Design method of carbon fiber composite material based ultrasonic motor stator and motor stator

Abstract

The application discloses a design method of a carbon fiber composite material based ultrasonic motor stator and a motor stator, and belongs to the technical field of ultrasonic motor, piezoelectric drive and carbon fiber composite material laminated structure design. The stator comprises a carbon fiber composite material elastomer, a piezoelectric ceramic excitation layer, an electrode layer and a driving foot, and the carbon fiber composite material elastomer and the piezoelectric ceramic excitation layer form a CFRP / PZT sandwich type laminated structure. The design method takes the layering angle, layering thickness, layering number and layering sequence as design variables, analyzes the in-plane cross coupling through unidirectional layering stiffness transformation, and then adopts the rule layering of positive and negative angle pairing to suppress the undesired torsional coupling, so that the stator forms in-plane longitudinal-bending composite vibration and the driving foot elliptical motion trajectory under the piezoelectric excitation. The application can utilize the anisotropy of the carbon fiber composite material to regulate the vibration characteristics of the stator, thereby reducing the mass of the stator and improving the output stability of the ultrasonic motor.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic motors, and in particular to a design method and stator for an ultrasonic motor based on carbon fiber composite material. Background Technology

[0002] Ultrasonic motors utilize the inverse piezoelectric effect of piezoelectric ceramics to generate high-frequency micro-vibrations and output macroscopic motion through the friction between the stator and rotor. They have advantages such as fast response, high positioning accuracy, power-off self-locking, and no electromagnetic interference, making them suitable for high-precision linear drive, rotary drive, and precision positioning mechanisms.

[0003] The stator is the core component of an ultrasonic motor. Traditional ultrasonic motor stator elastomers are mostly made of metal materials, resulting in a large mass, which is not conducive to the miniaturization and weight reduction of ultrasonic motors. Carbon fiber composite materials have advantages such as low density, high specific stiffness, and high specific strength, and can be used to replace metal elastomers.

[0004] However, carbon fiber composites exhibit significant anisotropy, and their equivalent stiffness, coupling stiffness, vibration frequency, and electromechanical coupling characteristics are all affected by the ply angle, ply thickness, number of ply layers, and ply sequence. If carbon fiber composites are simply used as a substitute for metallic materials, it may lead to in-plane vibration shift of the stator, excessive lateral coupling, enhanced torsional coupling, or instability of the elliptical trajectory of the driving foot. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a design method and stator for a carbon fiber composite material-based ultrasonic motor stator, which solves the problems of in-plane cross coupling, torsional coupling, and unstable drive trajectory caused by the anisotropy of the carbon fiber composite material stator, thereby improving the vibration output stability of the ultrasonic motor stator while reducing the stator mass.

[0006] To achieve the above objectives, the present invention provides a design method for a carbon fiber composite material-based ultrasonic motor stator, comprising:

[0007] S1, determine the structural parameters and target vibration parameters of the ultrasonic motor stator. The structural parameters include stator length, stator width, stator thickness, piezoelectric ceramic excitation layer thickness, carbon fiber composite elastomer thickness, and drive foot position. The target vibration parameters include in-plane longitudinal vibration frequency, in-plane bending vibration frequency, frequency difference, drive foot elliptical motion trajectory, and allowable torsional displacement.

[0008] S2. Establish a coordinate system for the CFRP / PZT sandwich laminated structure, with the stator length direction as the X direction, the stator width direction as the Y direction, and the stator thickness direction as the Z direction. Define the angle between the fiber direction of the unidirectional carbon fiber layer and the X direction as the layup angle. ;

[0009] S3, establish the single-layer stiffness matrix of the unidirectional ply CFRP / PZT laminated structure, and based on the ply angle... By performing coordinate transformation, the transformation stiffness matrix of the unidirectional carbon fiber layer in the structural coordinate system is obtained;

[0010] S4. Based on the transformed stiffness matrix, calculate the in-plane tensile stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the laminated structure, and analyze the ply angle. The influence of ply thickness on in-plane cross coupling, lateral coupling displacement and resonant frequency;

[0011] S5, Based on the unidirectional ply analysis results, the unidirectional ply scheme is converted into a scheme using... Layers and A regular layering scheme consisting of layers;

[0012] S6. Modal analysis and harmonic response analysis are performed on the CFRP / PZT laminated structure after regular layup to obtain the in-plane longitudinal vibration frequency, in-plane bending vibration frequency, tangential displacement of the driving foot, normal displacement of the driving foot, elliptical motion trajectory and torsional displacement.

