A rearrangement of the modal expansion for a damped two-dimensional vibratory system

Muggleton, J.M. and Pinnington, R.j. (2002) A rearrangement of the modal expansion for a damped two-dimensional vibratory system. Journal of Sound and Vibration, 211 (4), 637-661. (doi:10.1006/jsvi.1997.1395).

Abstract

When investigating the acoustic or vibrational behaviour of a two- or three dimensional system, the classical approach is to compute the response as a sum over all contributing modes. In this paper the modal summation of a two-dimensional system is rearranged, taking into account the physical nature of the modes. The modes are grouped according to the direction in which their constituent waves propagate, and are shown to be represented as an array of image line sources. Closed form expressions for the input impedance and the system's transfer impedances are obtained for each mode group. The modal summation is them performed over all contributing mode groups. A line source model is thus generated which approximates to the exact point source model. The closed form solutions obtained enable damping in the medium and at the boundaries to be taken into consideration. For heavy damping, the line source or modal models are shown to be in error. An alternative formulation, which allows for the time delay for line sources to be set up, is presented, with some justification. Results are presented of an experimental validation of the unmodified theory, as it relates to a rigid-walled two-dimensional enclosure. Measurements of input and transfer impedances were made in an air-filled, perspex enclosure. The effect of damping evenly distributed throughout the enclosure, was investigated. In general, the measured input and transfer impedances show good agreement with the theoretical predictions.

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