Dynamic modeling method for rotating FGM micro beam

Abstract

The invention relates to the field of system dynamic modeling, in particular to a dynamic modeling method of a rotating FGM micro-beam, which comprises the following steps: setting geometric parameters and material parameters of the FGM micro-beam, and establishing a rotating FGM micro-beam system based on a modified even stress theory and a scale effect; a mixed coordinate method is adopted to describe a deformation displacement field of any point on the FGM micro-beam in the FGM micro-beam system in a floating coordinate system, wherein the deformation displacement field rotates in a large range; discretizing the large-range rotational deformation of the FGM micro beam by adopting a meshless point interpolation method and a meshless radial base point interpolation method; establishing a high-order rigid-flexible coupling nonlinear kinetic equation of the rotating FGM micro-beam system by applying a second type of Lagrange equation, namely obtaining a kinetic simulation model of the rotating FGM micro-beam based on a meshless point interpolation method and a radial base point interpolation method; solving the kinetic equation by adopting a Newmark method to obtain a deformation schematic diagram of the FGM micro beam in large-range rotational motion; the simulation model and the simulation method provided by the invention have the advantages of high efficiency and high precision, and can also consider the dynamic response of the system.

Description

Technical Field

[0001] The invention relates to the field of system dynamics modeling, and in particular to a dynamics modeling method for a rotating FGM micro-beam. Background Art

[0002] With the deepening of research on micro-electromechanical systems (MEMS), most of the flexible attachments such as micro-rotor aircraft, micro gas turbine generators, and micro-electromechanical acceleration sensors are rigid-flexible coupling structures mounted on rigid bodies. This type of structure has both rigid motion and elastic deformation of flexible components during movement. The two are coupled with each other, and the dynamic behavior presented is very complex. Most of the components in its structure can be simplified as micro-beams with sizes of micrometers or submicrometers. When the geometric size of the component is in the micrometer or nanometer order, its mechanical properties will have a strong scale effect. Traditional continuum mechanics, which uses "continuum" as the basic assumption to study the mechanical properties of macroscopic objects, ignores the important influence of the gaps between microstructure particles at the microscale, and therefore cannot correctly predict the mechanical properties of materials. The dynamic modeling theory of beams moving in a large range developed for the macroscale is no longer applicable. Therefore, considering the scale effect, the theoretical study of dynamic modeling of micro-beam structures moving in a large range has become a development trend in the field of dynamics of flexible multi-body systems.

[0003] In practical applications, the system is often in extremely harsh working conditions such as high temperature and high speed. Traditional homogeneous materials are difficult to meet the requirements of the actual service environment due to the limitations of their own mechanical properties. Therefore, it is particularly important to design new composite materials that meet the requirements of the service environment and study their dynamic characteristics without affecting the structural strength. Among many new composite materials, functional gradient materials (FGM) have attracted extensive attention from researchers for their advantages such as heat resistance, high strength, and improved stress concentration, and have been applied in aerospace, nuclear industry, biology and other fields.

[0004] In the prior art, the rotating FGM micro-beam system is modeled dynamically, but the longitudinal shortening caused by the lateral bending deformation is ignored during the modeling. That is, the influence of the nonlinear coupling deformation term on the system is established by a first-order approximate rigid-flexible coupling dynamic model. The first-order model has certain errors in predicting high speed and large deformation. In addition, most of the related theories of the dynamics of flexible multi-body systems are studied using the traditional continuum theory, which is only applicable to the calculation of beams at macroscopic sizes. For the micro-beam system, the traditional continuum theory ignores the influence of the scale effect, which will also lead to certain system errors; and when the system is discretized using the assumed modal method, when the micro-beam undergoes a large deformation, this method also has theoretical defects. Summary of the invention

[0005] The purpose of the present invention is to provide a new discrete model based on the Euler-Bernoulli beam theory taking into account the scale effect based on the modified couple stress theory, so as to solve the influence of the scale effect on the transient dynamic response and steady-state free vibration of the rotating FGM microbeam.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] A dynamic modeling method of a rotating FGM micro-beam based on a gridless point interpolation method and a radial base point interpolation method, which at least includes:

[0008] S100, setting geometric parameters and material parameters of the FGM micro-beam, and establishing a rotating FGM micro-beam system based on the modified couple stress theory taking into account the scale effect;

[0009] S200, using a mixed coordinate method to describe the deformation displacement field of a large-scale rotational motion of any point on the FGM micro-beam in the FGM micro-beam system in a floating coordinate system;

[0010] S300, using gridless point interpolation method and radial base point interpolation method to discretize the deformation field of FGM microbeam;

[0011] S400. The second kind of Lagrange equation is used to establish the high-order rigid-flexible coupling nonlinear dynamic equation of the rotating FGM microbeam system, that is, the dynamic simulation model of the rotating FGM microbeam based on the meshless method under the modified couple stress theory and scale effect is obtained.

