Simulation method of dynamic response of IPMC link fishtail based on ANCF

Abstract

The present invention proposes a simulation method for the dynamic response of an IPMC connecting rod fishtail based on ANCF, simplifies the IPMC connecting rod fishtail into a double beam structure of an IPMC flexible beam consolidating a rigid beam; selects a one-dimensional two-node ANCF beam unit to discretize the double beam structure, and calculates the degree of freedom of each unit in an inertial coordinate system; calculates the mass matrix and elastic force matrix of each unit; obtains the output torque of the IPMC flexible beam through the Nemat‑Nasser theory, converts the output torque into the form of a generalized force matrix as a generalized torque, calculates the fluid resistance of each unit as a generalized concentrated force, and the generalized torque and the generalized concentrated force are used together as generalized external forces; constructs a group of dynamic equations, uses the generalized α method as a solution algorithm to iteratively solve the group of dynamic equations, obtains the displacement, velocity, and acceleration data of each degree of freedom of all nodes of the structure, and draws a motion trajectory diagram of the structure. The present invention can accurately describe the dynamic response of the IPMC connecting rod fishtail and predict the motion trajectory of the structure.

Description

Technical Field

[0001] The invention belongs to the field of multi-body system dynamics modeling, and in particular is a simulation method for the dynamic response of an ANCF-based ionic polymer metal composite (Ionic polymer metal composite, IPMC) connecting rod type fishtail. Background Art

[0002] The flexible bionic robot fish driven by the intelligent material IPMC is a typical flexible multi-body system. Starting from the theory of dynamic modeling of flexible multi-body systems, it is necessary to conduct in-depth research on the multi-field coupling dynamic characteristics of the flexible bionic robot fish system that considers the real physical field environment and has the ability to swim with large swing amplitude, as well as its large deformation mechanism driven by soft intelligent materials. The fluid-solid coupling effect underwater and the rigid-flexible coupling effect when the fish swims are factors that need to be considered in the dynamic modeling of the bionic robot fish system when the IPMC driver is applied. Therefore, it is of great significance to establish the IPMC connecting rod type fish tail large deformation dynamic model.

[0003] Wang et al. used the finite segment method to conduct dynamic modeling research on a flexible tail-driven robotic fish in the article "Dynamic Modeling of Robotic Fish With a Base-Actuated Flexible Tail", proving the effectiveness of the model in predicting the large deformation behavior of the flexible tail. However, this method is based on the floating frame of reference (FFR) method and adopts the small deformation assumption, which is still limited in dealing with the problem of large deformation of flexible bodies. Zhang Anfan et al. established a floating coordinate system consistent with the movement direction of the robotic fish in the article "Dynamic Modeling and Simulation of Eel Robot in Non-Inertial System", and used the finite segment method to analyze the force conditions of each unit to assemble the dynamic model of the underwater two-dimensional bionic eel in the non-inertial system, but did not consider the influence of multi-physics field coupling. Summary of the invention

[0004] The purpose of the present invention is to propose a simulation method for the dynamic response of an IPMC linkage fishtail based on ANCF.

[0005] The technical solution to achieve the purpose of the present invention is: a dynamic response simulation method of an IPMC connecting rod fishtail based on ANCF, comprising the following steps:

[0006] Step 1, simplifying the IPMC connecting rod fishtail into a double beam structure of an IPMC flexible beam consolidating a rigid beam, setting the geometric parameters and material parameters of the two beams, setting the environmental parameters, and the driving voltage amplitude and frequency of the IPMC flexible beam;

[0007] Step 2, select one-dimensional two-node ANCF beam element to discretize the double beam structure, and calculate the degree of freedom of each element in the inertial coordinate system;

[0008] Step 3, calculate the mass matrix of each unit, and calculate the elastic force matrix of each unit by using the Green-Lagrangian strain tensor in continuum mechanics and introducing curvature;

[0009] Step 4, according to the set driving voltage, the output torque of the IPMC flexible beam is obtained by Nemat-Nasser theory, the output torque is converted into the form of a generalized force matrix as a generalized torque, the fluid resistance of each unit is calculated as a generalized concentrated force, and the generalized torque and the generalized concentrated force are jointly used as a generalized external force;

[0010] Step 5, construct a group of dynamic equations, use the generalized-α method as a solution algorithm to iteratively solve the group of dynamic equations, obtain the displacement, velocity, and acceleration data of each degree of freedom of all nodes of the structure, and draw the motion trajectory diagram of the structure.

