can be improved.

[0076] The design method of a vibration absorber with dual mode coupling has the following basic steps:

[0077] Step 1: Use a laser vibrometer or attach an acceleration sensor to the base 7 to perform a vibration test on the base 7 to obtain the excitation frequency and excitation amplitude provided by the base 7 to the main vibration absorption system 5. Use an exciter to give a sweep frequency excitation to the main vibration absorption system 5, and use a laser vibrometer or attach an acceleration sensor to the main vibration absorption system 5 to measure the frequency corresponding to the resonance peak as the natural frequency ω of the main vibration absorption system nm The displacement time history curve of the main vibration absorption system attenuation is measured by the knocking method, and the damping ratio ζ3 of the spring is calculated by the ratio of the amplitudes of two adjacent peaks. The above parameters are used as input parameters for the vibration absorption structure design.

[0078] Step 2: If Figure 4 , according to the mechanical diagram and coordinate system of the vibration absorber, the dynamic control equation of the vibration absorption system is derived.

[0079] First, a displacement field model of the vibration absorbing beam 14 is established;

[0080] (1)

[0081] in: , , It is the relative displacement of any point on the beam in the x, y, and z directions with the vibration-absorbed main system 5 as the reference system. and Respectively represent the mid-plane displacement corresponding to x=0 and z=0, v and w represent the longitudinal and lateral displacements of the central axis on the mid-plane, t represents time, and φ represents the cross-sectional angle related only to the y-direction position. For a beam with one end subject to torsion fixed constraints, the warping deformation of the cross section cannot be ignored, so the fan coordinate ω is introduced to reflect the warping behavior, which is expressed as ω=xz for a rectangular beam with uniform cross-section.

[0082] Using the von Karman nonlinear geometric relationship, the positive strain in the y direction is obtained , shear strain in xy direction , shear strain in yz direction and .

[0083] (2)

[0084] Where: Subscript Respectively represent the first and second order partial derivatives with respect to the coordinate y.

[0085] Then, the following non-zero generalized internal forces M, R and .

[0086] (3)

[0087] Where: yy represents the normal stress in the y direction, represents the shear stress in the yz direction. b represents the width of the vibration absorbing beam 14, and h represents the thickness of the vibration absorbing beam. E represents the Young's modulus of the beam, G represents the shear modulus, Ix and Iz represent the moment of inertia of the cross section on the x and z axes, respectively, and I ω is the sector moment of inertia of the cross section, and J is the polar moment of inertia of the centroid of the cross section, defined by the following formula:

[0088] (4)

[0089] Through the Hamiltonian variation principle, the control equation for coupling the bending mode and torsional mode of the vibration absorbing beam 14 and the mode of the vibration absorbing main system 5 expressed by internal force is obtained.

[0090] (5)

[0091] in: represents the first-order derivative of displacement with respect to time, represents the second-order derivative of each displacement with respect to time; v m represents the displacement of the main vibration-absorbing system 5, represents the displacement of the base excitation. l represents the length of the vibration absorbing beam 14, ρ represents the density of the beam, m b is the mass of the beam, and , m d is the mass of the additional rubber mass ball 3. Since the hollow rod is a lightweight material, its mass can be ignored in the calculation model. c, c 01 、c 02 denote the damping coefficients of the supporting spring of the main vibration-absorbing system and the bending and torsional modes of the vibration-absorbing beam, respectively; and

[0092] (6)

[0093] Where: δ represents the Dirac function, R d It is the distance from the center of mass of a single rubber mass ball to the midpoint of the vibration absorbing beam.

[0094] Further using the above nonlinear geometric relationship (2) and the internal force equation (3) expressed in terms of displacement, and introducing the inextensibility condition:

[0095] (7)

[0096] The governing equation expressed in terms of displacement can be obtained:

[0097] (8)

[0098] The bending displacement w and torsional displacement φ of the vibration absorbing beam 14 can be represented by separate variables in time and space domains, wherein the space part needs to satisfy boundary conditions, i.e., for the bending mode, both ends are hinged, while for the torsional mode, the lower end is free and the upper end is fixed.