[0012] Among them, the geometric parameters of the FGM microbeam are: the length of the FGM microbeam is L, the width is b, the height is h, and the material characteristic length parameter is l; the material parameter elastic modulus E(y) and density ρ(y) are functions of the thickness direction coordinate y, and the expressions are as follows:

[0013]

[0014] Wherein, the subscripts c and m in P represent ceramic and metal materials, respectively, P(y) represents the Young's modulus E(y) and density ρ(y) of a point on the FGM microbeam, Vc(y) and Vm(y) represent the volume fractions of metal and ceramic materials along the height direction of the FGM microbeam, and N represents the non-negative power index of the material gradient distribution along the height direction, i.e., the functional gradient index. When N=0 and N=∞, it means that the microbeam is made of pure ceramic material and pure metal material, respectively.

[0015] The component materials of FGM microbeam are composed of metal Al and ceramic Al2O3. The elastic modulus and density of ceramic and metal are Ec=380GPa, Em=70GPa, ρc=3800kg / m3, ρm=2700kg / m3 respectively; the Poisson's ratio of ceramic and metal is νc=νm=0.3 respectively.

[0016] Preferably, in the establishment method, the expression of the deformation radius r of any point on the FGM micro-beam in the inertial coordinate system O-XYZ is:

[0017] r=Θ(R+ρ 0 +u)

[0018]

[0019] Where R is the radius vector from the center of mass O of the central rigid body to the base point o of the floating base, ρ0 is the radius vector about the floating base before deformation, u is the deformation displacement vector, Θ is the normal cosine matrix of the floating base relative to the inertial coordinate system;

[0020] The expression of the deformation vector u in the floating coordinate system is:

[0021]

[0022] w1 is the longitudinal deformation of the FGM microbeam, w2 is the transverse deformation of the FGM microbeam, and wc is the second-order nonlinear coupling deformation, which is the longitudinal shortening caused by the transverse bending deformation of the flexible microbeam;

[0023] Kinetic energy expression of FGM micro-beam system:

[0024]

[0025] Where Jch is the moment of inertia of the central rigid body around the center of rotation;

[0026] Ignoring the shear and torsion effects of the FGM microbeam, based on the modified couple stress theory, the expression of the deformation potential energy of the FGM microbeam at microscale is:

[0027]

[0028] Where ε and σ represent the components of the strain tensor and stress tensor, respectively; χ and m represent the components of the curvature tensor and the deviatoric component of the couple stress tensor, respectively; and l is the characteristic length parameter of the material.

[0029] Preferably, the establishment method includes: using a meshless method to discretize the FGM micro-beam into a number of nodes, calculating and obtaining the node information in the support domain of the calculation point x, and taking the longitudinal and lateral displacement functions as:

[0030]

[0031] In the formula, Φ x (x) and Φ y (x) are the shape functions of the longitudinal displacement and the transverse displacement, respectively. A(t) and B(t) are the column vectors of the longitudinal deformation and the transverse deformation of the node over time, respectively.

[0032] The second-order nonlinear coupling deformation of the longitudinal shortening caused by the lateral deformation is:

[0033]

[0034] Where H(x) is the coupling shape function, and its expression is:

[0035]

[0036] Preferably, the establishment method, wherein: the second kind of Lagrange equation is used to establish the high-order rigid-flexible coupling nonlinear dynamic equation of the rotating FGM micro-beam system considering the modified couple stress theory and scale effect, specifically, the generalized coordinate column vector q of the system is taken as (θ, A T ,B T ) T and the generalized force column vector F q =(τ,0,0) T , where τ is the total external input torque acting on the rigid body, and the kinetic energy expression Tk of the FGM micro-beam system and the potential energy expression U of the FGM micro-beam system are substituted into the second kind of Lagrange equation:

