Parametric Study of Sound Radiation Properties of Complex Vibration Patterns in Rectangular Plates using an Analytical Model

Abstract

Complex vibration modes, which can be characterised by the superposition of standing and travelling bending waves, occur for instance in structures with inhomogeneous damping distribution. The existence of complex structural modes raises the question of their influence on sound radiation properties. In this paper an analytical model of a simply supported rectangular plate is introduced. It allows a quick calculation of complex vibration patterns with different properties, avoiding time consuming and sometimes unstable damped modal analysis in finite-element-software. Using this model it is possible to generate vibration patterns with varying level and spatial distribution of travelling waves as well as different symmetry of amplitude distributions, in order to reveal the important influence factors on sound radiation. Despite the fact that the analytical model generates idealised vibration patterns, the presented consideraton significantly improves phenomenological understanding of acoustic effects in complex vibration modes. The accuracy of the presented model is validated by results of finite element modal analysis and is evaluated in terms of resulting amplitude and phase distributions of the vibrating surface. The results of both suggested approaches are compared using modal radiation efficiencies, spatial distributions of far field acoustic intensity and sound field directivity. Some additional conclusions are made using the analytical model concerning important acoustic metrics of structural vibration patterns. It is shown, that vibration shapes of even order are very sensitive to the presence of travelling waves regarding their radiation capability and character of sound pressure field.