Multi-branch shunt circuit electromechanical coupling diaphragm time domain response numerical simulation method

Abstract

The invention discloses a numerical simulation method for time domain response of an electromechanical coupling diaphragm of a multi-branch shunt circuit. The numerical simulation method comprises the following steps: initializing a simulation environment variable and determining a speed positive direction and a circuit current positive direction; receiving a diaphragm parameter, a shunt circuit parameter and a circuit time division multiplexing time sequence parameter; calculating an extra fluid load of external sound radiation of the vibrating diaphragm and extra rigidity of the cavity structure, and correcting incident excitation; assembling a lumped acoustic-vibration-electric coupling LTV differential equation set; parameters of a variable step size four-order explicit Runge-Kutta resolver are configured in an initialized mode; obtaining the vibration displacement and speed of the vibrating diaphragm, the time history of the trunk charge and current and the energy integral of each part of the system; judging the solution conservativeness of the resolver, adjusting the absolute tolerance and the relative tolerance of the resolver according to the residual magnitude when the solution conservativeness is not met, and executing the solution step again; when the condition is satisfied, the reflected wave and the transmitted wave in the waveguide are reconstructed by using the vibration speed of the diaphragm; and the sound absorption coefficient, the reflection coefficient and the transmission coefficient of the electrically coupled diaphragm are calculated.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation, and particularly relates to a numerical simulation method for the time-domain response of an electromechanical coupling diaphragm in a multi-branch shunt circuit. Background Art

[0002] The electromechanical coupling diaphragm, as an emerging acoustic device, has adjustable acoustic impedance, and thus has a wide range of application scenarios in low-frequency and broadband noise control, including but not limited to low-frequency broadband sound absorption, low-frequency broadband sound insulation of thin and light structures, thermoacoustic instability control, etc. The diaphragm is pushed by sound waves to vibrate, and the coil moves along with it and cuts the magnetic induction lines, generating an induced electromotive force at both ends, which drives the current to flow through the shunt circuit and the coil. The current-carrying coil will be applied with a Lorentz force in the magnetic field, and this Lorentz force is equivalent to an acoustic impedance, and the amplitude and phase of this acoustic impedance are determined by the impedance of the circuit, and the influence of mechanical and spatial parameters is small. By designing the shunt circuit parameters, the diaphragm can resonate at any frequency and generate any expected acoustic response.

[0003] Furthermore, the shunt circuit of the electromechanical coupling diaphragm is designed as a multi-branch circuit, and the impedance designed for each branch is different, and a metal-oxide-semiconductor field-effect transistor (MOSFET) is connected in series in each branch to serve as a switch controlled by a level to control the on-off of each branch. At this time, by controlling the level of the MOSFET tube in the branch, the acoustic impedance of the electromechanical coupling diaphragm can be controlled, and further the control of the manipulation of sound waves can be realized. Due to the extremely high response frequency (MHz level) of the circuit system and the MOSFET tube compared with sound waves, the change of the acoustic impedance of the electromechanical coupling diaphragm can be regarded as being completed instantaneously, so this structure can achieve time-division multiplexing to achieve advanced noise control designs such as ultra-wideband noise control and adaptive control for noise spectra.

[0004] However, this electromechanical coupling diaphragm structure involves multi-physical field coupling of sound field-vibration, vibration-electromagnetism, and electromagnetism-shunt circuit. Therefore, when performing time-division multiplexing noise control design based on this structure, there are certain difficulties in the simulation numerical calculation of the entire system to evaluate the performance of the design.

[0005] For the simulation of traditional acoustic materials or acoustic mechanisms, usually the variables of the linear time-invariant (LTI) differential equation describing the system dynamics and the wave equation of sound waves are separated. After separating the time variable, the system dynamics differential equation is transformed into an algebraic equation in the frequency domain, and the wave equation is transformed into the Helmholtz equation in the frequency domain. Then, through the finite element method, the frequency domain equation is solved to obtain the complex sound pressure distribution in the frequency domain, and then the incident wave, reflected wave, and transmitted wave are decomposed to realize the evaluation of the acoustic performance of acoustic materials or structures such as sound absorption coefficient, reflection coefficient, transmission coefficient, and sound transmission loss.