[0037]

[0038] The high-order rigid-flexible coupling nonlinear dynamic equation of the FGM micro-beam system with large-scale motion and rotation considering the modified couple stress theory and scale effect is obtained as follows:

[0039]

[0040] The specific matrix expression is:

[0041]

[0042] M 22 =M 1

[0043]

[0044]

[0045] The above formula is the high-order rigid-flexible coupling dynamic equation of the rotating FGM micro-beam system (referred to as the high-order model). The single underlined term and the double underlined term are additional coupling terms due to the consideration of the nonlinear coupling deformation wc, and the triple underlined term is the additional term due to the consideration of the scale effect. Y, Sx, Sy, Sx1, Sy1, Sy2, M1, M2, M3, M4, M5, C0, C1, D, K0, K1, K2, K3 are constant coefficient matrices; Jcb is the moment of inertia of the beam;

[0046] The correlation constant coefficient matrix is:

[0047]

[0048]

[0049]

[0050] Since the flexible beam mainly vibrates in transverse bending, ignoring the influence of the longitudinal deformation of the flexible beam, when the rotation angular velocity is constant, the free vibration equation of the FGM flexible microbeam is:

[0051]

[0052] The above formula is dimensionless, β is the dimensionless length parameter, is the dimensionless natural frequency, γ is the dimensionless angular velocity, υ and η are correlation coefficients. Substituting the dimensionless variables into the free vibration equation of the FGM flexible microbeam, the above formula can be rewritten as:

[0053]

[0054] By solving the eigenvalue problem of the dimensionless lateral bending free vibration equation above, the dimensionless natural frequencies of the lateral bending vibration of the rotating FGM flexible microbeam can be obtained.

[0055] A dynamic modeling method for a rotating FGM microbeam based on a gridless point interpolation method and a radial base point interpolation method as described above adopts the Newmark method to solve the dynamic equations and obtain a deformation diagram of a rotating FGM microbeam with a large range of motion.

[0056] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0057] 1. The present invention numerically solves the dynamic equation based on the modified couple stress theory and the Euler-Bernoulli beam theory taking into account the scale effect, and studies the scale effect on the dynamic response characteristics of the rotating FGM micro-beam system, which produces a non-negligible influence.

[0058] 2. The present invention takes into account all the high-order terms of nonlinear coupling terms that have been ignored in existing studies, and establishes a high-order rigid-flexible coupling nonlinear dynamic model of the rotating FGM microbeam. Compared with the previous zero-order model and first-order model, it is more suitable for high speed, large deformation and other situations, and has higher accuracy and a wider range of applications.

[0059] 3. The present invention adopts a meshless method for discretization, does not rely on the small deformation assumption, and has higher accuracy and a wider range of applications than the assumed modal method. It has broad application prospects in dealing with engineering calculation problems and can provide certain technical support for related workers. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0061] Figure 1 It is a simulation method flow chart of a dynamic modeling method of a rotating FGM micro-beam of the present invention.

[0062] Figure 2 It is a schematic diagram of the deformation of the FGM micro-beam system undergoing large-scale motion and rotation.

[0063] Figure 3 It is a schematic diagram of the cross-section of the FGM microbeam.

[0064] Figure 4 It is known that large-scale movement Transverse deformation diagram of the end of FGM microbeam.

[0065] Figure 5 Is the speed The end response of FGM microbeam under different N.

[0066] Figure 6 Is the speed Transverse deformation diagram considering the scale effect on the dynamic response of the end of the FGM microbeam under different dimensionless length parameters β = h / l.

[0067] Figure 7 It is the angular displacement and lateral deformation diagram of the end of the FGM microbeam when the large-scale motion is unknown τ = 250N·m.

[0068] Figure 8 It is the angular displacement and lateral deformation diagram of FGM microbeam under different N when the external driving force τ = 250N·m.

[0069] Fig. 9 The lateral deformation diagram considering the scale effect on the dynamic response of the end of the FGM microbeam when the external driving force τ = 250N·m is different under different dimensionless length parameters β = h / l.

[0070] Fig.10 This is a graph showing the first three-order dimensionless natural frequencies of the FGM microbeam system changing with the dimensionless angular velocity γ.