[0013] S7, with the goals of reducing the frequency difference between the in-plane longitudinal vibration frequency and the in-plane bending vibration frequency, stabilizing the elliptical motion trajectory of the driving foot, reducing torsional displacement, and reducing stator mass, adjusts the ply angle. Optimize the ply thickness, number of ply layers, and ply sequence;

[0014] S8. A carbon fiber composite elastomer is prepared according to the optimized layup scheme and assembled with the piezoelectric ceramic excitation layer, electrode layer and drive foot to form an ultrasonic motor stator.

[0015] Optionally, in step S3, the stiffness matrix of the unidirectional carbon fiber layer in the material's principal coordinate system is:

[0016] ;

[0017] in, , , , ; This is the elastic modulus in the fiber direction. This is the elastic modulus perpendicular to the fiber direction. It is the in-plane shear modulus. and It is Poisson's ratio.

[0018] Optionally, in step S3, the unidirectional carbon fiber layer is adjusted by the layup angle. The transformed stiffness matrix is ​​denoted as , In and Used to characterize ply angle The resulting in-plane cross-coupling; where, Stiffness components used to characterize the coupling relationship between X-direction normal strain and in-plane shear strain; Stiffness components used to characterize the coupling relationship between Y-direction normal strain and in-plane shear strain; when and When the value is not zero, the in-plane longitudinal vibration of the CFRP / PZT stacked structure generates a transverse coupled displacement.

[0019] Optional, and Determined according to the following relationship:

[0020] ;

[0021] ;

[0022] in, .

[0023] Optionally, in step S4, the in-plane tensile stiffness matrix A, coupling stiffness matrix B, and bending stiffness matrix D of the laminated structure are calculated using the following formula:

[0024] ;

[0025] ;

[0026] ;

[0027] in, For the first The equivalent stiffness components of the unidirectional carbon fiber layer or piezoelectric ceramic layer in the structural coordinate system. and The first The coordinates of the upper and lower surfaces of the layer in the thickness direction.

[0028] Optionally, in step S4, the ratio of lateral coupled displacement to longitudinal displacement is used to evaluate the vibration displacement caused by unidirectional plying, which is expressed as:

[0029] ;

[0030] in, The vibration offset ratio, This represents the longitudinal displacement of the stator. This refers to the stator's lateral coupling displacement.

[0031] Optionally, in step S5, the regular layup scheme includes , , or One of them; among them, Indicates will layer / The layer is a layup unit that is repeated r times along the thickness direction, where r is an integer not less than 2.

[0032] Optionally, for regular ply structures with paired positive and negative angles, the coupled stiffness components B16 and B26 in the coupled stiffness matrix B, which characterize the coupling relationship between mid-surface strain and torsional curvature in the X direction and the coupling stiffness components B26, which characterize the coupling relationship between mid-surface strain and torsional curvature in the Y direction, are evaluated according to the following relationship:

[0033] ;

[0034] in, This represents the total thickness of the carbon fiber composite elastomer. The number of times the positive and negative angle layup units are repeated.

[0035] Optionally, when the torsional displacement of the regular ply structure exceeds a set threshold, the number of repetitions of the positive and negative angle ply units can be increased. Reduce single-layer thickness, adjust Layers and Layer arrangement order or reducing ply angle One or more of these methods can reduce the torsional coupling caused by B16 and B26.

[0036] On the other hand, the present invention also provides a motor stator obtained by the design method described in any of the technical solutions, comprising: a carbon fiber composite elastomer; a piezoelectric ceramic excitation layer disposed on one or both sides of the carbon fiber composite elastomer; an electrode layer disposed on the piezoelectric ceramic excitation layer; and a drive foot disposed on the carbon fiber composite elastomer; wherein the carbon fiber composite elastomer is formed by laminating and curing multiple unidirectional carbon fiber layers, and each unidirectional carbon fiber layer is laid according to an optimized layup angle θ, layup thickness, number of layup layers and layup sequence, so that the CFRP / PZT sandwich laminate structure generates in-plane longitudinal vibration and in-plane bending vibration under piezoelectric excitation, and forms an elliptical motion trajectory at the drive foot.

