CN110376452B - Piezoelectric ceramic actuator electrical noise index determination method based on coupled electromechanical analysis - Google Patents
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Abstract
The invention provides a method for determining an electrical noise index of a piezoelectric ceramic actuator based on coupled electromechanical analysis, which comprises the following steps: s1) simplifying the piezoelectric ceramic actuator to obtain the mechanical structure type of the piezoelectric ceramic actuator, and calculating the mechanical impedance of the mechanical structure type; s2) establishing a kinematic model and a dynamic model of the mechanical structure, and obtaining an open-loop transfer function of the mechanical structure; s3) establishing a coupling electromechanical model of the piezoelectric ceramic and the mechanical structure by using the mechanical impedance obtained in S1), and obtaining a coupling electromechanical admittance of the piezoelectric ceramic actuator; s4) calculating the energy flow of the electric noise in the piezoelectric ceramic actuator by using the open-loop transfer function obtained in S2) and the coupling electromechanical admittance obtained in S3), and determining the electric noise index of the input signal of the piezoelectric ceramic actuator. The method fundamentally reveals how the electric noise responds in the piezoelectric ceramic actuator, reflects the influence of the electric noise on the system precision, and provides a theoretical basis for the design of the piezoelectric ceramic actuator.
Description
Technical Field
The invention belongs to the technical field of electromechanical integration, and particularly relates to a piezoelectric ceramic actuator electrical noise index determination method based on coupled electromechanical analysis.
Background
Piezoelectric ceramics are widely applied to various fields at present due to some excellent characteristics of the piezoelectric ceramics, and particularly in a micro-nano system, a piezoelectric ceramic actuator utilizes the inverse piezoelectric effect of the piezoelectric ceramics to generate force and displacement. When a voltage is applied to the piezoelectric ceramic, a responsive driving force is generated, which is applied to the mechanical structure to deform it, thereby creating a displacement. The piezoelectric ceramic actuator is widely applied to various micro-nano positioning technologies and driving systems due to the advantages of high positioning precision, large driving force, high response speed, high rigidity, no recoil, no friction and the like.
When the piezoelectric ceramic actuator is used, the piezoelectric ceramic actuator can be driven only by adopting a high-power high-voltage direct-current driving power supply, and due to the application occasion of the piezoelectric ceramic actuator, the displacement precision, the response speed and the frequency response characteristic of the piezoelectric ceramic actuator are directly influenced by the driving power supply; the output voltage signal of the piezoelectric ceramic actuator is required to have continuously adjustable high-voltage direct current voltage, enough transient driving current and enough signal-to-noise ratio so as to ensure that the output displacement precision of the piezoelectric ceramic actuator can meet the application occasions. Therefore, the response of the electrical noise to the piezoelectric ceramic actuator system must be considered at an early stage of the design process of the actuator system, because once the circuit device selection, the structural design and the like are completed, there is little way to reduce the influence of the intrinsic electrical noise on the system.
At present, the mainstream piezoelectric ceramic driving power supply design does not consider the problems of response of which electrical noise indexes to a piezoelectric ceramic actuator system and determination of the electrical noise indexes of the piezoelectric ceramic actuator, and even if the electrical noise indexes are determined, the method for determining the electrical noise indexes by adopting the voltage amplitude in the traditional sense is low in precision and small in reference sense, and the method brings great manpower and material burden to the driving system design work. Therefore, according to the requirements of the application occasions of the piezoelectric ceramic actuator, the electrical noise index of the piezoelectric ceramic actuator is determined and given in advance, then necessary theoretical basis is provided for the design of the piezoelectric ceramic driving power supply according to the index, and time-consuming and labor-consuming redesign work can be reduced.
Disclosure of Invention
The invention aims to solve the defects that which electrical noise indexes respond to a piezoelectric ceramic actuator system and how to determine the electrical noise indexes of the piezoelectric ceramic actuator are not considered in the design work of the conventional piezoelectric ceramic driving power supply, and provides a piezoelectric ceramic actuator electrical noise index determining method based on coupling electromechanical analysis, which obtains the signal-to-noise ratio index of the system and provides a necessary theoretical basis for the design of the piezoelectric ceramic driving power supply.