[0099] (9)

[0100] Where: , , .

[0101] Substituting equation (9) into equation (8) yields the residual equations for the bending and torsion modes. The bending and torsion equations are subjected to Galerkin truncation, yielding the following equations:

[0102] (10)

[0103] Using the first-order Galerkin cutoff, the time domain control equations for the coupling between the bending mode and torsional mode of the vibration absorbing beam and the main vibration absorbing system can be obtained:

[0104] (11)

[0105] Where w1 and w2 represent the first-order modal displacement of the midpoint of the bending mode of the vibration absorbing beam and the first-order modal displacement of the lower boundary of the torsion mode of the vibration absorbing beam, respectively. q 、m 01 、m 02 represents the generalized mass parameter of the main vibration-absorbing system and the bending and torsional modes of the vibration-absorbing beam; k, k ij Represents the stiffness coefficient of each subsystem, where ij represents 01, 11, 21, 22, 31, 32, 02, 12, 23, 33; The coefficients represent the nonlinear inertia generated by the bending and torsion modes of the beam. The expressions for these coefficients can be derived as:

[0106] (12)

[0107] Step 3: Measure the natural frequency ω of the vibration-absorbed system according to step 1 nm and damping ratio ζ3, and use the control equation formula of the vibration-absorbing system obtained in step 2 to determine the parameters of the vibration-absorbing system. Subsequently, the first-order bending and torsional natural frequency formulas of the vibration-absorbing beam are derived according to the control equation, and the sizes of the two are designed according to the self-parameter resonance mode coupling conditions. The material of the vibration-absorbing beam is selected, the first-order bending and torsional vibration damping ratios are tested, and the parameter values ​​related to the stiffness and damping of the vibration-absorbing beam are inversely calculated.

[0108] First, due to the natural frequency , while M q is known, ω nm Has been measured, the stiffness k can be calculated. , then the damping coefficient c can be calculated. Thus, all parameters of all vibration-absorbing systems can be determined.

[0109] Secondly, according to equation (11), the general formula of the bending and torsional natural frequencies of the vibration absorbing beam can be obtained, and the relationship between the first-order bending and torsional natural frequencies of the vibration absorbing beam and the mass and position of the attached ball can be obtained:

[0110] (13)

[0111] in: and represents the first-order bending and torsional natural frequencies of the vibration-absorbing beam.

[0112] The condition for strict self-parameter resonance mode coupling to occur is the natural frequency ω of the main system being absorbed. nm is the first-order bending natural frequency of the vibration-absorbing beam and torsional natural frequency However, this condition does not need to be strictly met. In order to widen the vibration absorption frequency band, it is necessary to design the first-order bending and torsional natural frequencies of the vibration absorption beam to deviate from half of the natural frequency of the main vibration absorption system, so that the two are staggered and work together to achieve the effect of widening the vibration absorption frequency band. As the beginning of the design iteration, firstly according to the natural frequency ω of the main vibration absorption system nm The first-order bending natural frequency of the vibration absorbing beam is determined by half of and the first-order torsional natural frequency The initial value of . Select the vibration absorber material, the optional range is steel, alloy. Then, using the above formula (13), the length l, width b, height h of the series of vibration absorbing beams that meet the above natural frequency conditions can be obtained, and then I can be obtained x ,I z ,I ω , J. Determine the mass m of the additional mass ball that satisfies the first-order bending and torsional natural frequency conditions of the above vibration-absorbing beam. d And the distance R from the ball to the middle point of the beam d .

[0113] Define the mass ratio of the total mass M0 of the main vibration-absorbing system 5, the fixed plate 14, and the hinge support 12 to the mass of the additional vibration-absorbing beam 14: α = M0 / (m b +m d ). Since the weight of the additional vibration absorbing structure is too light to achieve the vibration absorbing effect, the designed vibration absorber needs to satisfy 5≤α≤10, and the parameters of the vibration absorbing beam that meet this condition are selected.

