Even harmonics in the geometrically non-linear vibrations of perfect plates

Abstract

The goal of this paper is to demonstrate that even and odd harmonics can be simultaneously present in free, large amplitude displacement, periodic vibrations of perfect plates. It is assumed that time and space can be separated and the principle of the virtual work applied in order to obtain ordinary differential equations of motion in the time domain. These equations are mapped into the frequency domain by expressing the solution in the form of a truncated Fourier series that includes odd and even harmonics. In a demonstrative example, a bifurcation due to a 1:2 resonance is found and this results in a branch of solutions that contains odd and even harmonics.