Formulation of the problem of thermomechanics for a flexible cylindrical shell with piezoactive layers with taking into account to displacements

Abstract

The formulation of problem on the forced resonant vibration and dissipative heating of layered element of structure containing both piezoelectric and electrically passive layers is considered. The improved problem statement taking account of both shear strain and rotatory inertia as well as geometrical nonlinearity is developed. Particular statement of the problem of axisymmetric vibration and dissipative heating of three layer cylidrical shell is formulated. It is assumed that the core layer of the shell is composed of the electrically passive material while the outer layers are manufactured from the piezoceramics. Theory of coupled thermo-electro-viscoelasticity is used to derive the problem statement in the case of monoharmonic loading. Within this theory, the concept of complex-value modulae is applied to formulate the relations between main field characteristics. It is also supposed that the piezo-active material characteristics do not depend on the temperature. Then the coupled problem is reduced to the problem of mechanics on the forced nonlinear vibrations and dissipative heating of the layered plate. Complete set of complex analogs of motion equations, geometric equations and constitutive relations was used to derive the resolving system of equations. Numerical method to attack this nonlinear system of ordinary differential equations supplemented with necessary boundary conditions is developed.