[0011] Furthermore, in step 1, the geometric parameters and material parameters of the two beams are set, and the environmental parameters and the driving voltage amplitude and frequency of the IPMC flexible beam are set, wherein the geometric parameters include length, width and height, the material parameters include density and elastic modulus, and the environmental parameters include fluid density and resistance coefficient.

[0012] Further, in step 2, a one-dimensional two-node ANCF beam element is selected to discretize the double-beam structure, and the degree of freedom of each element in the inertial coordinate system is calculated. The specific method is:

[0013] The IPMC flexible beam and rigid beam are equally divided into multiple beam elements using one-dimensional two-node ANCF beam elements;

[0014] Describe the degrees of freedom of each beam unit in the inertial coordinate system. Assume that the inertial coordinate system is O-XYZ and the unit coordinate system is o-xyz. Then the absolute position vector r of any point on the unit axis is expressed as:

[0015]

[0016] Among them, r 1 With r 2 are the two components of vector r in the X and Y directions, a n For r 1 The coefficients of the interpolation polynomial, b n For r 2 The coefficients of the interpolation polynomial;

[0017] S is the unit shape function, expressed as:

[0018]

[0019]

[0020] in l is the length of the beam element when it is not deformed, and x is the position coordinate of any point on the beam element when it is not deformed;

[0021] Each beam unit node coordinate array q includes 2 nodes and a total of 8 degrees of freedom, expressed as:

[0022]

[0023] Furthermore, in step 3, the mass matrix of each unit is calculated. By adopting the Green-Lagrangian strain tensor calculation method in continuum mechanics and introducing curvature, the elastic force matrix of each unit is calculated. The specific method is:

[0024] M is the unit mass matrix, expressed as

[0025]

[0026] Where ρ and A are the density and cross-sectional area of ​​the beam element, respectively;

[0027] ε x is the strain at any point other than the midline, written as

[0028] ε x =ε x0 -yκ (6)

[0029] Among them, ε x0 is the strain corresponding to the point on the midline, y is the distance between the two points in the y direction in the unit coordinate system, and κ is the curvature of the point on the midline. According to symmetry, According to the principle of virtual work, the virtual work done by the unit elastic force δW fe for

[0030]

[0031] Where V is the unit volume, E is the elastic modulus, I z is the section inertia moment. According to the Green-Lagrangian strain tensor calculation method in continuum mechanics, ε x0 Expressed as

[0032]

[0033] Variation

[0034] δε x0 =δq T S′ T S′q (9)

[0035] The curvature κ is

[0036]

[0037] in, According to the vector multiplication rules, we can get

[0038]

[0039]

[0040] Substituting equations (8), (9), and (12) into equation (7), we can obtain the virtual work δW done by the unit elastic force: fe At the same time, the virtual work done by the elastic force of the beam element is also expressed as

[0041] δW fe =δq T Q fe (13)

[0042] Then Q fe The elastic force matrix of the unit is expressed as

[0043]

[0044] Further, in step 4, according to the set driving voltage, the output torque of the IPMC flexible beam is obtained by the Nemat-Nasser theory, the output torque is converted into the form of a generalized force matrix as a generalized torque, the fluid resistance of each unit is calculated as a generalized concentrated force, and the generalized torque and the generalized concentrated force are used together as a generalized external force. The specific method is:

[0045] According to the set driving voltage parameters, the output torque M of the IPMC flexible beam is obtained using the Nemat-Nasser theory. IPMC for:

[0046]

[0047]

[0048]

[0049] Among them, V C is the input voltage, w is the width, h is the height, α 0 is the coupling constant, κ e is the effective dielectric constant, F is the Faraday constant, C - is the anion concentration, R is the gas constant, and T is the absolute temperature;

[0050] The generalized moment applied to the first node by the output moment is written as

[0051]

[0052] in, Fluid resistance F fluid Expressed as

[0053]

[0054] Among them, ρ w is the fluid density, v is the velocity of the fish unit segment (obtained from the node velocity data of each time step iteration), S is the wet area of ​​the fish unit, C D is the fluid resistance coefficient;

[0055] F f_x and F f_y F fluid The components in the x and y directions, written as generalized concentrated forces, are

[0056] Q F =[F f_x F f_y 0 0 F f_x F f_y 0 0] T (20).