[0114] According to the parameters obtained in this step, materials are selected and processed into vibration absorbing beams. The displacement time history curve of the attenuated vibration is tested by the knocking method, and the bending and torsional damping ratios ζ1 and ζ2 of the vibration absorbing beam are measured. , we can calculate c 01 、c 02 . Thus, all parameters of the vibration absorbing beam (including stiffness and damping related parameters) can be determined. The material parameters of the vibration absorbing beam obtained above are used as the final design parameters, and the size and position of the obtained rubber ball are used as the initial design parameters, which will be finally determined in the subsequent steps.

[0115] Step 4: Use the incremental harmonic balance method to solve the time domain control equations (11) of the bending mode and torsional mode of the vibration absorbing beam coupled with the main vibration absorbing system, and then adjust the size m of the rubber mass ball with different d and relative to the midpoint position R of the vibration absorbing beam d , and obtain the system's self-parametric resonance stable boundary spectrum (phase diagram of excitation amplitude and excitation frequency).

[0116] Step 5: According to the characteristics of the drawn stable boundary, the size of the mass ball 3 is designed and adjusted so that the natural frequency of the bending mode of the vibration absorbing beam 14 is close to half of the natural frequency of the main system being absorbed, but less than 1 / 100. In this way, the bending self-parameter resonance mode is strongly coupled with the forced resonance mode of the main system being absorbed, and the bending mode is used to absorb the resonance energy of the main system being absorbed, and there will be no large amplitude overflow on the left side of the resonance peak frequency band. At the same time, the position of the mass ball is adjusted so that the torsional natural frequency is greater than half of the natural frequency of the main system 5 being absorbed, and the excitation amplitude at the intersection of the stable boundary of the torsional self-parameter resonance and the stable boundary of the bending self-parameter resonance is within the range of plus or minus 1 / 10 of the actual excitation amplitude, so that the torsional mode of the vibration absorbing beam can absorb the amplitude overflow generated by the bending mode.

[0117] The size and position of the mass ball corresponding to the stable boundary that meets the above conditions are selected as the final design parameters of the vibration absorber.

[0118] Step 6: Use the numerical integration method to calculate the frequency response curve and transmissibility of the main system to be absorbed (the ratio of the amplitude with the vibration absorber to the amplitude without the vibration absorber). By judging the magnitude of the transmissibility and the frequency band where the transmissibility is less than 1, the vibration absorption performance of the vibration absorber is confirmed, including the vibration absorption band and the magnitude of the transmissibility. Numerical integration methods include: Runge-Kutta method, Newmark method, etc.

[0119] Embodiment 1

[0120] The present invention provides a technical solution for suppressing broadband vibration of a mechanical system and improving the amplitude spillover effect on both sides of a vibration absorbing belt: a broadband vibration absorber that generates modal coupling through self-parametric resonance of bending and torsion modes of a vibration absorbing main system and a vibration absorbing beam, and a design method for realizing a dual-mode natural frequency staggered configuration using stable boundary characteristics. The vibration absorbing system includes a vibration absorbing main system 5 and a vibration absorbing beam 13.

[0121] The vibration-absorbed system 5 is connected to the base 7 via a spring 6. The base 7 provides displacement excitation, which can be expressed as: , where the subscript g represents the foundation, represents the excitation displacement, Indicates the excitation amplitude. There are four springs 6 on the base 7, which are mounted on four guide columns 4. The function of the guide column 4 is to prevent the main vibration absorption system from tilting and limit it to up and down vibration. The cross section of the guide column is circular, and its diameter is 1 / 2-3 / 4 of the spring. The length of the spring is 1 / 6-1 / 3 of the length of the guide column, and the height of the main vibration absorption system block is 1 / 3-1 / 2 of the length of the cylinder, so that the mass block will not separate from the guide column during the up and down vibration of the main vibration absorption system.

