PLANAR OSCILLATIONS AND DISSIPATIVE HEATING OF VISCOELASTIC PLATES WITH A PIEZOEFFECT

Planar oscillations of thin piezoplates are important within the conte xt of using this type of piezoelements as resonator frequency filters, frequency stabilizers, elements of piezotransformers, and other techn ological devices. In the publications currently known one usually cons iders piezoplates with elastic material behavior and linear governing equations. By their mechanical nature, however, a number of piezoeleme nts, particularly piezoceramics, are viscoelastic, which, depending on the loading conditions, can lead to substantial dissipative heating o f the piezoelement and confine its operation [3]. The use of piezopoly mers and their composites raises particularly important issues of diss ipative hearing. At the present time the behavior of a piezoelement in cluding heating can be described by the theory of thermoelectroviscoel asticity (TEVE) [2, 3], including the interaction between electromecha nical and thermal fields. The complexity of TEVE problems leads to the necessity of using numerical methods to solve them, with the finite e lement method (FEM) being widely used in recent years. The present stu dy is devoted to stating and solving TEVE problems concerning thin pie zoceramic plates by the FEM. We treat a thin piezoceramic plate, confi ned by an: arbitrary contour L and polarized across its thickness. A h armonic potential difference Delta phi e(i omega t) is supplied to ele ctrodes located on the smooth boundaries of the plate. Convective heat exchange with the surrounding media of temperatures T-k(s) and T-s is implemented at the contour surfaces and boundaries free of electrodes . The heat transfer coefficients equal, respectively, alpha(k)(T) and alpha(T). The initial plate temperature is T-0. The smooth boundary ar e free of mechanical loading. The mechanical forces at the contour sur faces are distributed symmetrically with respect to the mean plane of the plate.