[0037] The advantages of this invention over the prior art are:

[0038] First, the present invention will lay up the ply angle. The thickness, number of layers, and sequence of the layup are key design variables for the stator of the ultrasonic motor, rather than simply replacing the metal elastomer with carbon fiber composites.

[0039] Second, this invention utilizes stiffness components to characterize the coupling relationship between X-direction normal strain and in-plane shear strain. and stiffness components used to characterize the coupling relationship between Y-direction normal strain and in-plane shear strain Characterizing in-plane cross-coupling caused by unidirectional ply layup, and using vibration offset ratio. Evaluating the effect of ply angle on lateral coupling displacement provides a clear mechanical basis for ply design.

[0040] Third, this invention through Regular plying reduces the torsional coupling caused by the coupling stiffness component B16, which characterizes the coupling relationship between mid-surface strain and torsional curvature in the X direction, and the coupling stiffness component B26, which characterizes the coupling relationship between mid-surface strain and torsional curvature in the Y direction, thereby improving the stability of the driving foot elliptical motion trajectory.

[0041] Fourth, this invention can improve the in-plane longitudinal-bending composite vibration stability of CFRP / PZT laminated stators while reducing the stator mass of ultrasonic motors, making it suitable for lightweight, high-precision ultrasonic motors. Attached Figure Description

[0042] Figure 1 and Figure 2 This is a schematic diagram of the CFRP / PZT sandwich laminated structure and ply angle definition provided in an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the motor stator structure provided in an embodiment of the present invention;

[0044] Figure 4 This is a flowchart illustrating the design method of a carbon fiber composite material-based ultrasonic motor stator provided in an embodiment of the present invention.

[0045] In the figure, 1 is a carbon fiber composite elastomer; 2 is a piezoelectric ceramic excitation layer; 3 is a unidirectional carbon fiber layer; 4 is a CFRP / PZT sandwich laminate structure; 5 is a drive foot; 6 is an electrode layer; and 7 is a rotor. Detailed Implementation

[0046] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0047] The design method for the carbon fiber composite-based ultrasonic motor stator provided in this embodiment is based on a CFRP / PZT sandwich laminate structure. To facilitate the explanation of the design principle of this invention, the following describes the method in conjunction with... Figure 1 and Figure 2 This section provides a detailed introduction to CFRP / PZT sandwich laminated structures and the definition of ply angles. For example... Figure 1 and Figure 2As shown, the CFRP / PZT sandwich laminate structure 4 includes a carbon fiber composite elastomer 1 and a piezoelectric ceramic excitation layer 2. The carbon fiber composite elastomer 1 is located between two piezoelectric ceramic excitation layers 2, forming a sandwich laminate structure.

[0048] In this embodiment, the carbon fiber composite elastomer 1 is formed by laminating and curing several unidirectional carbon fiber layers 3. A coordinate system for the laminated structure is established, defining the stator length direction as the X direction, the stator width direction as the Y direction, and the thickness direction as the Z direction. The fiber direction of the unidirectional carbon fiber layer 3 forms a layup angle relative to the stator length direction. .

[0049] In this embodiment, for the unidirectional carbon fiber layer 3, when the layup angle... When changing, and Consequently, the degree of in-plane cross-coupling of the CFRP / PZT sandwich laminated structure 4 also changes. This is determined by calculating the vibration offset ratio. It can determine the ply angle The effect of longitudinal vibration offset within the surface.

[0050] In this embodiment, the regular layup sequence can be adopted. , , or By pairing positive and negative angles, some in-plane cross-coupling can be mutually canceled out, and the torsional displacement caused by B16 and B26 can be reduced.