[0006] However, for the time-division multiplexing noise control design based on the electromechanical coupling system, the coefficients of its system dynamics equation (the resistance of the MOSFET tube) vary with time (the set electrical timing sequence), so its system differential equation is a linear time-varying (LTV) differential equation. The variable separation method cannot separate the time variable from the system differential equation, so the traditional frequency-domain method fails for the time-division multiplexing noise control design. A commonly used alternative method is to add the absorption, reflection, and transmission coefficients corresponding to each branch of the time-division multiplexing with the duty cycle of each branch connection as the weight, and approximately obtain the corresponding acoustic performance of the time-division multiplexing system in a frequency-domain averaging manner.

[0007] As mentioned above, the traditional frequency-domain method is not applicable to the time-division multiplexing system with the control equation being an LTV equation. Although frequency-domain averaging can make a certain prediction of the acoustic performance of the time-division multiplexing system, it is only an average of a long-term stationary process and ignores the transient response of the system when each branch switches, so its calculation accuracy cannot be guaranteed. Summary of the Invention

[0008] The present invention provides a numerical simulation method for the time-domain response of an electromechanical coupling diaphragm with a multi-branch shunt circuit, which can solve the problems in the prior art.

[0009] The present invention provides a numerical simulation method for the time-domain response of an electromechanical coupling diaphragm with a multi-branch shunt circuit, wherein the method includes:

[0010] Initialize the simulation environment variables and determine the positive direction of velocity and the positive direction of circuit current;

[0011] Receive diaphragm parameters, shunt circuit parameters, and circuit time-division multiplexing timing parameters;

[0012] According to the configuration mode of the diaphragm, with the conditions of sound pressure continuity and air volume flow conservation, calculate the additional fluid load of the diaphragm's external sound radiation and the additional stiffness of the cavity structure, and correct the incident excitation;

[0013] Take the additional fluid load, additional stiffness, and corrected excitation as the input of the system mechanical part dynamics equation, generate the MOSFET resistance time sequence varying with time according to the circuit time-division multiplexing timing parameters And take the generated time sequence as the input of the system multi-branch circuit part dynamics equation, and assemble the lumped acoustic- vibration - electrical coupling LTV differential equation set;

[0014] Initialize the configuration of the variable-step fourth-order explicit Runge - Kutta solver parameters;

[0015] Use the configured solver parameters to solve the acoustic - vibration - electrical coupling LTV differential equation set, and obtain the time history of the diaphragm vibration displacement and velocity, the trunk circuit charge and current, and the energy integrals of each part of the system;

[0016] Analyze the energy integrals of each part of the system, judge the conservation of the solver's solution, and when the conservation does not meet the predetermined accuracy requirements, adjust the absolute tolerance and relative tolerance of the solver according to the residual magnitude, and re-execute the solution steps;

[0017] When the conservation meets the predetermined accuracy requirements, reconstruct the reflected wave and transmitted wave in the waveguide according to the configuration of the diaphragm;

[0018] Calculate the sound absorption coefficient, reflection coefficient and transmission coefficient of the electromechanical coupling diaphragm using the energy ratio of the reconstructed reflected wave, transmitted wave and incident wave.

[0019] Preferably, the simulation environment variables include the cross-sectional area A of the waveguide D , the air density ρ0, the speed of sound c0 in air, and the normalized incident sound pressure waveform function P I .

[0020] Preferably, the diaphragm parameters include the geometric area A d , the parameters of the mechanical part of the diaphragm and the parameters of the circuit part of the diaphragm. The parameters of the mechanical part of the diaphragm include the moving mass M of the diaphragm, the equivalent suspension stiffness K and the damping loss factor D. The parameters of the circuit part of the diaphragm include the internal resistance R s , the internal inductance L s and the electromagnetic coupling coefficient Bl. The shunt circuit parameters include the resistance values R n , inductance values L n and capacitance values C n , where the subscript n represents the nth branch. The time-division multiplexing circuit timing parameters include the timing switching frequency and the conduction duty cycle of each branch.

