Power dissipation and temperature distribution in piezoelectric ceramic slabs

A method is presented to determine power dissipation in one-dimensional piezoelectric slabs with internal losses and the resulting temperature distribution. The length of the slab is much greater than the lateral dimensions. Losses are represented using complex piezoelectric coefficients. It is shown that the spatially non-uniform power dissipation density in the slab can be determined by considering either hysteresis loops or the Poynting vector. The total power dissipated in the slab is obtained by integrating the power dissipation density over the slab and is shown to be equal to the power input to the slab for special cases of mechanically and electrically excited slabs. The one-dimensional heat equation that includes the effect of conduction and convection, and the boundary conditions, are then used to determine the temperature distribution. When the analytical expression for the power dissipation density is simple, direct integration is used. It is shown that a modified Fourier series approach yields the same results. For other cases, the temperature distribution is determined using only the latter approach. Numerical results are presented to illustrate the effects of internal losses, heat conduction and convection coefficients, and boundary conditions on the temperature distribution.