In order to achieve the purpose, the technical solution provided by the invention is as follows:
the piezoelectric ceramic actuator electrical noise index determination method based on coupled electromechanical analysis is characterized by comprising the following steps of:
s1) simplifying the piezoelectric ceramic actuator, obtaining the mechanical structure type of the piezoelectric ceramic actuator, and calculating the mechanical impedance of the mechanical structure type;
s2) establishing a kinematic model and a dynamic model of the mechanical structure, and obtaining an open-loop transfer function of the mechanical structure;
s3) establishing a coupling electromechanical model of the piezoelectric ceramic and the mechanical structure by using the mechanical impedance obtained in S1), and obtaining a coupling electromechanical admittance of the piezoelectric ceramic actuator;
s4) calculating the energy flow of the electric noise in the piezoelectric ceramic actuator by utilizing the open-loop transfer function obtained in S2) and the coupling electromechanical admittance obtained in S3), and determining the electric noise index of the input signal of the piezoelectric ceramic actuator; the method comprises the following specific steps:
s4.1) calculating basic parameters m, c, k of the mechanical structure through a system identification test and combining the open-loop transfer function obtained in S2)s；
S4.2) voltage and current pass through the coupling electromechanical admittance of the piezoelectric ceramic actuator obtained in the S3), and three types of electric power of apparent power, dissipation power and reactive power are obtained;
s4.3) regarding the electrical noise as a random vibration load, and calculating to obtain the relationship between the amplitude and the frequency of the apparent power of the piezoelectric ceramic actuator along with the voltage of the electrical noise. I.e., the response of the electrical noise load in the piezoceramic actuator system, and how the electrical noise power flows in the system.
Further, the specific steps of S1) are as follows:
s1.1) simplifying a piezoelectric ceramic actuator into a one-degree-of-freedom spring-mass-damping system; certainly, the piezoelectric ceramic actuator can be simplified into other mechanical structure types, but the piezoelectric ceramic actuator can be regarded as a mechanical structure driven by piezoelectric ceramic and used for single-degree-of-freedom displacement extension, so that the piezoelectric ceramic actuator is simplified into a one-degree-of-freedom spring-mass-damping system, the system is closer to a real piezoelectric ceramic actuator, the degree of reality is higher, subsequent calculation is simpler and more convenient, and the calculation amount is greatly reduced;
s1.2) calculating the mechanical impedance of the one-degree-of-freedom spring-mass-damping system by using the definition of the mechanical impedance:
wherein Z is the mechanical impedance of the spring-mass-damping system; i is a complex number defined as (-1)1/2(ii) a c is the system damping coefficient; m is mass; ω is the frequency of the electrical noise load, ωnIs the natural frequency of the system, whose value can be expressed as
Wherein k issIs the spring rate.
Further, in S1.2), the interaction between the piezoelectric ceramic and the mechanical structure is controlled by the dynamic output characteristics of the piezoelectric ceramic and the mechanical structure, and the specific relationship is as follows:
where F is the force exerted by the piezoelectric ceramic on the mechanical structure, Z is the mechanical impedance of the spring-mass-damping system, and x is the displacement in the Y direction.
Further, the specific steps of S2) are as follows:
s2.1) establishing a kinematic model of a mechanical structure
Calculating an object motion differential equation by using a single-degree-of-freedom damped vibration system mechanical model:
the single-degree-of-freedom damped vibration system comprises a spring, a damper and an object mass; establishing a coordinate system by taking the object balance position 0 as an origin and taking the positive direction of the object motion as the positive direction of an X axis;
s2.2) establishing a dynamic model of the mechanical structure
Establishing a mechanical structure dynamic model by utilizing Newton's theorem:
wherein F (t) is the driving force provided by the piezoelectric ceramics, F1(t) is the damping force of the damper, F2(t) is the spring force of the spring;
s2.3) obtaining an open-loop transfer function of the spring-mass-damping system:
establishing a differential equation of a system through a kinematic model and a dynamic model of the mechanical structure:
then, the above formula is subjected to pull type transformation to obtain an open loop transfer function of the spring-mass-damping system:
wherein s represents a complex frequency domain after the pull-type transformation; k is a radical ofsIs the spring rate.
The order of obtaining the above S2.1) and S2.2) can be exchanged according to actual conditions.