[0021] Preferably, according to the configuration of the diaphragm, calculate the additional fluid load of the external sound radiation of the diaphragm and the additional stiffness of the cavity structure on the condition of sound pressure continuity and air volume flow conservation, and correct the incident excitation, including:

[0022] When the configuration of the diaphragm is normal incidence sound insulation, the additional fluid load is D F = 2ρ0c0A d , the additional stiffness is K A = 0, and the incident excitation correction is F I = 2A d P I ;

[0023] When the configuration of the diaphragm is normal incidence sound absorption, the additional fluid load is D F = ρ0c0A d , the additional stiffness K A is the air stiffness of the resonance cavity, and the incident excitation correction is F I = 2Ad P I ;

[0024] When the configuration of the diaphragm is grazing-incidence sound insulation, the additional fluid load is D F = 0.5ρ0c0A d , and the additional stiffness K A is the air stiffness of the resonance cavity, and the incident excitation is corrected to F I = A d P I ;.

[0025] Preferably, the dynamic equation of the mechanical part of the system is:

[0026]

[0027] The dynamic equation of the multi-branch circuit part of the system is:

[0028]

[0029] where x is the vibration displacement of the diaphragm, is the vibration velocity of the diaphragm, is the vibration acceleration of the diaphragm, q is the trunk charge, is the trunk current, is the rate of change of the trunk current, and the subscript n represents the nth branch.

[0030] Preferably, according to the configuration of the diaphragm, reconstructing the reflected wave and the transmitted wave in the waveguide by using the vibration velocity of the diaphragm includes:

[0031] When the diaphragm configuration is normal-incidence sound insulation, the transmitted wave is The reflected wave is

[0032] When the diaphragm configuration is normal-incidence sound absorption, there is no transmitted wave, and the reflected wave is

[0033] When the diaphragm configuration is grazing-incidence sound insulation, the transmitted wave is The reflected wave is P R = P T - P I .

[0034] Preferably, the normalized incident sound pressure waveform function P I is:

[0035] P I = 1 Pa·sin2πft,

[0036] where Pa is Pascal, and f t is the predetermined incident frequency.

[0037] Preferably, the time sequence of the MOSFET resistance varying with time is generated by the following formula

[0038]

[0039] where Ω is ohm, Sign is the sign function, and t is time.

[0040] Preferably, the coupled acoustic-vibration-electrical LTV differential equations are as follows:

[0041]

[0042]

[0043] where U is the diaphragm state variable, is the derivative of the diaphragm state variable, F is a column vector, D M is a matrix, C1 is the capacitance value of the first branch, R1 is the resistance value of the first branch, and L1 is the inductance value of the first branch.

[0044] Preferably, the time histories of the diaphragm vibration displacement and velocity, the trunk charge and current are obtained by the following formula:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] where k1, k2, k3, and k4 are the first intermediate variable, the second intermediate variable, the third intermediate variable, and the fourth intermediate variable of the solver respectively, t n represents the nth moment, t n+1 represents the (n + 1)th moment, is the diaphragm state variable at the nth moment, is the derivative of the diaphragm state variable at the nth moment, is the derivative of the diaphragm state variable at the (n + 1)th moment, is the column vector at the nth moment, is the column vector at the (n + 1)th moment, is the matrix at the nth moment, is the matrix at the (n + 1)th moment.

[0052] Through the above technical solution, the time-domain response of the LTV system is solved through time-domain simulation, which completely and accurately describes the reflection and projection of the time-division multiplexed electromechanical coupling diaphragm on the incident sound wave. Through energy conservation analysis and corresponding solver tolerance adjustment, the calculation accuracy is guaranteed; moreover, the partial differential equation of multi-physical field coupling can be simplified to an ordinary differential equation, avoiding the use of the time-dependent finite element method to model the system, reducing the complexity of the model and the calculation cost; in addition, the unsteady partial differential equation can be simplified to an ordinary differential equation, and the convergence performance of the explicit algorithm is well guaranteed. Brief Description of the Drawings

[0053] The accompanying drawings included are used to provide a further understanding of the embodiments of the present invention, which form a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description are used to explain the principles of the present invention. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0054] Figure 1 The flowchart of a numerical simulation method for the time-domain response of a multi-branch shunt circuit electromechanical coupling diaphragm according to an embodiment of the present invention is shown;

[0055] Figure 2 The energy spectra of each part of the system according to an embodiment of the present invention are shown;

[0056] Figure 3 The schematic diagrams of the state variable velocity, current and reconstructed reflected sound pressure curves obtained by solving according to an embodiment of the present invention are shown;

[0057] Figure 4 The schematic diagram of the sound absorption coefficient curve of the time-division multiplexed electromechanical coupling absorber according to an embodiment of the present invention is shown. Detailed Embodiments

[0058] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. The description of at least one exemplary embodiment below is actually only illustrative and in no way limits the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0059] Note that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprises" and / or "comprising" are used in this specification, they specify the presence of the stated features, steps, operations, devices, components, and / or combinations thereof.