[0071] Fig.11 This is a graph showing the first three-order dimensionless natural frequencies of the FGM microbeam system changing with the functional gradient index N when the dimensionless angular velocity γ=30.

[0072] Fig.12 This is a curve diagram of the influence of scale effect on the first three dimensionless natural frequencies of the FGM microbeam system when the dimensionless angular velocity γ=30. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in 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.

[0074] See also Figure 1-Figure 12 , the present invention provides a technical solution:

[0075] Embodiment 1:

[0076] The embodiment of the present invention discloses a method for calculating the dynamic response of a rotating FGM micro-beam based on a gridless point interpolation method and a radial base point interpolation method. The specific method is as follows:

[0077] Step 1: Set the geometric parameters of the central rigid body-rigid-flexible coupling system and establish Figure 2 A rotating FGM micro-beam system considering scale effect; the FGM of this embodiment takes a metal / ceramic composite material as an example, and other specific parameters are shown in Table 1.

[0078] The movement rules are as follows:

[0079]

[0080] In the formula, T0 = 10ms, and the angular velocity of the rigid body reaches a stable state.

[0081] Table 1

[0082]

[0083]

[0084] Step 2, using a mixed coordinate method to describe the deformation displacement field of any point on the FGM micro-beam in the rotating FGM micro-beam system performing a large-scale rotational motion in a floating coordinate system;

[0085] Step 3, using the assumed modal method (comparison), the finite element method (comparison), the gridless point interpolation method (PIM), and the gridless radial point interpolation method (RPIM) to discretize the large-scale rotational deformation of the FGM microbeam;

[0086] Step 4: Use the second kind of Lagrange equation to establish the high-order rigid-flexible coupling nonlinear dynamic equation of the FGM micro-beam system considering the modified couple stress theory and scale effect;

[0087] Step 5: Use the Newmark method to solve the dynamic equation and output the deformation diagram of the FGM microbeam with large-scale rotational motion.

[0088] from Figure 4 It can be seen that when the applied speed is 250rad / s, the simulation result curves of the four discrete methods are approximately overlapped in the acceleration stage of the speed. However, in the 10-15ms local lateral deformation displacement magnification diagram, it can be clearly observed that the simulation results of the meshless method and the finite element method are always highly fitted, but the simulation results of the assumed modal method have certain errors with the simulation results of the other three discrete methods, which shows that the assumed modal method does have defects.

[0089] from Figure 5 It can be seen that under the RPIM discretization method, when the rotation speed is 250 rad / s, the lateral deformation increases with the increase of the functional gradient index N. When the large-scale movement reaches a steady state, the vibration equilibrium curve is approximately distributed above and below the axis of the beam, and exhibits reciprocating vibration around 0, and with the increase of N, the amplitude of the vibration curve increases and the frequency decreases.

[0090] from Figure 6 It can be seen that when the rotation speed is 250rad / s under RPIM discretization, considering the scale effect will reduce the amplitude of the lateral deformation response of the end of the FGM microbeam and increase the vibration frequency, and as the dimensionless length parameter h / l decreases, the influence of this scale effect will become more obvious. It can be seen that this influence is inversely proportional to the dimensionless length parameter h / l, that is, the smaller the thickness of the FGM microbeam, or the larger the characteristic length parameter of the material, the more obvious the influence of the scale effect, and at this time the influence of the scale effect on the dynamic characteristics of the FGM microbeam becomes non-negligible.

[0091] from Figure 7 It can be seen that when the applied external driving force is 250 N·m, the simulation results of the four discrete methods in the angular displacement diagram fit well. However, there is a gap between the results of the assumed modal method and the other three discrete methods in the lateral deformation diagram of the beam end. This also further illustrates the shortcomings of the assumed modal method and the applicability and accuracy of the meshless method in dealing with large-scale motion problems.

[0092] from Figure 8 It can be seen that under RPIM discretization and with an external driving force of 250 N·m, the angular displacement of the FGM micro-beam system does not change significantly with the increase of the functional gradient index N. Only in the local magnification of 10-15ms can it be clearly observed that the change of the angular displacement increases with the increase of the functional gradient index N. The lateral deformation increases with the increase of the functional gradient index N, and the change amplitude is larger and more obvious than the angular displacement. In addition, the vibration during the steady-state motion of 10-15ms increases with the increase of the functional gradient index N, and the frequency decreases.

