Resonance Response of Nonlinear Circular Plates Subjected to Uniform Static Load

Abstract

The axisymmetric resonant frequency response of static pressure loaded, nonlinear clamped, circular plates have been investigated analytically and experimentally. In the analysis, the set of nonlinear partial differential equations of motion and compatibility are solved by applying Galerkin’s method with Dini-Bessel and Fourier-Bessel series expansions for the assumed solution forms. These expansions satisfy the boundary conditions exactly. The equations are solved to yield a second approximation for the first mode response and a first approximation for the second mode response. Experiments were conducted on a number of circular plates. The analytical and experimental results are found to be in good agreement for plates with β ≤ 57.3. The agreement was only fair for plates with β > 57.3.