[0060] Unless otherwise specifically stated, the relative arrangements of the components and steps, numerical expressions, and numerical values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that, for the sake of convenience of description, the dimensions of the various parts shown in the drawings are not drawn in actual proportional relationships. Technologies, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the said technologies, methods, and devices should be regarded as part of the authorized specification. In all the examples shown and discussed herein, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that like reference numerals and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0061] Figure 1 The flowchart of a numerical simulation method for the time-domain response of a multi-branch shunt circuit electromechanical coupling diaphragm according to an embodiment of the present invention is shown.

[0062] As Figure 1 shown, the embodiment of the present invention provides a numerical simulation method for the time-domain response of a multi-branch shunt circuit electromechanical coupling diaphragm, wherein the method includes:

[0063] Initialize the simulation environment variables and determine the positive direction of velocity and the positive direction of circuit current;

[0064] For example, the incident wave direction can be determined as the positive coordinate direction, and the direction of the current generated by the diaphragm movement is the positive direction;

[0065] Receive the diaphragm parameters, shunt circuit parameters, and circuit time-division multiplexing timing parameters;

[0066] According to the configuration mode of the diaphragm, taking the sound pressure continuity and the air volume flow conservation as conditions, calculate the additional fluid load of the diaphragm's external sound radiation and the additional stiffness of the cavity structure, and correct the incident excitation;

[0067] Use the additional fluid load, additional stiffness, and corrected excitation as the input of the dynamic equation of the mechanical part of the system, and generate the MOSFET resistance time-varying sequence according to the circuit time-division multiplexing timing parameters And use the generated time series as the input of the dynamic equations of the multi-branch circuit part of the system to assemble the lumped acoustic- vibration - electric coupling LTV differential equation set;

[0068] For example, according to the on - resistance value, off - resistance value of the MOSFET and the time - sharing multiplexing time - series parameters of the circuit, encode the time series of the MOSFET resistance changing with time

[0069] Initialize the parameters of the variable - step - size fourth - order explicit Runge - Kutta solver;

[0070] Among them, the solver parameters include the initial time step, the time - step scaling factor, the absolute tolerance and relative tolerance of the solver;

[0071] Use the configured solver parameters to solve the acoustic - vibration - electric coupling LTV differential equation set, and obtain the time history of the vibration displacement and velocity of the diaphragm, the charge and current in the main circuit, and the energy integrals of each part of the system;

[0072] Among them, the energy integrals of each part of the system include: the dissipated energy of the mechanical part of the diaphragm, the elastic potential energy of the mechanical part of the diaphragm, the kinetic energy of the mechanical part of the diaphragm, the electric potential energy of the shunt - circuit part, the current energy of the shunt - circuit part, the dissipated energy of the shunt - circuit part, and the mechanical - circuit coupling transfer energy.

[0073] Analyze the energy integrals of each part of the system to judge the conservation of the solver solution (that is, judge the conservation of the energy integrals of each part, and the input - output energy spectrum of the system is as Figure 2 shown), and when the conservation does not meet the predetermined accuracy requirements, adjust the absolute tolerance and relative tolerance of the solver according to the residual magnitude, and re - execute the solution steps;

[0074] For example, when the relative error value of the energy is less than 10 -7 times the incident energy, it is determined that the conservation meets the accuracy requirements.

[0075] When the conservation meets the predetermined accuracy requirements, according to the configuration mode of the diaphragm, use the vibration velocity of the diaphragm to reconstruct the reflected wave and transmitted wave in the waveguide;

[0076] Use the reconstructed reflected wave and transmitted wave and the energy ratio of the incident wave to calculate the sound absorption coefficient, reflection coefficient and transmission coefficient of the electro - acoustic coupling diaphragm.

[0077] Through the above technical solution, the time-domain response of the LTV system is solved through time-domain simulation, which completely and accurately describes the reflection and transmission of the time-division multiplexed electromechanical coupling diaphragm to the incident sound wave. Through energy conservation analysis and corresponding solver tolerance adjustment, the calculation accuracy is guaranteed; moreover, the partial differential equation of multi-physics field coupling can be simplified to an ordinary differential equation, avoiding the use of the time-domain finite element method to model the system, reducing the complexity of the model and the calculation cost; in addition, the unsteady partial differential equation can be simplified to an ordinary differential equation, and the convergence performance of the explicit algorithm is better guaranteed.

