Product: ABAQUS/Standard
The model is the cylinder described in “Static analysis for piezoelectric materials,” Section 3.5.1 of the ABAQUS Verification Manual. Three analyses are performed with two models. One model has 16 CAX4E elements, and the other has four CAX8E elements. The modal dynamic analyses use the eigendata from the restart files generated in “Frequency extraction analysis for piezoelectric materials,” Section 3.5.2 of the ABAQUS Verification Manual. The first two problems have no damping and are intended for comparison with the results from Mercer, Reddy, and Eve (1987). For these problems a pressure load is applied sinusoidally on the top surface at a frequency of 100000 rad/sec (15.9 kHz). The third problem introduces Rayleigh modal damping terms for the previous problem to illustrate the effect of damping.
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 1.7.2–1. 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 1.7.2–2. In Figure 1.7.2–3 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 *SECTION FILE and *SECTION PRINT options are used to output the total force on the restrained bottom edge of the CAX8E model; 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,” Section 1.7.3.
Modal dynamic analysis, CAX4E elements, no damping.
Modal dynamic analysis, CAX8E elements, no damping.
Modal dynamic analysis, CAX4E elements, damping included.