[0093] from Fig. 9 It can be seen that in the case of unknown large-scale motion, applying an external driving force τ0 = 250 N·m, considering the scale effect will reduce the maximum amplitude of the lateral displacement at the end of the FGM microbeam. As the dimensionless length parameter h / l decreases, the influence of this scale effect will become more obvious. At this time, the gap between the dynamic response considering the scale effect and not considering the scale effect is also getting bigger and bigger.

[0094] from Fig.10 It can be seen that the transverse bending dimensionless natural frequency of the FGM microbeam is positively correlated with its dimensionless angular velocity, and the simulation result error of the assumed modal method increases with the increase of the dimensionless angular velocity γ; while the results of the meshless method are always consistent with the other results. It can be seen that the assumed modal method always overestimates the natural frequency of the system.

[0095] from Fig.11 It can be seen that the dimensionless natural frequency is negatively correlated with the change of the functional gradient index N. It is assumed that the modal method overestimates the natural frequency of the system, and its error increases with the increase of N, while the meshless method always has good applicability.

[0096] from Fig.12 It can be seen that the first three dimensionless natural frequencies considering the scale effect decrease with the increase of the dimensionless length parameter, but the change of the first three dimensionless natural frequencies without considering the scale effect is very small and can be ignored. When the dimensionless length parameter gradually increases, the results of considering the scale effect and not considering the scale effect will gradually converge. It can be seen that when the thickness of the beam is reduced to close to the characteristic length parameter of the material, the influence of the scale effect on the transient dynamic response and steady-state free vibration of the FGM micro-beam system can no longer be ignored, and then the influence of the scale effect on the system must be considered.

[0097] Although the embodiment 1 of the present case takes metal / ceramic composite materials as an example, the simulation model and simulation method of the present case can be fully applicable to including but not limited to non-metal / ceramic composite materials, metal / non-metal composite materials, ceramic / ceramic composite materials, etc.

[0098] Embodiment 2:

[0099] The computer-readable storage medium of this embodiment stores a computer program thereon, and when the program is executed by a processor, the steps in the method for dynamic modeling of a rotating FGM micro-beam in Embodiment 1 are implemented.

[0100] The computer-readable storage medium of this embodiment may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal; the computer-readable storage medium of this embodiment may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash memory card, etc. equipped on the terminal; further, the computer-readable storage medium may also include both an internal storage unit of the terminal and an external storage device.

[0101] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or is to be output.

[0102] Embodiment 3:

[0103] The computer device of this embodiment includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the method for dynamic modeling of a rotating FGM micro-beam in Embodiment 1 are implemented.

[0104] In this embodiment, the processor may be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, readily available programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0105] Those skilled in the art will appreciate that the disclosed content of the embodiments may be provided as methods, systems, or computer program products. Therefore, the present solution may adopt the form of hardware embodiments, software embodiments, or embodiments combining software and hardware. Moreover, the present solution may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program codes.

[0106] The present solution is described with reference to the method according to the embodiment of the present solution and the flowchart and / or block diagram of the computer program product. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions; these computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 one or more processes and / or methods Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0107] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 one or more processes and / or methods Figure 1 A function specified in one or more boxes.

[0108] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 one or more processes and / or methods Figure 1 The steps for the functions specified in one or more boxes.

[0109] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0110] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A dynamic modeling method for a rotating FGM microbeam, characterized in that: The method comprises: S100, setting the geometric parameters and material parameters of the FGM micro-beam, and establishing a FGM micro-beam system that performs large-scale motion rotation based on the modified couple stress theory and taking into account the scale effect; S200, using a mixed coordinate method to describe the deformation displacement field of a large-scale rotational motion of any point on the FGM micro-beam in the FGM micro-beam system in a floating coordinate system; S300, using gridless point interpolation method and radial base point interpolation method to discretize the deformation field of FGM microbeam; S400. The second kind of Lagrange equation is used to establish the high-order rigid-flexible coupling nonlinear dynamic equation of the FGM microbeam system that performs large-scale motion and rotation, thus obtaining the dynamic simulation model of the FGM microbeam that performs large-scale motion and rotation based on the modified couple stress theory and scale effect.

