Application of the complex envelope vectorization to vibroacoustic systems

The complex envelope displacement analysis (CEDA) is a procedure to solve high frequency vibration and vibroacoustic problems, providing the envelope of the physical solution. CEDA, based originally on a variable transformation that maps the high frequency oscillations into a quasi-static displacement field, has been successfully applied to one-dimensional systems but the extension to plates and vibroacoustic cavities met several difficulties and required a general revision of the theory. In this paper a generalization of CEDA is presented and called Complex Envelope Displacement Vectorization (CEDV): its feature is that of transforming any high dimensional problem into a one-dimensional problem, through a suitable vectorization procedure of the physical discrete system. Some results related to flexural plates and vibroacoustic cavities are provided to enlighten the capability of the method.