[0057] Further, in step 5, a group of dynamic equations is constructed, and the generalized-α method is used as a solution algorithm to iteratively solve the group of dynamic equations, obtain the displacement, velocity, and acceleration data of each degree of freedom of all nodes of the structure, and draw a motion trajectory diagram of the structure, wherein the specific construction method of the group of dynamic equations is:

[0058] The mass matrices of all units are assembled in node order to form the mass matrix M of the entire structure. a , the elastic force matrix and generalized external force matrix of all units are assembled in node order to form the generalized external force Q of the structure a ,;

[0059] The constraint equations are introduced using the Lagrange multiplier method to obtain the dynamic equations:

[0060]

[0061] Among them, λ is the Lagrange multiplier, Φ q is the Jacobian matrix of the constraint. Depending on the constraint form, Φ q The manifestation will also change;

[0062] Under hinge constraint:

[0063]

[0064] Under consolidation constraints:

[0065]

[0066] A dynamic response simulation system of an IPMC connecting rod type fishtail based on ANCF realizes the dynamic response simulation of an IPMC connecting rod type fishtail based on ANCF based on the dynamic response simulation method of the IPMC connecting rod type fishtail.

[0067] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, based on the dynamic response simulation method of the IPMC connecting rod type fish tail, the dynamic response simulation of the IPMC connecting rod type fish tail based on ANCF is realized.

[0068] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the dynamic response simulation of an IPMC connecting rod type fish tail based on ANCF is realized based on the dynamic response simulation method of the IPMC connecting rod type fish tail.

[0069] Compared with the prior art, the present invention has the following significant advantages: (1) The ANCF is used to establish the dynamic model of the IPMC connecting rod fishtail, which is more suitable for calculating the dynamic response of the large deformation of the fishtail. The slope vector is used to replace the transfer coordinates, and there is no small deformation and small rotation assumption. The established equation has a constant mass matrix, and there is no Coriolis force and centrifugal force. It can accurately describe the large deformation behavior of the fishtail, and provides a new technical method for the dynamic research of flexible bionic robot fish. (2) The influence of multiple physical fields is taken into account, including the electromechanical relationship of the intelligent material IPMC and the influence of fluid resistance. By changing the parameter setting, the displacement, velocity, and acceleration dynamic response of the structure can be accurately calculated under different voltage drives and with or without fluid resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flow chart of the method of the present invention.

[0071] Figure 2 It is a schematic diagram of the IPMC beam-rigid beam connecting rod type fishtail structure.

[0072] Figure 3 This is the ANCF beam element model diagram.

[0073] Figure 4 It is a generalized-alpha method iterative flow chart for solving the equation.

[0074] Figure 5 It is the initialization diagram of the APP visual interface.

[0075] Figure 6 It is a diagram of the running results of the embodiment.

[0076] Figure 7 Schematic diagram of the overall configuration change of the embodiment system. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0078] like Figure 1 As shown, the simulation method of the IPMC connecting rod fishtail dynamic response based on ANCF calculation of the present invention includes the following steps:

[0079] (1) Simplify the IPMC connecting rod fishtail as follows Figure 2 The double-beam structure of the IPMC flexible beam consolidating the rigid beam shown in the figure sets the geometric parameters of the two beams in the structure, including length, width, height, and material parameters such as density and elastic modulus, sets the environmental parameters such as fluid density and resistance coefficient, and sets the driving voltage amplitude and frequency of the IPMC flexible beam.