[0122] The vibration-absorbing main system 5 has a boss 8, a reinforcing rib 9, a hinge support 12 of a ball joint, a fixing plate 15 and four holes. The guide column is passed through the hole and a clearance fit is generated to achieve the limiting effect of the vibration-absorbing main system. The role of the boss 8 is to increase the fitting area and play a better limiting role. The fixing plate plays the role of providing boundary constraints for the upper end of the vibration-absorbing beam. The thickness of the fixing plate 15 should be relatively thick, and the ratio of its thickness to length should be greater than 1 / 10, and the ratio of its width to thickness should be less than 2 / 1. Its thickness should be twice the thickness of the vibration-absorbing beam, and its length should be the same as that of the vibration-absorbing beam. The role of the reinforcing rib is to increase the bending stiffness of the fixing plate and prevent large deformation. Its height is 1 / 4-1 / 3 of the length of the fixing plate, and its thickness is 1 / 4-3 / 4 of the width of the fixing plate. The width is flush with the outer edge of the mass block. The outer diameter of the hinge support 12 is 1.1-1.3 times the width of the vibration-absorbing beam.

[0123] The size of the vibration absorbing beam 14 should be designed according to its bending and torsional natural frequencies. Figure 3 As shown, there is a rigid cylindrical pin 16 on the top, whose outer diameter is half of the thickness of the vibration absorbing beam 14 and is the same as the slide slot 1 on the fixed plate 15, and is inserted into the slide slot 1 with a clearance fit, which is used to limit the torsion of the upper end of the vibration absorbing beam and provide a movable simply supported boundary condition for the beam bending mode. The length of the cylindrical pin is just flush with the two sides of the fixed plate. In the initial equilibrium state, the position of the cylindrical pin should be at the upper 1 / 5-1 / 4 of the length of the slide slot, leaving a gap for the vibration absorbing beam torsional warping deformation. There is a hollow rod 2 on each side of the midpoint of the vibration absorbing beam 14, which adopts a hollow round rod structure. The outer diameter of the rod does not exceed the width of the vibration absorbing beam, the wall thickness is 1 / 30-1 / 3 of the outer diameter of the rod, and the maximum length does not exceed 3 / 5 of the beam length. A rubber mass ball 3 is sleeved on the hollow rod 2, whose diameter does not exceed one times the outer diameter of the hollow rod, and its function is to adjust the natural frequency of the first-order bending mode and the first-order torsional mode of the vibration absorbing beam. The rubber mass ball has the advantages of adjustable position, easy fixation and avoidance of mechanical connection.

[0124] like Figure 2 As shown, a hinge support cover 11 is provided on the hinge support 12, and the two are connected by a hinge support screw 10. The hinge support contains a smooth ball joint 13, and the two are closely matched. The ball joint can rotate freely inside it, but no gap can be generated with the hinge support.

[0125] The above boundary constraint features can obtain the following boundary conditions: for the upper end of the beam, the lateral displacement is 0, the bending moment is 0, the axial internal force is 0, and the rotation angle is 0; the lower end of the beam has a lateral displacement of 0, a bending moment of 0, and a torque of 0. Such boundary constraints make the bending and torsional natural frequencies of the vibration-absorbing beam closest and easier to adjust to be the same. By adding concentrated mass with inertia moment, the bending natural frequency of the beam is reduced to a certain extent, while the torsional natural frequency can be greatly reduced until both the bending and torsional natural frequencies are equal to half of the natural frequency of the main system to be absorbed. When the bending and torsional natural frequencies are both half of the natural frequency of the main system to be absorbed, the forced resonance of the main system to be absorbed will excite the bending self-parameter resonance and torsional self-parameter resonance of the vibration-absorbing beam through modal coupling, and the vibration-absorbing beam will undergo bending and torsional coupled vibration, and the vibration energy is also absorbed from the main system to be absorbed to the bending and torsional modes of the vibration-absorbing beam. On the contrary, the vibration of the main system to be absorbed is suppressed. By staggered tuning of the bending and torsional natural frequencies, the vibration absorption frequency band can be broadened and the amplitude overflow phenomenon on both sides of the vibration absorption frequency band can be improved.

