The characteristics, the structural scheme and the matrix transfer function of the piezo actuator for the nanomedicine research are obtained. The transfer functions of the piezo actuator are described the characteristics of the actuator with regard to its physical parameters and external load.

The piezo actuator is the piezo mechanical device intended for actuation of the mechanisms, the systems or the management based on the piezo effect, converts electrical signals into mechanical movement or force. The piezo actuators for nano and micro displacement are provided the movement range from several nanometers to tens of microns, the sensitivity of up to 10 nm/V, the loading capacity of up to 1000 N.^1‒5 The piezo actuator is used in the majority of the scanning tunneling microscopes and the atomic force microscopes. The mathematical model, the structural scheme and the transfer functions of the piezo actuator are calculated for designing the control mechatronics systems for the nanomedicine research.^3‒12 The structural scheme and transfer functions the piezo actuator make it possible to describe the dynamic and static properties of the piezo actuator for the nanomedicine research with regard to its physical parameters and external load.^11‒24

The method of mathematical physics with Laplace transform is applied for the solution the wave equation. The structural scheme of the piezo actuator for the nanomedicine research is changed from Cady and Mason electrical equivalent schemes,^6,7 of the piezo actuator. The equation of the inverse piezo effect,^7,9,11 has form $S_i=d_{mi}{\Psi }_m+s_{ij}^{\Psi }{T}_j$ ,

where $S_i$ is the relative displacement along axis i, ${\Psi }_m=\left\{E_m,D_m\right\}$ is the control parameter, $E_m$ is the electric field strength for the voltage control along axis m,  is the electric induction for the current control along axis m, $d_{mi}=\left\{d_{mi},g_{mi}\right\}$ is the piezo module for the voltage control or for the current control, $T_j$ is the mechanical stress along axis j, $s_{ij}^{\Psi }$ is the elastic compliance for the control parameter , the indexes i= 1, 2, … , 6; j = 1, 2, … , 6; m = 1, 2, 3. The main size of the piezo actuator along axis i is determined $l=\left\{\delta ,h,b\right\}$ in form the thickness, the height, the width for the longitudinal, transverse, shift piezo effect. For the construction the structural scheme of the piezo actuator is used the wave equation for the wave propagation in the long line with damping but without distortions. With using Laplace transform is obtained the linear ordinary second-order differential equation. The problem for the partial differential equation of hyperbolic type using the Laplace transform is reduced to the simpler problem for the linear ordinary differential equation,^9,11,12

The structural scheme of the piezo actuator,^4,9,11,12 on Figure 1 are determined, using method of the mathematical physics for the solution of the wave equation, the boundary conditions and the equation of the inverse piezo effect, where  is the cross section area, ,  are the mass of load, , , ,  are the Laplace transforms of the displacements, the forces on the faces 1, 2. The structural schemes and the matrix transfer function of the voltage controlled or current controlled piezo actuator are obtained from its mathematical model. The deformations of the piezo actuator are described by the matrix transfer function.

Figure 1 Structural scheme of piezo actuator for nanomedicine research.

The structural scheme, the transfer functions of the piezo actuators for the nanomedicine research are described the characteristics of the piezo actuator with regard to its physical parameters, external load.

None.

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