[0080] (2) Use Figure 3 The ANCF one-dimensional two-node beam element shown divides the IPMC flexible beam and rigid beam into any number of beam elements. The degrees of freedom of each beam element are described in the inertial coordinate system. The inertial coordinate system is O-XYZ, the unit coordinate system is o-xyz, and the absolute position vector r of any point on the unit axis is expressed as

[0081]

[0082] Among them, r 1 With r 2 are the two components of vector r in the X and Y directions, a n For r 1 The coefficients of the interpolation polynomial, b n For r 2 The coefficients of the interpolation polynomial, S is the unit shape function expressed as

[0083]

[0084]

[0085] in l is the length of the beam unit when it is not deformed, and x is the position coordinate of any point on the beam unit when it is not deformed. Each beam unit node coordinate array q includes 2 nodes and a total of 8 degrees of freedom, which can be specifically expressed as

[0086]

[0087] (3) The mass matrix of the calculated unit is obtained by using the Green-Lagrangian strain tensor calculation method in continuum mechanics and introducing curvature to calculate the unit elastic force matrix.

[0088] M is the unit mass matrix, expressed as

[0089]

[0090] where ρ and A are the density and cross-sectional area of ​​the beam element, respectively.

[0091] ε x is the strain at any point other than the midline, written as

[0092] ε x =ε x0 -yκ (6)

[0093] Among them, ε x0 is the strain corresponding to the point on the midline, y is the distance between the two points in the y direction in the unit coordinate system, and κ is the curvature of the point on the midline. According to symmetry, According to the principle of virtual work, the virtual work done by the unit elastic force δW fe for

[0094]

[0095] Where V is the unit volume, E is the elastic modulus, I z is the section inertia moment. According to the Green-Lagrangian strain tensor calculation method in continuum mechanics, ε x0 It can be expressed as

[0096]

[0097] Variation

[0098] δε x0 =δq T S′ T S′q (9)

[0099] The curvature κ is

[0100]

[0101] in, According to the vector multiplication rules, we can get

[0102]

[0103]

[0104] Substituting equations (8), (9), and (12) into equation (7), we can obtain the virtual work δW done by the unit elastic force: fe At the same time, the virtual work done by the elastic force of the beam element is also expressed as

[0105] δW fe =δq T Q fe (13)

[0106] So, Q fe The elastic force matrix of the unit can be expressed by calculation as

[0107]

[0108] (4) According to the driving voltage parameters set in step (1), the output torque M of the IPMC flexible beam is obtained by using the Nemat-Nasser theory. IPMC for

[0109]

[0110]

[0111]

[0112] Among them, V C is the input voltage, w is the width, h is the height, α 0 is the coupling constant, κ e is the effective dielectric constant, F is the Faraday constant, C - is the anion concentration, R is the gas constant, and T is the absolute temperature.

[0113] The generalized moment applying the output torque to the first node can be written as

[0114]

[0115] in,

[0116] The fluid resistance is expressed as

[0117]

[0118] Among them, ρ w is the fluid density, v is the velocity of the fish unit segment (obtained from the node velocity data of each time step iteration), S is the wet area of ​​the fish unit, C D is the fluid resistance coefficient.

[0119] F f_x and F f_y F fluid The components in the x and y directions, written as generalized concentrated forces, are

[0120] Q F =[F f_x F f_y 0 0 F f_x F f_y 0 0] T (20)

[0121] (5) According to the items obtained in steps (2), (3), and (4), the mass matrices of all units are assembled into the mass matrix M of the whole structure in node order. a , the elastic force matrix and generalized external force matrix of all units are assembled in node order to form the generalized external force Q of the structure a The constraint equations and dynamic equations are introduced by Lagrange multiplier method and expressed as:

[0122]

[0123] Among them, λ is the Lagrange multiplier, Φ q is the Jacobian matrix of the constraint. Depending on the constraint form, Φ q The manifestation will also change.

[0124] Hinge Constraint

[0125] Under consolidation constraints,

[0126] Use Figure 4 The generalized-α method shown is used as a solution algorithm to iteratively solve the dynamic equations, obtain the displacement, velocity, and acceleration data of each degree of freedom of all nodes of the structure, and obtain the motion trajectory diagram of the structure.

[0127] Example

[0128] In order to verify the effectiveness of the solution of the present invention, the following simulation experiment is carried out.

[0129] (1) In this embodiment, the two beams use the parameter settings shown in Table 1, and the driving voltage is set to a square wave voltage with an amplitude of 2V and a frequency of 5Hz.