[0051] Reference Figure 3 This embodiment provides a motor stator, including a CFRP / PZT sandwich laminated structure 4, a drive foot 5, and an electrode layer 6. The electrode layer 6 is attached to the piezoelectric ceramic excitation layer 2 and is used to apply AC excitation to it. Further, the electrode layer includes a group of electrodes A and a group of electrodes B, which are used to excite the drive foot to form elliptical motion trajectories in opposite directions, thereby realizing the forward and reverse motion of the rotor. The front electrode of the piezoelectric ceramic excitation layer 2 is divided into four electrode regions, where two diagonally arranged electrode regions are connected to form a group of electrodes A, and the other two diagonally arranged electrode regions are connected to form a group of electrodes B. The back electrode of the piezoelectric ceramic excitation layer serves as a ground electrode.

[0052] In this embodiment, the drive foot 5 is disposed at the end or side of the CFRP / PZT sandwich laminate structure 4 and is in frictional contact with the rotor 7.

[0053] In this embodiment, under AC excitation, the CFRP / PZT sandwich laminated structure 4 generates in-plane longitudinal vibration and in-plane bending vibration. The two vibrations superimpose at the driving foot 5 to form an elliptical motion trajectory of the driving foot. This elliptical motion trajectory drives the rotor 7 to rotate through friction.

[0054] Reference Figure 4 This embodiment also provides a design method for a carbon fiber composite material-based ultrasonic motor stator, including the following steps:

[0055] S1, determine the structural parameters and target vibration parameters of the ultrasonic motor stator. The structural parameters include stator length, stator width, stator thickness, piezoelectric ceramic excitation layer thickness, carbon fiber composite elastomer thickness, and drive foot position. The target vibration parameters include in-plane longitudinal vibration frequency, in-plane bending vibration frequency, frequency difference, drive foot elliptical motion trajectory, and allowable torsional displacement.

[0056] S2. Establish a coordinate system for the CFRP / PZT sandwich laminated structure, with the stator length direction as the X direction, the stator width direction as the Y direction, and the stator thickness direction as the Z direction. Define the angle between the fiber direction of the unidirectional carbon fiber layer and the X direction as the layup angle. .

[0057] S3, establish the single-layer stiffness matrix of the unidirectional ply CFRP / PZT laminated structure, and based on the ply angle... By performing coordinate transformation, the transformation stiffness matrix of the unidirectional carbon fiber layer in the structural coordinate system is obtained.

[0058] Specifically, the stiffness matrix of the unidirectional carbon fiber layer in the material's principal coordinate system is:

[0059] ;

[0060] in, , , , ; This is the elastic modulus in the fiber direction. This is the elastic modulus perpendicular to the fiber direction. It is the in-plane shear modulus. and It is Poisson's ratio.

[0061] In this embodiment, when the unidirectional carbon fiber layer deflects the layup angle relative to the X direction... When, defined: .

[0062] The in-plane cross-coupling term in the single-layer transform stiffness matrix is:

[0063] ;

[0064] ;

[0065] in, and Used to characterize in-plane cross-coupling caused by fiber orientation deflection in unidirectional layups. When and When the value is not zero, the CFRP / PZT laminated structure will generate transverse coupling displacement during in-plane longitudinal vibration.

[0066] S4. Based on the transformed stiffness matrix, calculate the in-plane tensile stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the laminated structure, and analyze the ply angle. The influence of ply thickness on in-plane cross coupling, lateral coupling displacement and resonant frequency.

[0067] Specifically, for the CFPR / PZT sandwich laminated structure, calculate its in-plane tensile stiffness matrix A, coupling stiffness matrix B, and bending stiffness matrix D:

[0068] ;

[0069] ;

[0070] ;

[0071] in, For the first The equivalent stiffness components of the unidirectional carbon fiber layer or piezoelectric ceramic layer in the structural coordinate system. and The first The coordinates of the upper and lower surfaces of the layer in the thickness direction.

[0072] The force-deformation relationship of a laminated structure is expressed as follows:

[0073] ;

[0074] Where N is the in-plane force matrix and M is the bending moment matrix. The mid-surface strain matrix, Here is the curvature matrix.

[0075] Furthermore, the vibration offset ratio is used. Evaluate the degree of lateral coupling caused by unidirectional layup:

[0076] ;

[0077] in, This represents the longitudinal displacement of the stator. This refers to the stator's lateral coupling displacement.

[0078] S5, Based on the unidirectional ply analysis results, the unidirectional ply scheme is converted into a scheme using... Layers and A regular layering scheme consisting of layers.