[0078] According to an embodiment of the present invention, the simulation environment variables include the waveguide cross-sectional area A D , the air density ρ0, the speed of sound c0 in the air, and the normalized incident sound pressure waveform function P I (usually a sine function P I (t) with the incident frequency as the frequency).

[0079] According to an embodiment of the present invention, the diaphragm parameters include the geometric area A d , the diaphragm mechanical part parameters and the diaphragm circuit part parameters. The diaphragm mechanical part parameters include the diaphragm moving mass M, the equivalent suspension stiffness K, and the damping loss factor D. The diaphragm circuit part parameters include the internal resistance R s , the internal inductance L s and the electromagnetic coupling coefficient Bl. The shunt circuit parameters include the resistance values R n , the inductance values L n and the capacitance values C n of each branch, where the subscript n represents the nth branch. The time-division multiplexing circuit timing parameters include the timing switching frequency and the conduction duty cycle of each branch.

[0080] According to an embodiment of the present invention, according to the configuration mode of the diaphragm, taking the sound pressure continuity and the air volume flow conservation as conditions, the additional fluid load of the diaphragm's external sound radiation and the additional stiffness of the cavity structure are calculated, and the incident excitation is corrected, including:

[0081] When the configuration mode of the diaphragm is normal incidence sound insulation, the additional fluid load is D F = 2ρ0c0A d , the additional stiffness is K A = 0 (that is, there is no additional stiffness), and the incident excitation correction is F I = 2A d P I ;

[0082] When the configuration mode of the diaphragm is normal incidence sound absorption, the additional fluid load is D F = ρ0c0A d , the additional stiffness K Ais the air stiffness of the resonance cavity, and the incident excitation is corrected to F I = 2A d P i ;

[0083] When the configuration of the diaphragm is grazing-incidence sound insulation, the additional fluid load is D F = 0.5ρ0c0A d , and the additional stiffness K A is the air stiffness of the resonance cavity, and the incident excitation is corrected to F I = A d P I ;.

[0084] According to an embodiment of the present invention, the dynamic equation of the mechanical part of the system is:

[0085]

[0086] The dynamic equation of the multi-branch circuit part of the system is:

[0087]

[0088] where x is the vibration displacement of the diaphragm, is the vibration velocity of the diaphragm, is the vibration acceleration of the diaphragm, q is the trunk charge, is the trunk current, is the change rate of the trunk current, and the subscript n represents the nth branch.

[0089] According to an embodiment of the present invention, according to the configuration of the diaphragm, reconstructing the reflected wave and transmitted wave in the waveguide by using the vibration velocity of the diaphragm includes:

[0090] When the diaphragm configuration is normal-incidence sound insulation, the transmitted wave is The reflected wave is

[0091] When the diaphragm configuration is normal-incidence sound absorption, there is no transmitted wave, and the reflected wave is

[0092] When the diaphragm configuration is grazing-incidence sound insulation, the transmitted wave is The reflected wave is P R = P T - P I .

[0093] According to an embodiment of the present invention, the normalized incident sound pressure waveform function P I is:

[0094] P I = 1Pa·sin2πft,

[0095] where Pa is Pascal and f t is the predetermined incident frequency.

[0096] According to an embodiment of the present invention, the time sequence of the MOSFET resistance changing with time is generated by the following formula

[0097]

[0098] where Ω is ohm, Sign is the sign function, and t is time.

[0099] For example, for the sign function Sign, its value is 1 when the independent variable is greater than 0, -1 when it is less than 0, and 0 when it is equal to 0;

[0100] According to an embodiment of the present invention, the acoustic-vibration-electricity coupling LTV differential equation set is:

[0101]

[0102]

[0103] where U is the diaphragm state variable, is the derivative of the diaphragm state variable, F is a column vector, and D M is a matrix, C1 is the capacitance value of the first branch, R1 is the resistance value of the first branch, and L1 is the inductance value of the first branch.

[0104] The above-mentioned acoustic-vibration-electricity coupling LTV differential equation set corresponds to the first branch, and other branches are similar to it, which will not be elaborated here.