[0126] This example gives the vibration absorption performance results of a specific dual-mode self-parametric resonance vibration absorber. According to the above vibration absorber design method, the vibration absorption beam length is l=0.18m, thickness is h=3mm, width is b=6mm, Young's modulus of the vibration absorption beam is E=117GPa, and density is ρ=8960kg / m 3 , the total stiffness of the foundation is k=0.384MPa, and the mass of the vibration absorbing beam is m b =ρbhl, the mass of the additional rubber ball is m d =3.5m b l. The distance from the ball to the midpoint of the vibration absorbing beam is the same as the length of the hollow rod, which is R d =0.52l, the mass ratio of the main vibration-absorbing system to the vibration-absorbing beam and the additional ball is defined as: α=M0 / (m b +m d ), and α=5.34, the bending and torsion damping ratios are measured to be ζ1=ζ2=0.005, and the damping ratio of the foundation spring is ζ3=0.0008. Therefore, the natural frequency, bending mode, and torsion mode of the main system being absorbed are 680.91rad / s, 336.64rad / s, and 346.56rad / s, respectively. Figure 6 As shown, the stability boundary of the dual self-parameter resonance has a multi-valley characteristic.

[0127] By designing the beam bending mode slightly lower than half of the natural frequency of the main system to be absorbed, the frequency of the optimal bending self-parameter resonance absorption point is lower than the resonance frequency, and there is a small amplitude overflow at the lower frequency position, while the amplitude overflow effect mainly appears at the higher frequency position, such as Figure 6Then, by designing the torsional natural frequency of the beam to be exactly the frequency band of the amplitude overflow, the overflow amplitude is suppressed and delayed to a higher frequency. Although the torsional self-parameter resonance vibration absorption also has an amplitude overflow effect, the increased amplitude is relatively small. By frequency scanning, it can be observed that there is a quasi-periodic transition band between the bending and torsional self-parameter resonance frequency bands, which can be seen from Figure 7 The displacement time history curve when the excitation frequency is 54.8Hz and Figure 8 This is confirmed in the Poincare map when the excitation frequency is 54.8 Hz. This quasi-periodic band is understood to be the coupling effect that occurs during the synergistic operation of the bending and torsional self-parametric resonances. This non-periodic motion also has a suppressive effect on the vibration of the main system being absorbed.

[0128] In general, it can be seen that the resonance suppression frequency band of the vibration-absorbing main system has been widened, and the amplitude spillover effect on both sides of the vibration-absorbing belt has been improved.

[0129] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the embodiments. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A broadband vibration absorber with dual mode coupling, characterized in that: The invention comprises a base (7), the top surface of the base (7) being provided with a guide column (4), a vibration-absorbing main system (5) being slidably mounted on the guide column (4), the guide column (4) being sleeved with a spring (6), the spring (6) being located between the vibration-absorbing main system (5) and the base (7), the top surface of the vibration-absorbing main system (5) being provided with two fixed plates (15) arranged relatively spaced apart, a slide groove (1) being arranged in a vertical direction above the two fixed plates (15), and the top surface of the vibration-absorbing main system (5) being provided with a guide column (4). A hinge support (12) is provided, the hinge support (12) is located between the two fixed plates (15), a smooth ball joint (13) is provided at the hinge support (12), a vibration absorbing beam (14) is connected to the top surface of the smooth ball joint (13), a cylindrical pin (16) is fixed above the vibration absorbing beam (14), two ends of the cylindrical pin (16) are located in the two slide grooves (1), the vibration absorbing beam (14) is connected to a hollow rod (2) arranged in a horizontal direction, and mass balls (3) are provided at both ends of the hollow rod (2).

2. The broadband vibration absorber with dual mode coupling according to claim 1, characterized in that: The number of the guide columns (4) is four and they are evenly distributed around the base (7).

3. The broadband vibration absorber with dual mode coupling according to claim 1, characterized in that: The vibration-absorbed main system (5) is provided with reinforcing ribs (9), and the reinforcing ribs (9) are connected to the fixing plate (15).

4. The broadband vibration absorber with dual mode coupling according to claim 1, characterized in that: The hollow rod (2) is located at the midpoint of the vibration absorbing beam (14), and the distances between the two mass balls (3) and the vibration absorbing beam (14) are the same.