Further, the specific steps of S3) are as follows:
s3.1) piezoceramic material constitutive relation given by IEEE (Institute of Electrical and Electronics Engineers), according to which an electric field is applied in the Z direction and expands and contracts in the Y direction in a piezoceramic actuator, stress and piezoceramic constitutive relation is obtained:
wherein D is3Is a 3 x 1 matrix representing the potential shift (C/m)2)；S2Is a 6 x 1 matrix representing strain; e is a 3 × 1 matrix representing the electric field strength (V/m); sigma2Is a 6 x 1 matrix representing stress (N/m)2)；
Is a 3X 3 matrix representing the piezoelectric constant (F/m), d32Is a 3 x 6 matrix representing the piezoelectric coefficient (C/N);
is a 6 x 6 matrix representing the modulus of elasticity (m)2/N)；
S3.2) decomposing the displacement of the piezoelectric ceramic in the Y direction into a time domain and a space domain, and solving to obtain a vibration motion equation of the piezoelectric ceramic in the Y direction as follows:
wherein x is the displacement in the Y direction; ρ is the density of the piezoelectric ceramic;
is the complex modulus of the piezoelectric ceramic at zero electric field;
is the complex modulus of the piezoelectric ceramics; η is the mechanical loss factor of the piezoelectric ceramic;
s3.3) calculating the mechanical impedance of the piezoelectric ceramics by using the short-circuit mechanical impedance definition of the piezoelectric ceramics as follows:
wherein, KAIs formed by
Calculated static state of piezoelectric ceramicRigidity,. lAIs the length of the piezoelectric ceramic; k is derived from
Calculating to obtain; ω is the electrical noise loading frequency;
the short-circuit mechanical impedance of the piezoelectric ceramic is defined as the ratio of external excitation to speed response;
s3.4) calculating current by utilizing the piezoelectric ceramic output potential displacement field, so that the coupling electromechanical admittance of the piezoelectric ceramic actuator is obtained by the ratio of the current to the voltage as follows:
wherein, wA、hAThe width and thickness of the piezoelectric ceramic are respectively.
Further, in S4.2), the apparent power represents the power supplied to the piezoelectric ceramic by the external excitation, and is defined as:
the dissipated power representation is converted into other forms of energy, defined as:
the reactive power represents the energy that remains flowing in the system and is not consumed, defined as:
in the above formulas, the same parameters have the same meaning, and are not described again.
The invention has the advantages that:
1. the invention obtains the energy flow of the electric noise in the electromechanical system by adopting a coupled electromechanical analysis method, fundamentally discloses how the electric noise responds in the piezoelectric ceramic actuator system, has higher precision compared with the traditional method for determining the electric noise index by adopting the voltage amplitude, can better reflect the influence of the electric noise on the system precision, and provides a powerful theoretical basis for the design of the piezoelectric ceramic actuator. According to the method, the energy loss of the system is disclosed while the electric noise index of the piezoelectric ceramic actuator is analyzed by adopting an energy flow method, and a theoretical basis is provided for improving the output displacement precision of the system. Therefore, determining and providing an index of system electrical noise in advance according to the requirements of the application of the piezoceramic actuator, and then designing a circuit according to the index can reduce the expensive redesign cost.
2. The method is suitable for occasions such as a single-degree-of-freedom high-precision displacement structure and the like based on piezoelectric ceramic driving; the method not only fundamentally reveals how the electrical noise responds in the piezoelectric ceramic actuator system, but also can determine the electrical noise index of the piezoelectric ceramic actuator with higher precision.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a simplified model schematic of a piezoceramic actuator system;
FIG. 3 is a graph of the electromechanical admittance of a piezo-ceramic actuator coupled to an excitation frequency;
FIG. 4 is a graph of apparent power versus excitation voltage and frequency for a coupled electromechanical system.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
referring to fig. 1, the specific steps of the present invention are described as follows:
s1) simplifying the piezoelectric ceramic actuator, obtaining the mechanical structure type of the piezoelectric ceramic actuator, and calculating the mechanical impedance of the mechanical structure of the type
S1.1) simplifying the piezoelectric ceramic actuator into a one-degree-of-freedom spring-mass-damping system driven by piezoelectric ceramic, wherein the simplified mechanical structure model of the piezoelectric ceramic actuator is shown in figure 2.