[0105] According to an embodiment of the present invention, the time histories of the diaphragm vibration displacement and velocity, the trunk road charge and current are obtained by the following formula:

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] where k1, k2, k3, and k4 are respectively the first intermediate variable, the second intermediate variable, the third intermediate variable, and the fourth intermediate variable of the solver, t n represents the nth moment, and t n+1Denote the (n + 1)-th moment, is the diaphragm state variable at the n-th moment, is the derivative of the diaphragm state variable at the n-th moment, is the derivative of the diaphragm state variable at the (n + 1)-th moment, is the column vector at the n-th moment, is the column vector at the (n + 1)-th moment, The matrix at the n-th moment, is the matrix at the (n + 1)-th moment.

[0113] The method of the present invention will be described below with reference to an example. Specifically, at the terminal of a one-dimensional waveguide, an electromechanical coupling absorber and a back cavity with a volume of V form a resonance absorber. The shunt circuit is a single branch, which switches between on and off, with a switching frequency of 125 Hz and a circuit conduction duty cycle of 50%. And, in this example, the diaphragm operates in a normal incidence sound absorption configuration, there is no transmitted wave in the waveguide, and the additional stiffness is The reflected wave obtained by the method of the present invention is as Figure 3 shown, and the sound absorption coefficient curve of the absorber obtained by the method of the present invention is as Figure 4 shown.

[0114] It can be seen that, compared with the sound absorption coefficient obtained by frequency domain averaging, the method of the present invention can fully reflect the transient response of the time-division multiplexing system.

[0115] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by orientation words such as "front, back, up, down, left, right", "lateral, vertical, perpendicular, horizontal" and "top, bottom" is usually based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description. Without contrary description, these orientation words do not indicate and imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation on the protection scope of the present invention; the orientation words "inside, outside" refer to the inside and outside relative to the contour of each component itself.

[0116] For ease of description, spatial relative terms such as "above", "over", "on the upper surface", "upper", etc. may be used herein to describe the spatial positional relationship of one device or feature to other devices or features as shown in the figures. It should be understood that the spatial relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is inverted, a device described as "above" or "over" other devices or structures will then be positioned "below" or "under" the other devices or structures. Thus, the exemplary term "above" can include both the orientations of "above" and "below". The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and corresponding interpretations of the spatial relative descriptions used herein will be made.

[0117] In addition, it should be noted that the use of terms such as "first" and "second" to define components is only for the convenience of differentiating the corresponding components. Without additional statements, the above terms have no special meanings, and thus should not be construed as limiting the protection scope of the present invention.

[0118] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A numerical simulation method for the time-domain response of an electromechanically coupled diaphragm of a multi-branch shunt circuit, characterized in that The method includes: Initializing the simulation environment variables and determining the positive direction of velocity and the positive direction of circuit current; Receiving the diaphragm parameters, shunt circuit parameters, and circuit time-division multiplexing timing parameters; Calculating the additional fluid load of the diaphragm's external acoustic radiation and the additional stiffness of the cavity structure based on the configuration of the diaphragm, with the conditions of continuous sound pressure and conservation of air volume flow rate, and correcting the incident excitation; Taking the additional fluid load, additional stiffness, and corrected excitation as the inputs of the dynamic equation of the mechanical part of the system, generate the time-varying MOSFET resistance according to the time-sequential parameters during circuit time-division multiplexing. And take the generated time sequence as the input of the dynamic equation of the multi-branch circuit part of the system, and assemble the lumped acoustic-vibration-electric coupling LTV differential equation set. Initializing the parameters of the configured variable-step fourth-order explicit Runge-Kutta solver; Solving the acoustic-elastic-electric coupled LTV differential equations using the configured solver parameters to obtain the time histories of the diaphragm's vibration displacement and velocity, trunk circuit charge and current, and the energy integrals of each part of the system; Analyzing the energy integrals of each part of the system to judge the conservation of the solver's solution. In the case where the conservation does not meet the predetermined accuracy requirements, adjusting the absolute tolerance and relative tolerance of the solver according to the residual magnitude, and re-executing the solution steps; When the conservation meets the predetermined accuracy requirements, reconstructing the reflected wave and transmitted wave in the waveguide using the diaphragm's vibration velocity according to the configuration of the diaphragm; Calculating the sound absorption coefficient, reflection coefficient, and transmission coefficient of the electro-acoustic coupled diaphragm using the energy ratio of the reconstructed reflected wave, transmitted wave, and incident wave; 2. The method according to claim 1, characterized in that, The simulation environment variables include the waveguide cross-sectional area A D , the air density ρ0, the speed of sound c0 in air, and the normalized incident sound pressure waveform function P I .

