Abstract
Operation of structures and equipment in dynamic conditions led to the problems of vibration isolation and vibration suppression. For vibration isolation and vibration suppression passive, active systems and their combinations are used. Passive vibration isolation usually consists in the fact that the protected object relies on extremely dimensional springs and vibration isolators. Vibration isolation systems containing only passive elastic and damping elements are called passive. Active vibration isolation and vibration damping systems use external energy sources. These are pneumatic, hydropneumatic and hydromechanical devices. Recently, electro-elastic and magneto-elastic systems [1], [2] began to be used for vibration isolation and active vibration suppression. As a rule, the analysis of the work of such systems consists in the development of an experimental layout and a schematic diagram. In this paper, a mathematically based model is used to solve the problem in question. The calculations are performed and the results are presented in the form of graphs.
Highlights
A three-layer beam with one elastic layer and two piezoelectric layers located symmetrically with respect to the elastic layer is considered
The axis x1 is directed along the length of the beam, the axis x2 is directed along the width of the beam, the axis x3 is orthogonal to them
It is assumed that the piezoelectric layers are pre-polarized in the direction x3 [3] - [5]
Summary
A three-layer beam with one elastic layer and two piezoelectric layers located symmetrically with respect to the elastic layer is considered. The beam is related to Cartesian coordinates. We will consider piezoelectric layers, in which the faces x 3 const are completely covered with electrodes. In [6], we obtain the elastic relations for a multilayer electroelastic beam. Taking into account the assumptions made, the equations for the elastic and electroelastic layers will be written as The system of equilibrium equations takes the form In formulas (3) - (8) u1 and e1 are the displacement and deformation in the direction x1 , respectively, E3 and D3 are the components of the electric field vector and electric induction vector in the direction x3 , s1E1 is the elastic compliance at zero electric field, d31 is the piezoelectric constant, is the dielectric constant at zero voltages. On the surfaces of the beam, the mechanical surface load is usually specified as ( 2) 13
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