Modal dynamic analysis for piezoelectric materials

The deflection at the center of the top surface for the sinusoidally applied pressure load for the two models without damping is shown in Figure 1. These results closely resemble the normalized results given in Mercer, Reddy, and Eve (1987) for similar models. The potential at the center of the top surface for this problem is shown in Figure 2. In Figure 3 the deflection at the center of the top surface for the CAX4E model with Rayleigh modal damping is shown, along with the result for the case without damping. The reduction in the response and the phase shift are obvious from the figure. The total force on the restrained bottom edge of the CAX8E model is output; the total force in the vertical direction matches the sum of the reaction forces on the edge.

The steady-state response for these problems is illustrated in Steady-state dynamic analysis for piezoelectric materials.