3. The method according to claim 2, wherein The diaphragm parameters include the geometric area A d , the parameters of the mechanical part of the diaphragm and the parameters of the circuit part of the diaphragm. The parameters of the mechanical part of the diaphragm include the moving mass M of the diaphragm, the equivalent suspension stiffness K, and the damping loss factor D. The parameters of the circuit part of the diaphragm include the internal resistance R s , the internal inductance L s and the electromagnetic coupling coefficient Bl. The shunt circuit parameters include the resistance values R n , the inductance values L n and the capacitance values C n , where the subscript n represents the nth branch. The timing parameters for circuit time-division multiplexing include the timing switching frequency and the conduction duty cycle of each branch.

4. The method according to claim 3, wherein Calculating the additional fluid load of the diaphragm's external acoustic radiation and the additional stiffness of the cavity structure based on the configuration of the diaphragm, with the conditions of continuous sound pressure and conservation of air volume flow rate, and correcting the incident excitation includes: When the configuration of the diaphragm is for normal incidence sound insulation, the additional fluid load is D F = 2ρ0c0A d , the additional stiffness is K A = 0, the incident excitation correction is F I = 2A d P I ; When the configuration of the diaphragm is for normal incidence sound absorption, the additional fluid load is D F = ρ0c0A d , the additional stiffness K A is the air stiffness of the resonance cavity, and the incident excitation is corrected to F I = 2A d P I ; When the configuration of the diaphragm is grazing-incidence sound insulation, the additional fluid load is D F = 0.5ρ0c0A d , the additional stiffness K A is the air stiffness of the resonance cavity, and the incident excitation is corrected to F I = A d P I ;.

5. The method according to claim 4, characterized in that, The dynamic equation of the mechanical part of the system is: The dynamic equation of the multi-branch circuit part of the system is: where x is the vibration displacement of the diaphragm, is the vibration velocity of the diaphragm, is the vibration acceleration of the diaphragm, q is the main circuit charge, is the main circuit current, is the change rate of the main circuit current, and the subscript n represents the nth branch.

6. The method according to claim 5, wherein Reconstructing the reflected wave and transmitted wave in the waveguide using the diaphragm's vibration velocity according to the configuration of the diaphragm includes: When the diaphragm configuration is for normal incidence sound insulation, the transmitted wave is The reflected wave is When the diaphragm configuration is for normal incidence sound absorption, there is no transmitted wave, and the reflected wave is When the diaphragm configuration is grazing-incidence sound insulation, the transmitted wave is The reflected wave is P R = P T - P I .

7. The method according to claim 6, characterized in that, Normalized incident sound pressure waveform function P I is as follows: P I = 1 Pa·sin(2πft), where Pa is Pascal and f t is a predetermined incident frequency.

8. The method according to claim 7, wherein Generate the timing of the MOSFET resistance change over time according to the following formula Where, Ω is ohm, Sign is the sign function, and t is time.

9. The method according to claim 8, wherein The acoustic-elastic-electric coupled LTV differential equations are: where U is the diaphragm state variable, is the derivative of the diaphragm state variable, F is a column vector, D M is a matrix, C1 is the capacitance value of the first branch, R1 is the resistance value of the first branch, and L1 is the inductance value of the first branch.

10. The method according to claim 9, wherein The time histories of the diaphragm's vibration displacement and velocity, trunk circuit charge and current are obtained through the following formula: where k1, k2, k3, and k4 are the first intermediate variable, the second intermediate variable, the third intermediate variable, and the fourth intermediate variable of the solver, respectively, and t n represents the nth moment, and t n+1 represents the (n + 1)th moment. is the diaphragm state variable at the nth moment, is the derivative of the diaphragm state variable at the nth moment, is the derivative of the diaphragm state variable at the (n + 1)th moment, is the column vector at the nth moment, is the column vector at the (n + 1)th moment, is the matrix at the nth moment, is the matrix at the (n + 1)th moment.

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