S1.2) the mechanical impedance of the spring-mass-damping system is Z, the interaction between the piezoelectric ceramic and the mechanical structure is controlled by the dynamic output characteristic of the piezoelectric ceramic and the dynamic output characteristic of the mechanical structure, and the specific relation is as follows:
where F is the force exerted by the piezoelectric ceramic on the mechanical structure, Z is the mechanical impedance of the spring-mass-damping system, and x is the displacement in the Y direction.
With the definition of the mechanical impedance, the mechanical impedance of the spring-mass-damping system is calculated:
wherein Z is the mechanical impedance of the spring-mass-damping system; i is a complex number defined as (-1)1/2(ii) a c is the system damping coefficient; m is mass; ω is the frequency of the electrical noise load, ωnIs the natural frequency of the system, whose value can be expressed as
Wherein k issIs the spring rate.
S2) establishing a kinematic model and a dynamic model of the mechanical structure and obtaining an open-loop transfer function of the mechanical structure
S2.1) establishing a kinematic model of a mechanical structure
Calculating an object motion differential equation by using a single-degree-of-freedom damped vibration system mechanical model:
the single-degree-of-freedom damped vibration system comprises a spring, a damper and an object mass; and establishing a coordinate system by taking the object balance position 0 as an origin and taking the positive direction of the object motion as the positive direction of the X axis.
S2.2) establishing a dynamic model of the mechanical structure
Establishing a mechanical structure dynamic model by utilizing Newton's theorem:
wherein F (t) is the driving force provided by the piezoelectric ceramics, F1(t) is the damping force of the damper, F2(t) is the spring force of the spring;
s2.3) obtaining an open-loop transfer function of the spring-mass-damping system:
establishing a differential equation of a system through a kinematic model and a dynamic model of the mechanical structure:
then, the above formula is subjected to pull type transformation to obtain an open loop transfer function of the spring-mass-damping system:
wherein s represents a complex frequency domain after the pull-type transformation; k is a radical ofsIs the spring rate.
S3) establishing a coupling electromechanical model of the piezoelectric ceramics and the mechanical structure by using the mechanical impedance obtained in S1), and obtaining the coupling electromechanical admittance of the piezoelectric ceramic actuator
S3.1) obtaining the constitutive relation of stress and piezoelectric ceramic according to the constitutive relation of the piezoelectric ceramic given by IEEE by applying an electric field in the piezoelectric ceramic actuator in the Z direction and stretching and contracting in the Y direction:
wherein D is3Is a 3 x 1 matrix representing the potential shift (C/m)2)；S2Is a 6 x 1 matrix representing strain; e is a 3 × 1 matrix representing the electric field strength (V/m); sigma2Is a 6 x 1 matrix representing stress (N/m)2)；
Is a 3X 3 matrix representing the piezoelectric constant (F/m), d32Is a 3 x 6 matrix representing the piezoelectric coefficient (C/N);
is a 6 x 6 matrix representing the modulus of elasticity (m)2/N)；
S3.2) decomposing the displacement of the piezoelectric ceramic in the Y direction into a time domain and a space domain, and solving to obtain a vibration motion equation of the piezoelectric ceramic in the Y direction as follows:
wherein x is the displacement in the Y direction; ρ is the density of the piezoelectric ceramic;
is the complex modulus of the piezoelectric ceramic at zero electric field;
is the complex modulus of the piezoelectric ceramics; η is the mechanical loss factor of the piezoelectric ceramic;
s3.3) calculating the mechanical impedance of the piezoelectric ceramics by using the short-circuit mechanical impedance definition of the piezoelectric ceramics as follows:
wherein, KAIs formed by
Calculated static rigidity of piezoelectric ceramicAIs the length of the piezoelectric ceramic; k is derived from
Calculating to obtain; ω is the electrical noise loading frequency;
the short-circuit mechanical impedance of the piezoelectric ceramic is defined as the ratio of external excitation to speed response;
s3.4) calculating current by utilizing the piezoelectric ceramic output potential displacement field, so that the coupling electromechanical admittance of the piezoelectric ceramic actuator is obtained by the ratio of the current to the voltage as follows:
wherein, wA、hAThe width and thickness of the piezoelectric ceramic are respectively.