5. The broadband vibration absorber with dual-mode coupling according to claim 1, characterized in that: The top surface of the hinge support (12) is recessed downward to form a rotation space, and a hinge support cover (11) is fixed to the top surface of the hinge support (12) via a hinge support screw (10), and the hinge support cover (11) limits the smooth ball joint (13) to the rotation space.

6. The broadband vibration absorber with dual mode coupling according to claim 1, characterized in that: A boss (8) is provided on the top surface of the vibration-absorbed main system (5), and the guide column (4) passes through the boss (8).

7. The broadband vibration absorber with dual-mode coupling according to claim 1, characterized in that: The outer diameter of the hollow rod (2) does not exceed the width of the vibration absorbing beam (14), the length of the hollow rod (2) does not exceed 3 / 5 of the height of the vibration absorbing beam (14), and the diameter of the mass ball (3) is less than twice the outer diameter of the hollow rod (2).

8. The design method of a broadband vibration absorber with dual-mode coupling according to claim 1, characterized in that: The following steps are involved: S1. Perform a vibration test on the base (7) to obtain the excitation frequency and excitation amplitude provided by the base (7) to the vibration-absorbing main system (5), and obtain the natural frequency ω of the vibration-absorbing main system nm and the damping ratio of the spring ζ3; S2. Derive the dynamic control equations of the vibration absorption system; Firstly, the displacement field model of the vibration absorbing beam is established; （1） in: , , It is the relative displacement of any point on the vibration absorbing beam in the x, y, and z directions with the main vibration absorbing system as the reference system. and denote the mid-plane displacements corresponding to x=0 and z=0, respectively; v and w denote the longitudinal and transverse displacements of the central axis on the mid-plane; t denotes time; φ denotes the cross-sectional angle related only to the y-direction position; is the sector coordinate; Using the von Karman nonlinear geometric relationship, the positive strain in the y direction is obtained , shear strain in xy direction , shear strain in yz direction and , （2） Where: Subscript Respectively represent the first and second order partial derivatives of the coordinate y; （3） Where: yy represents the normal stress in the y direction, represents the shear stress in the yz direction, b represents the width of the vibration absorbing beam, h represents the thickness of the vibration absorbing beam, E represents the Young's modulus of the vibration absorbing beam, G represents the shear modulus, Ix and Iz are the moments of inertia of the cross section on the x and z axes respectively, is the sector moment of inertia of the cross section, J is the polar moment of inertia of the centroid of the cross section; （4）； The control equations for the coupling of the bending mode and torsional mode of the vibration absorbing beam expressed by internal force and the mode of the main vibration absorbing system are obtained. （5） in: represents the first-order derivative of displacement with respect to time, represents the second-order derivative of each displacement with respect to time; v m represents the displacement of the main system being absorbed, represents the base excitation displacement, l represents the length of the vibration absorbing beam, Represents the density of the vibration absorbing beam, m b is the mass of the vibration absorbing beam, , m d is the mass of the additional rubber mass ball, c, c 01 、c 02 They represent the damping coefficients of the supporting spring of the main vibration-absorbing system and the bending and torsional modes of the vibration-absorbing beam respectively; （6） Where: represents the Dirac function, R d is the distance from the center of mass of a single rubber mass ball to the midpoint of the vibration absorbing beam; Using the above nonlinear geometric relationship (2) and the internal force equation (3) expressed in terms of displacement, and introducing the inextensibility condition, （7） The control equation expressed in terms of displacement is obtained: （8） Bending displacement of vibration absorbing beam w and torsional displacement Represented by separating variables in time and space domains; （9） Where: , , ; Substituting equation (9) into equation (8) we get the residual equations of the bending and torsion modes. Performing Galerkin truncation on the bending and torsion equations we get the following equations: （10）； Using the first-order Galerkin cutoff, the time domain control equations for the coupling between the bending mode and torsional mode of the vibration absorbing beam and the main vibration absorbing system can be obtained: （11） In the formula w 1. w 2 respectively represent the first-order modal displacement of the midpoint of the bending mode of the vibration absorbing beam and the first-order modal displacement of the lower boundary of the torsion mode of the vibration absorbing beam. M q , m 01 , m 02 Generalized mass parameters representing the bending and torsional modes of the main vibration-absorbing system and the vibration-absorbing beam; k , k ij represents the stiffness coefficient of each subsystem, where ij It means 01,11,21,22,31,32,02,12, 23,33; The coefficients representing the nonlinear inertia generated by the bending and torsional modes of the beam; S3: the natural frequency of the vibration-absorbed system measured in step S1 and damping ratio , using the control equation formula of the vibration-absorbing system obtained in step S2, determine the parameters of the vibration-absorbing system, then derive the first-order bending and torsional natural frequency formulas of the vibration-absorbing beam according to the control equation, design the sizes of the two according to the self-parameter resonance mode coupling conditions, select the material of the vibration-absorbing beam, test the first-order bending and torsional vibration damping ratios, and inversely calculate the parameter values ​​related to the stiffness and damping of the vibration-absorbing beam; S4. Use the incremental harmonic balance method to solve the time domain control equations (11) of the coupling between the bending mode and torsional mode of the vibration absorbing beam and the main vibration absorbing system, and then adjust the size m of the rubber mass ball with different d and relative to the midpoint position R of the vibration absorbing beam d , obtain the system self-parametric resonance stable boundary spectrum; S5. Design and adjust the size of the mass ball so that the bending modal natural frequency of the vibration absorbing beam is close to half of the natural frequency of the main system being absorbed, but less than 1 / 100; adjust the position of the mass ball so that the torsional natural frequency is greater than half of the natural frequency of the main system being absorbed, and the excitation amplitude at the intersection of the stable boundary of the torsional self-parameter resonance and the stable boundary of the bending self-parameter resonance is within the range of plus or minus 1 / 10 of the actual excitation amplitude; select the size and position of the mass ball corresponding to the stable boundary that meets the above conditions as the final design parameters of the vibration absorber; S6. Calculate the frequency response curve and transmissibility of the main system to be absorbed by numerical integration method, and confirm the vibration absorption performance of the vibration absorber by judging the magnitude of the transmissibility and the frequency band where the transmissibility is less than 1.

