Abstract

In this work we determined the mathematical description of multilayer actuator for nano biomedicine. The displacements of the multilayer actuator are received from its mathematical description.

Keywords: Multilayer actuator; Mathematical description

Introduction

For mathematical description of the multilayer actuator we used the equation of the relative deformation, the mechanical fourterminal scheme and the boundary conditions [1-30].

Mathematical Description Actuator

The equation S_i relative deformation [7-11] has the following form

where mi are parameters

We received the equation the causes force in the form

where S₀ is the area actuator.

For the mechanical four-terminal scheme [23] actuator we have the matrix in the form.

where l, γ are length and coefficient.

The mathematical description and diagram on Figure 1 of the multilayer actuator we obtained as the system of the equations in the form

Figure 1: Structural Diagram of Multilayer Actuator.

where are the Laplace transforms of the displacements and forces for the faces.

From the mathematical description of the multilayer actuator we have the matrix equation

where are the matrices.

For time for the inertial load on the two faces of piezoactuator we obtain the expressions of its displacements

where n, U are the number piezolayers and the voltage.

At kg we obtained the displacements = 160 nm.

Conclusion

We determined the mathematical description of the multilayer actuator for nano biomedicine. We obtained the displacements of the multilayer actuator from its mathematical description.

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Abstract

In this work we determined the mathematical description of multilayer actuator for nano biomedicine. The displacements of the multilayer actuator are received from its mathematical description.

Keywords: Multilayer actuator; Mathematical description