2. A method for dynamic modeling of a rotating FGM micro-beam as claimed in claim 1, characterized in that: The S100 includes: S101. Geometric parameters of the FGM micro-beam: The length of the FGM microbeam is L, the width is b, and the height is h; the material characteristic length parameter is l; The material parameters elastic modulus E(y) and density ρ(y) are functions of the thickness coordinate y, and the expressions are as follows: Wherein, P(y) represents the Young's modulus E(y) and density ρ(y) of a certain point on the FGM microbeam, the subscripts c and m of P represent ceramic and metal materials respectively, Vc(y) and Vm(y) represent the volume fractions of metal and ceramic materials along the height direction of the FGM microbeam, and N represents the non-negative power index of the gradient distribution of the material along the height direction, i.e., the functional gradient index; when N=0 and N=∞, it means that the microbeam is made of pure ceramic material and pure metal material respectively; The component materials of S102 and FGM microbeams are composed of metal Al and ceramic Al2O3. The elastic modulus and density of ceramic and metal are Ec=380GPa, Em=70GPa, ρc=3800kg / m3, ρm=2700kg / m3 respectively; the Poisson's ratio of ceramic and metal is νc=νm=0.3 respectively.

3. A method for dynamic modeling of a rotating FGM micro-beam as claimed in claim 1, characterized in that: The S200 includes: S201. The expression of the radius vector r of the deformation of any point on the FGM micro-beam in the inertial coordinate system O-XYZ is: r = Θ(R + ρ0 + u); Where R represents the radius vector from the center of mass O of the central rigid body to the base point o of the floating base, ρ0 represents the radius vector about the floating base before deformation, u is the deformation displacement vector, Θ represents the normal cosine matrix of the floating base relative to the inertial coordinate system; Confirm that the expression of the deformation displacement vector u in the floating coordinate system is: Among them, w1 represents the longitudinal deformation of the FGM microbeam, w2 represents the transverse deformation of the FGM microbeam, and wc represents the second-order nonlinear coupling deformation, which is the longitudinal shortening caused by the transverse bending deformation of the flexible microbeam; The kinetic energy expression of S202 and FGM micro-beam system is: Among them, J ch represents the moment of inertia of the central rigid body around the center of rotation, represents the angular velocity of the rigid body; The shear and torsion effects of the FGM microbeam are ignored. Based on the modified couple stress theory, the expression of the deformation potential energy of the FGM microbeam at microscale is: Among them, ε and σ represent the components of the strain tensor and stress tensor, respectively, χ and m represent the components of the curvature tensor and the deviatoric component of the couple stress tensor, respectively, and l is the characteristic length parameter of the material.

4. A method for dynamic modeling of a rotating FGM micro-beam as claimed in claim 1, characterized in that: The S300 includes: S301, using two gridless point interpolation methods and radial base point interpolation methods to discretize the FGM micro-beam into several nodes, calculate and obtain the node information in the support domain of the calculation point x, and take the longitudinal and lateral displacement functions as: Among them, Φ x (x) and Φ y (x) represents the shape functions of longitudinal displacement and transverse displacement, respectively. A(t) and B(t) represent the column vectors of longitudinal deformation and transverse deformation of the node over time, respectively. S302. The second-order nonlinear coupling deformation of the longitudinal shortening caused by the lateral deformation is: Among them, H(x) is the coupling shape function, and its expression is:

5. The method for dynamic modeling of a rotating FGM micro-beam as claimed in claim 1, characterized in that: The S400 includes: Get the system's generalized coordinate column vector q=(θ,A T ,B T ) T and the generalized force column vector F q =(τ,0,0) T , where τ is the total external input torque acting on the rigid body, and the kinetic energy expression Tk of the FGM micro-beam system and the potential energy expression U of the FGM micro-beam system are substituted into the second kind of Lagrange equation: The high-order rigid-flexible coupling nonlinear dynamic equation of the FGM micro-beam system with large-scale motion and rotation considering the modified couple stress theory and scale effect is obtained as follows:

6. A dynamic modeling method for a rotating FGM microbeam, characterized in that: The Newmark method is used to solve the dynamic equations, and the deformation diagram of the FGM microbeam with large-scale rotational motion and the dynamic response of the FGM microbeam system are obtained.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the dynamic modeling method of a rotating FGM micro-beam as described in any one of claims 1-6 are implemented.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the program, the steps in the dynamic modeling method of a rotating FGM micro-beam as described in any one of claims 1-6 are implemented.

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