9. The design method of a broadband vibration absorber according to claim 8, characterized in that: The step S3 specifically The process includes: Due to the natural frequency , while M q is known, Has been measured, then the stiffness k can be calculated, because , then the damping coefficient c can be calculated; Secondly, according to equation (11), the general formula of the bending and torsional natural frequencies of the vibration absorbing beam can be obtained, and the relationship between the first-order bending and torsional natural frequencies of the vibration absorbing beam and the mass and position of the attached ball can be obtained: （13） in: and represents the first-order bending and torsional natural frequencies of the vibration absorbing beam; According to the natural frequency of the main system being absorbed The first-order bending natural frequency of the vibration absorbing beam is determined by half of and the first-order torsional natural frequency The initial value of the vibration absorber is selected as steel or alloy; and then the length l, width b and height h of the vibration absorbing beam of the series that meets the above natural frequency conditions are obtained by using the above formula (13), and then I can be obtained x ,I z ,I ω , J, determine the mass m of the additional mass ball that satisfies the first-order bending and torsional natural frequency conditions of the above vibration-absorbing beam d and the distance Rd from the ball to the midpoint of the beam; Define the ratio of the total mass M0 of the main vibration-absorbing system, the fixed plate, and the hinge support to the mass of the additional vibration-absorbing beam , must meet , select the parameters of the vibration absorbing beam that meets this condition; According to the parameters obtained in this step, materials are selected and processed into vibration-absorbing beams. The displacement time history curve of the attenuated vibration is tested by the tapping method, and the bending and torsional damping ratios of the vibration-absorbing beam are measured. ,because , we can calculate c 01 , c 02 .

10. The design method of a broadband vibration absorber according to claim 8, characterized in that: In step S6, the numerical integration method includes the Runge-Kutta method and the Newmark method.

Images