[0130] Table 1 System geometry parameters and environmental parameter settings used in this embodiment

[0131]

[0132] (2) Discretize the structure into units, divide the IPMC beam into 5 units and the rigid beam into 1 unit. Describe the degrees of freedom of each unit in the system in the inertial coordinate system, and obtain the node coordinate array q of each beam unit.

[0133] (3) Calculate the mass matrix and unit elastic force matrix of each beam unit.

[0134] (4) Using the parameters set in Table 2, the output torque is obtained by Nemat-Nasser theory. The generalized torque and generalized concentrated force are calculated.

[0135] Table 2 Material parameter settings used in this embodiment

[0136]

[0137]

[0138] (5) According to the items obtained in steps (2), (3), and (4), the mass matrices of all units are assembled into the mass matrix M of the whole structure in node order. a , the generalized external forces of all units are assembled in node order to form the generalized external force Q of the structure a After assembling according to the traditional finite element assembly method, the constraints of the system are considered, and the constraint equations are introduced by the Lagrange multiplier method to obtain the dynamic equations. The dynamic equations are iteratively solved using the generalized-α method. In this embodiment, the spectral radius is 0.8, the iteration step is 0.0001s, and the calculation time is 1s.

[0139] Output like Figure 6 The Y-direction displacement diagram of the beam end node and the Y-direction velocity diagram of the beam end node are shown in the output. Figure 7 The overall motion trajectory change diagram shown in the figure can also obtain the data of the degree of freedom of all unit nodes of the structure changing with time. Changing the voltage amplitude and frequency of the drive will obtain different dynamic responses of the system.

[0140] The present invention uses the absolute node coordinate method to carry out dynamic modeling of the IPMC connecting rod fish tail, and writes an algorithm program according to the dynamic equation. It can accurately output a series of dynamic responses of each unit node of the structure within a period of time, including velocity, displacement, acceleration, etc., and can intuitively see the changes in the overall motion trajectory. It is of great value for the design of IPMC driven robotic fish.

