Thermomechanics of Coupled Fields in Passive and Piezoactive Inelastic Bodies Under Harmonic Deformation

Abstract

ABSTRACT The present article gives a brief overview of studies made at S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine on thermomechanics of coupled fields in nonlinear inelastic passive and piezoactive materials and bodies under monoharmonic deformation. Our attention will be focused on the following subjects: (1) development of the nonlinear models of passive (without piezoeffect) and piezoactive (with piezoeffect) materials for monoharmonic vibrations with accounting for influence of such factors as material nonlinearity, dissipation, and temperature of dissipative heating; (2) development of the thermomechanical models of nonhomogeneous thin-walled inelastic elements under monoharmonic deformation; (3) development of numerical and analytical methods of the solution of coupled problems; (4) investigation of the influence of material nonlinearity, dissipation and temperature of dissipative heating on regularities of vibrations of the bodies with the passive and piezoactive materials, including influence of these factors on the efficiency of vibration control of elements with distributed sensors and actuators. Problem 1 is solved on the basis of concept of complex material characteristics. Accordingly the simplified nonlinear constitutive equations of passive and piezoactive materials are identical to the constitutive equations of linear theory of viscoelasticity, but the complex mechanical and electromechanical characteristics are temperature and field-dependent quantities. Averaged for period the rate of dissipation coincides with averaged electromechanical power. On the basis of these simplified constitutive equations the statement of coupled problems of thermomechanics in the passive and piezoactive inelastic spatial bodies are given. To solve Problem 2, the mechanical hypotheses of Kirchhoff–Love and similar hypotheses for electric field quantities and temperature are introduced. As a result the statement of coupled nonlinear problems of thermomechanics in the passive and piezoactive inelastic thin-walled elements are given. To solve Problem 3 one needs to use some iterative techniques such as method of step-by-step integration in time, method of variable characteristics and accelerating Steffensen-Eitken procedure. At each iteration, the linearized electromechanical and heat conductivity problems are solved by a method of discrete orthogonalization or by a finite element method. By the use of variational methods, the analytical solutions are also obtained. On the basis of the mentioned models, methods, and analytical and numerical solutions obtained, the influence of material nonlinearity, dissipation, and self-heating on the vibrations of nonhomogeneous spatial and thin-walled elements (in particular on the efficiency of active damping of vibrations of the elements) are investigated (Problem 4).