[0079] Specifically, based on the results of unidirectional ply analysis, candidate ply angles are determined. And candidate ply thickness. Then, the unidirectional ply structure is converted into a regular ply structure. Layered structure. The regular layered structure includes... , , or One of them. Among them, Indicates that " layer / The "layer" layup unit is repeated r times along the thickness direction, where r is an integer not less than 2.

[0080] For a regular ply structure with positive and negative angle pairings, the coupling stiffness components B16 and B26 in the coupling stiffness matrix B, which characterize the coupling relationship between mid-surface strain and torsional curvature in the X direction and the coupling stiffness components B26, which characterize the coupling relationship between mid-surface strain and torsional curvature in the Y direction, are evaluated according to the following relationship:

[0081] ;

[0082] in, This represents the total thickness of the carbon fiber composite elastomer. The number of repetitions of positive and negative angle ply units. for The stiffness component used to characterize the coupling relationship between X-direction normal strain and in-plane shear strain. for The stiffness component is used to characterize the coupling relationship between the Y-direction normal strain and the in-plane shear strain.

[0083] S6. Modal analysis and harmonic response analysis are performed on the CFRP / PZT laminated structure after regular layup to obtain the in-plane longitudinal vibration frequency, in-plane bending vibration frequency, tangential displacement of the driving foot, normal displacement of the driving foot, elliptical motion trajectory and torsional displacement.

[0084] S7, with the goals of reducing the frequency difference between the in-plane longitudinal vibration frequency and the in-plane bending vibration frequency, stabilizing the elliptical motion trajectory of the driving foot, reducing torsional displacement, and reducing stator mass, adjusts the ply angle. The ply thickness, number of ply layers, and ply sequence were optimized.

[0085] S8. A carbon fiber composite elastomer is prepared according to the optimized layup scheme and assembled with the piezoelectric ceramic excitation layer, electrode layer and drive foot to form an ultrasonic motor stator.

[0086] The present invention provides a design method and a driving stator for a carbon fiber composite ultrasonic motor stator, which can be achieved through carbon fiber prepreg cutting and laying, lamination and curing, piezoelectric ceramic bonding, electrode processing, and precision assembly. This solution utilizes the anisotropy of carbon fiber composite materials to control the in-plane vibration characteristics of the CFRP / PZT ultrasonic motor stator, improving the stability of the driven elliptical motion trajectory while achieving lightweight design. It is suitable for applications in aerospace, medical equipment, precision positioning, and precision drive mechanisms in special environments.

[0087] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A design method for a carbon fiber composite material-based ultrasonic motor stator, characterized in that, include: S1, determine the structural parameters and target vibration parameters of the ultrasonic motor stator. The structural parameters include stator length, stator width, stator thickness, piezoelectric ceramic excitation layer thickness, carbon fiber composite elastomer thickness, and drive foot position. The target vibration parameters include in-plane longitudinal vibration frequency, in-plane bending vibration frequency, frequency difference, drive foot elliptical motion trajectory, and allowable torsional displacement. S2. Establish a coordinate system for the CFRP / PZT sandwich laminated structure, with the stator length direction as the X direction, the stator width direction as the Y direction, and the stator thickness direction as the Z direction. Define the angle between the fiber direction of the unidirectional carbon fiber layer and the X direction as the layup angle. ; S3, establish the single-layer stiffness matrix of the unidirectional ply CFRP / PZT laminated structure, and based on the ply angle... By performing coordinate transformation, the transformation stiffness matrix of the unidirectional carbon fiber layer in the structural coordinate system is obtained; S4. Based on the transformed stiffness matrix, calculate the in-plane tensile stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the laminated structure, and analyze the ply angle. The influence of ply thickness on in-plane cross coupling, lateral coupling displacement and resonant frequency; S5, Based on the unidirectional ply analysis results, the unidirectional ply scheme is converted into a scheme using... Layers and A regular layering scheme consisting of layers; S6. Modal analysis and harmonic response analysis are performed on the CFRP / PZT laminated structure after regular layup to obtain the in-plane longitudinal vibration frequency, in-plane bending vibration frequency, tangential displacement of the driving foot, normal displacement of the driving foot, elliptical motion trajectory and torsional displacement. S7, with the goals of reducing the frequency difference between in-plane longitudinal vibration frequency and in-plane bending vibration frequency, stabilizing the elliptical motion trajectory of the driving foot, reducing torsional displacement, and reducing stator mass, adjusts the ply angle. Optimize the ply thickness, number of ply layers, and ply sequence; S8. A carbon fiber composite elastomer is prepared according to the optimized layup scheme and assembled with the piezoelectric ceramic excitation layer, electrode layer and drive foot to form an ultrasonic motor stator.

