Influence of material functional heterogeneity on non-stationar oscillations of piezoceramic bodies

Abstract

The influence of material functional heterogeneity on mechanical oscillations of piezoelement under non-stationary electrical loading is investigated. Within the assumption of functional distribution of material characteristics by thickness of the piezoelectric element, which corresponds to the physical properties of the body, a unified system of solving equations was obtained to describe the thickness fluctuations of piezoelectric plates, cylinders, and balls. For controllingof accuracy, the calculation is carried out using an explicit and implicit difference scheme. Unsteady oscillations of a flat piezoceramic layer, cylinder, and sphere are investigated with a parabolic distribution of all material characteristics along the thickness of the element. It is assumed that the average value of the function along the thickness is equal to the tabular value of the material characteristic, and the value on electrodes is proportional to the area of electrodes. At such conditions, we obtained a decrease in the speed of disturbances propagation and a slight change in the amplitude associated with the curvature of the element. The increase in amplitude reaches 3% for balls. It should be noted that at given load oscillations occur in the compressed zone without entering the undeformed state. The considered cylinder and ball have a rather large curvature, for bodies with a smaller curvature the influence of the described effect will be smaller. The additional analysis indicates that the shape of the distribution curve under described above conditions also has little effect on the results. It was established that the effect of functional heterogeneity within the same material has little effect on the oscillations of the piezoelement, that is, it is really possible to average the material characteristics by thickness at calculating, since the deviation between the results is within acceptable limits (up to 2.5%). Also, an important result is the confirmation of the assumption that for curved bodies such as cylinder and sphere, the material characteristics can be considered constant on thickness, regardless of the curvature of the body. The proposed technique can be applied for studyingof the vibrations of different geometries bodies with significantly heterogeneous functional material or what are combined from several materials with a gradient transition between them.