[0141] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0142] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A dynamic response simulation method of IPMC connecting rod fishtail based on ANCF, It is characterized in that The steps include: Step 1, simplifying the IPMC connecting rod fishtail into a double beam structure of an IPMC flexible beam consolidating a rigid beam, setting the geometric parameters and material parameters of the two beams, setting the environmental parameters, and the driving voltage amplitude and frequency of the IPMC flexible beam; Step 2, select one-dimensional two-node ANCF beam element to discretize the double beam structure, and calculate the degree of freedom of each element in the inertial coordinate system; Step 3, calculate the mass matrix of each unit, and calculate the elastic force matrix of each unit by using the Green-Lagrangian strain tensor calculation method in continuum mechanics and introducing curvature; Step 4, according to the set driving voltage, the output torque of the IPMC flexible beam is obtained by Nemat-Nasser theory, the output torque is converted into the form of a generalized force matrix as a generalized torque, the fluid resistance of each unit is calculated as a generalized concentrated force, and the generalized torque and the generalized concentrated force are jointly used as a generalized external force; Step 5, construct a group of dynamic equations, use the generalized-α method as a solution algorithm to iteratively solve the group of dynamic equations, obtain the displacement, velocity, and acceleration data of each degree of freedom of all nodes of the structure, and draw a motion trajectory diagram of the structure; Step 2: Select one-dimensional two-node ANCF beam element to discretize the double-beam structure and calculate the degree of freedom of each element in the inertial coordinate system. The specific method is: The IPMC flexible beam and rigid beam are equally divided into multiple beam elements using one-dimensional two-node ANCF beam elements; Describe the degrees of freedom of each beam unit in the inertial coordinate system. Assume that the inertial coordinate system is O-XYZ and the unit coordinate system is o-xyz. Then the absolute position vector r of any point on the unit axis is expressed as: Among them, r 1 With r 2 are the two components of vector r in the X and Y directions, a n For r 1 The coefficients of the interpolation polynomial, b n For r 2 The coefficients of the interpolation polynomial; S is the unit shape function, expressed as: in l is the length of the beam element when it is not deformed, and x is the position coordinate of any point on the beam element when it is not deformed; Each beam unit node coordinate array q includes 2 nodes and a total of 8 degrees of freedom, expressed as: Step 3: Calculate the mass matrix of each unit. By using the Green-Lagrangian strain tensor calculation method in continuum mechanics and introducing curvature, the elastic force matrix of each unit is calculated. The specific method is as follows: M is the unit mass matrix, expressed as Where ρ and A are the density and cross-sectional area of ​​the beam element, respectively; ε x is the strain at any point other than the midline, written as e x =e x0 -yk (6) Among them, ε x0 is the strain corresponding to the point on the midline, y is the distance between the two points in the y direction in the unit coordinate system, and κ is the curvature of the point on the midline. According to symmetry, According to the principle of virtual work, the virtual work done by the unit elastic force δW fe for Where V is the unit volume, E is the elastic modulus, I z is the section inertia moment. According to the Green-Lagrangian strain tensor calculation method in continuum mechanics, ε x0 Expressed as Variation δε x0 =δq T S′ T S′q (9) The curvature κ is in, According to the vector multiplication rules, we can get Substituting equations (8), (9), and (12) into equation (7) yields the virtual work done by the unit elastic force. At the same time, the virtual work done by the beam unit elastic force is also expressed as δW fe =δq T Q fe (13) Then Q fe The elastic force matrix of the unit is expressed as Step 4: According to the set driving voltage, the output torque of the IPMC flexible beam is obtained through the Nemat-Nasser theory, and the output torque is converted into the form of a generalized force matrix as a generalized torque. The fluid resistance of each unit is calculated as a generalized concentrated force. The generalized torque and the generalized concentrated force are used together as a generalized external force. The specific method is as follows: According to the set driving voltage parameters, the output torque M of the IPMC flexible beam is obtained using the Nemat-Nasser theory. IPMC for: Among them, V C is the input voltage, w is the width, h is the height, α 0 is the coupling constant, κ e is the effective dielectric constant, F is the Faraday constant, C - is the anion concentration, R is the gas constant, and T is the absolute temperature; The generalized moment applied to the first node by the output moment is written as in, Fluid resistance F fluid Expressed as Among them, ρ w is the fluid density, v is the velocity of the fish unit segment, S is the wet area of ​​the fish unit, C D is the fluid resistance coefficient; F f_x and F f_y F fluid The components in the x and y directions are written as generalized concentrated forces Q F =[F f_x F f_y 00F f_x F f_y 00] T (20) Step 5, construct the dynamic equations, use the generalized-α method as the solution algorithm to iteratively solve the dynamic equations, obtain the displacement, velocity, and acceleration data of each degree of freedom of all nodes of the structure, and draw the motion trajectory diagram of the structure. The specific construction method of the dynamic equations is: The mass matrices of all units are assembled in node order to form the mass matrix M of the entire structure. a , the elastic force matrix and generalized external force matrix of all units are assembled in node order to form the generalized external force Q of the structure a ; The constraint equations are introduced using the Lagrange multiplier method to obtain the dynamic equations: Among them, λ is the Lagrange multiplier, Φ q is the Jacobian matrix of the constraint. Depending on the constraint form, Φ q The manifestation will also change; Under hinge constraint: Under consolidation constraints:

2. According to the ANCF-based IPMC connecting rod fishtail dynamic response simulation method of claim 1, It is characterized in that Step 1, set the geometric parameters and material parameters of the two beams, set the environmental parameters and the driving voltage amplitude and frequency of the IPMC flexible beam, where the geometric parameters include length, width and height, the material parameters include density and elastic modulus, and the environmental parameters include fluid density and resistance coefficient.

3. A dynamic response simulation system of IPMC connecting rod fishtail based on ANCF, It is characterized in that Implement the method for simulating the dynamic response of an IPMC connecting rod type fishtail based on ANCF as described in any one of claims 1-2 to realize the simulation of the dynamic response of an IPMC connecting rod type fishtail based on ANCF.

4. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for simulating the dynamic response of an IPMC connecting rod type fishtail based on ANCF as described in any one of claims 1 to 2 is implemented to realize the simulation of the dynamic response of an IPMC connecting rod type fishtail based on ANCF.

5. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for simulating the dynamic response of an IPMC connecting rod type fishtail based on ANCF according to any one of claims 1 to 2 is implemented to achieve the dynamic response simulation of an IPMC connecting rod type fishtail based on ANCF.

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