Nonlinear vibrations analysis in acoustics.

Mechanisms of nonlinear coupling between the normal modes of vibrating mechanical structures have been explored, previously particularly in the context of struck idiophones (percussive instruments). However, the analysis of the vibrations resulting from impulsive loads has been restricted by our ability to solve the nonlinear equations of motion. In recent times, numerical methods for solving the equations have burgeoned, and we are now in a position to apply the methods to structures of interest such as musical plates and gongs. In this paper, we consider the nonlinear coupling of modes of vibration whereby energy is transferred between the normal modes of a kinked bar. A finite element analysis package is employed to analyse the response. The results confirm that initially missing modes of vibration are generated through nonlinear coupling mechanisms.