Experimental and numerical study on vibrations and static deflection of a thin hyperelastic plate

The hyperelastic behavior of a thin square silicone rubber plate has been investigated analytically, numerically and experimentally; the case of small-amplitude vibrations has been considered, as well as the case of large static deflection under aerostatic pressure. The Mooney-Rivlin hyperelastic model has been chosen to describe the material nonlinear elasticity. The material parameters have been identified by a fitting procedure on the results of a uniaxial traction test. For the analytical model, the equations of motion have been obtained by a unified energy approach, and geometrical nonlinearities are modeled according to the Novozhilov nonlinear shell theory. A numerical model has also been developed by using a commercial Finite-Element code. In the experiments, the silicone rubber plate has been fixed to a heavy metal frame; a certain in-plane pre-load, applied by stretching the plate, has been given in order to ensure a flatness of the surface. An experimental modal analysis has been conducted; results have been used to identify the applied in-plane loads by optimization procedure with two different models: a numerical and an analytical one. The first four experimental and numerical natural modes and frequencies are in good agreement with the experiments after the pre-load identification. The static deflection has been measured experimentally for different pressures. Results have been compared to those obtained by analytical and numerical models. The static deflections are also satisfactorily compared, up to a deflection 50 times larger than the plate thickness, corresponding to a 30 percent strain.