S4) utilizing the open-loop transfer function obtained in S2) and the coupling electromechanical admittance obtained in S3), calculating the energy flow of the electric noise in the piezoelectric ceramic actuator, and determining the electric noise index of the input signal of the piezoelectric ceramic actuator
S4.1) calculating basic parameters m, c, k of the one-degree-of-freedom spring-mass-damping system through a system identification test and combining the open-loop transfer function obtained in S2)s；
S4.2) voltage and current pass through the coupling electromechanical admittance of the piezoelectric ceramic actuator obtained in the S3), and three types of electric power of apparent power, dissipation power and reactive power are obtained;
apparent power represents the power supplied to the piezoelectric ceramic by an external stimulus, defined as:
the dissipated power represents the conversion to other forms of energy, defined as:
reactive power, which represents the energy that remains flowing in the system and is not consumed, is defined as:
s4.3) regarding the electrical noise as a random vibration load, and calculating to obtain the relationship between the amplitude and the frequency of the apparent power of the piezoelectric ceramic actuator along with the voltage of the electrical noise. I.e., the response of the electrical noise load in the piezoceramic actuator system, and how the electrical noise power flows in the system.
For example, the basic parameter table of the piezoelectric ceramic actuator used in the present invention is shown in table 1:
the basic parameters in table 1 are known parameters of the material used for the piezoceramic actuator, and the basic parameters m, c, k of the one-degree-of-freedom spring-mass-damping system are calculated by passing a system identification test and combining the open loop transfer function obtained in S2)s；
The change relation of coupling electromechanical admittance and apparent power of the piezoelectric ceramic actuator under certain voltage amplitude and frequency range is calculated and simulated as shown in fig. 3 and fig. 4, the energy change relation of random electric noise excitation in the piezoelectric ceramic actuator system is obtained by the simulation means, and how much response of electric noise load in the system can be intuitively obtained from fig. 4 through the change relation, and how the electric noise power is transmitted in the system can be obtained.
For the requirement of the piezoelectric ceramic actuator output displacement resolution ratio expected by the system, the equivalent electrical noise voltage amplitude can be obtained through the system piezoelectric coefficient, and the maximum power value corresponding to the random electrical noise in the electrical noise frequency band can be obtained through the result in fig. 4.
So far, the electrical noise index of the piezoelectric ceramic actuator under a certain driving voltage can be obtained, and the signal-to-noise ratio index of a system calculated by only using the voltage is far from the system index, because a considerable part of loss of electrical noise voltage energy in the transfer process is not taken into consideration.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
Claims (5)
1. The piezoelectric ceramic actuator electrical noise index determination method based on coupled electromechanical analysis is characterized by comprising the following steps of:
s1) simplifying the piezoelectric ceramic actuator, obtaining the mechanical structure type of the piezoelectric ceramic actuator, and calculating the mechanical impedance of the mechanical structure type;
s2) establishing a kinematic model and a dynamic model of the mechanical structure, and obtaining an open-loop transfer function of the mechanical structure;
s3) establishing a coupling electromechanical model of the piezoelectric ceramic and the mechanical structure by using the mechanical impedance obtained in S1), and obtaining a coupling electromechanical admittance of the piezoelectric ceramic actuator;
s4) calculating the energy flow of the electric noise in the piezoelectric ceramic actuator by using the open-loop transfer function obtained in S2) and the coupling electromechanical admittance obtained in S3), and determining the electric noise index of the input signal of the piezoelectric ceramic actuator; the method comprises the following specific steps:
s4.1) calculating basic parameters m, c, k of the mechanical structure through a system identification test and combining the open-loop transfer function obtained in S2)s(ii) a M is mass, c is system damping coefficient, ksIs the spring force coefficient;
s4.2) voltage and current pass through the coupling electromechanical admittance of the piezoelectric ceramic actuator obtained in the S3), and three types of electric power of apparent power, dissipation power and reactive power are obtained;
s4.3) regarding the electrical noise as a random vibration load, and calculating to obtain the relationship between the amplitude and the frequency of the apparent power of the piezoelectric ceramic actuator along with the voltage of the electrical noise.