2. The design method according to claim 1, characterized in that, In step S3, the stiffness matrix of the unidirectional carbon fiber layer in the principal coordinate system of the material is: ； in, , , , ; This is the elastic modulus in the fiber direction. This is the elastic modulus perpendicular to the fiber direction. It is the in-plane shear modulus. and It is Poisson's ratio.

3. The design method according to claim 2, characterized in that: In step S3, the unidirectional carbon fiber layer is adjusted by the layup angle. The transformed stiffness matrix is ​​denoted as , In and Used to characterize ply angle The resulting in-plane cross-coupling; where, Stiffness components used to characterize the coupling relationship between X-direction normal strain and in-plane shear strain; Stiffness components used to characterize the coupling relationship between Y-direction normal strain and in-plane shear strain; when and When the value is not zero, the in-plane longitudinal vibration of the CFRP / PZT stacked structure generates a transverse coupled displacement.

4. The design method according to claim 3, characterized in that: and Determined according to the following relationship: ； ； in, .

5. The design method according to claim 1, characterized in that, In step S4, the in-plane tensile stiffness matrix A, coupling stiffness matrix B, and bending stiffness matrix D of the laminated structure are calculated using the following formula: ； ； ； in, For the first The equivalent stiffness components of the unidirectional carbon fiber layer or piezoelectric ceramic layer in the structural coordinate system. and The first The coordinates of the upper and lower surfaces of the layer in the thickness direction.

6. The design method according to claim 1, characterized in that, In step S4, the vibration displacement caused by unidirectional ply layup is evaluated using the ratio of lateral coupled displacement to longitudinal displacement, which is expressed as: ； in, The vibration offset ratio, This represents the longitudinal displacement of the stator. This refers to the stator's lateral coupling displacement.

7. The design method according to claim 1, characterized in that, In step S5, the regular layup scheme includes , , or One of them; among them, Indicates will layer / The layer is a layup unit that is repeated r times along the thickness direction, where r is an integer not less than 2.

8. The design method according to claim 1, characterized in that: For regular ply structures with positive and negative angle pairings, the coupled stiffness components B16 and B26 in the coupled stiffness matrix B, which characterize the coupling relationship between mid-surface strain and torsional curvature in the X direction and the coupling stiffness components B26, which characterize the coupling relationship between mid-surface strain and torsional curvature in the Y direction, are evaluated according to the following relationship: ； in, This represents the total thickness of the carbon fiber composite elastomer. The number of times the positive and negative angle layup units are repeated.

9. The design method according to claim 8, characterized in that, When the torsional displacement of a regular ply structure exceeds a set threshold, the number of repetitions of the positive and negative angle ply units is increased. Reduce single-layer thickness, adjust Layers and Layer arrangement order or reducing ply angle One or more of these methods can reduce the torsional coupling caused by B16 and B26.

10. A motor stator obtained using the design method according to any one of claims 1 to 9, characterized in that, include: Carbon fiber composite elastomers; Piezoelectric ceramic excitation layer disposed on one or both sides of the carbon fiber composite elastomer; Electrode layer disposed on the piezoelectric ceramic excitation layer; And a driving foot disposed on the carbon fiber composite elastomer; The carbon fiber composite elastomer is formed by laminating and curing multiple unidirectional carbon fiber layers. Each unidirectional carbon fiber layer is laid according to the optimized layup angle θ, layup thickness, number of layup layers and layup sequence, so that the CFRP / PZT sandwich laminate structure generates in-plane longitudinal vibration and in-plane bending vibration under piezoelectric excitation, and forms an elliptical motion trajectory at the driving foot.

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