Abstract
A study of the expression for the response spectral density of linear systems to random pressures shows that the response problem essentially reduces to evaluating the joint acceptance of the system with the pressure field. A novel method using a coordinate transformation is presented. This method enables the joint acceptance for a simply supported beam with a pressure field, which has a spatial pressure correlation function which is easily described mathematically, to be determined in a simple manner. The joint acceptance for a beam in a reverberant acoustic field as a function of mode number and nondimensionalized frequency parameter (beam length/wavelength) has been computed for the first 16 modes. An engineering approximation for the joint acceptance for a simply supported flat plate in a reverberant acoustic field may be obtained from the beam results. The method can also be used to determine beam and flat-plate joint acceptance with a turbulent boundary-layer pressure field and with acoustic waves in a very simple manner.
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