2. The method for determining the electrical noise index of the piezoelectric ceramic actuator based on the coupled electromechanical analysis according to claim 1, wherein the specific steps of S1) are as follows:
s1.1) simplifying a piezoelectric ceramic actuator into a one-degree-of-freedom spring-mass-damping system;
s1.2) calculating the mechanical impedance of the one-degree-of-freedom spring-mass-damping system by using the definition of the mechanical impedance:
wherein Z is the mechanical impedance of the spring-mass-damping system; i is a complex number defined as (-1)1/2(ii) a c is the system damping coefficient; m is mass; ω is the frequency of the electrical noise load, ωnIs the natural frequency of the system, whose value can be expressed as
Wherein k issIs the spring rate.
3. The method for determining the electrical noise index of the piezoelectric ceramic actuator based on the coupled electromechanical analysis according to claim 2, wherein:
s1.2), the interaction between the piezoelectric ceramic and the mechanical structure is controlled by the dynamic output characteristics of the piezoelectric ceramic and the mechanical structure, and the specific relation is as follows:
where F is the force exerted by the piezoelectric ceramic on the mechanical structure, Z is the mechanical impedance of the spring-mass-damping system, and x is the displacement in the Y direction.
4. The method for determining the electrical noise index of the piezoelectric ceramic actuator based on the coupled electromechanical analysis according to claim 3, wherein the specific steps of S2) are as follows:
s2.1) establishing a kinematic model of a mechanical structure
Calculating an object motion differential equation by using a single-degree-of-freedom damped vibration system mechanical model:
the single-degree-of-freedom damped vibration system comprises a spring, a damper and an object mass; establishing a coordinate system by taking the object balance position 0 as an origin and taking the positive direction of the object motion as the positive direction of an X axis;
s2.2) establishing a dynamic model of the mechanical structure
Establishing a mechanical structure dynamic model by utilizing Newton's theorem:
wherein F (t) is the driving force provided by the piezoelectric ceramics, F1(t) is the damping force of the damper, F2(t) is the spring force of the spring;
s2.3) obtaining an open-loop transfer function of the spring-mass-damping system:
establishing a differential equation of a system through a kinematic model and a dynamic model of the mechanical structure:
then, the above formula is subjected to pull type transformation to obtain an open loop transfer function of the spring-mass-damping system:
wherein s represents a complex frequency domain after the pull-type transformation; k is a radical ofsIs the spring rate.
5. The method for determining the electrical noise index of the piezoelectric ceramic actuator based on the coupled electromechanical analysis according to claim 4, wherein the specific steps of S3) are as follows:
s3.1) obtaining the constitutive relation of stress and piezoelectric ceramic according to the constitutive relation of the piezoelectric ceramic given by IEEE by applying an electric field in the piezoelectric ceramic actuator in the Z direction and stretching and contracting in the Y direction:
wherein D is3Is a 3 x 1 matrix representing the electrical shift, unit: c/m2；S2Is a 6 x 1 matrix representing strain; e is a 3 × 1 matrix representing the electric field strength, unit: v/m; sigma2Is a 6 x 1 matrix representing stress in units: n/m2；
Is a 3 x 3 matrix representing the piezoelectric constant, unit: f/m, d32Is a 3 x 6 matrix representing the piezoelectric coefficients, in units: C/N;
is a 6 x 6 matrix representing the elastic modulus: unit: m is2/N；
S3.2) decomposing the displacement of the piezoelectric ceramic in the Y direction into a time domain and a space domain, and solving to obtain a vibration motion equation of the piezoelectric ceramic in the Y direction as follows:
wherein x is the displacement in the Y direction; ρ is the density of the piezoelectric ceramic;
is the complex modulus of the piezoelectric ceramic at zero electric field;
is the complex modulus of the piezoelectric ceramics; η is the mechanical loss factor of the piezoelectric ceramic;
s3.3) calculating the mechanical impedance of the piezoelectric ceramics by using the short-circuit mechanical impedance definition of the piezoelectric ceramics as follows:
wherein, KAIs formed by
Calculated static rigidity of piezoelectric ceramicAIs the length of the piezoelectric ceramic; k is derived from
Calculating to obtain; ω is the electrical noise loading frequency;
the short-circuit mechanical impedance of the piezoelectric ceramic is defined as the ratio of external excitation to speed response;
s3.4) calculating current by utilizing the piezoelectric ceramic output potential displacement field, so that the coupling electromechanical admittance of the piezoelectric ceramic actuator is obtained by the ratio of the current to the voltage as follows:
wherein, wAAnd hARespectively, the width and thickness of the piezoelectric ceramic.
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