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Computation of the transmission loss factor of single and double plates with random inhomogeneities
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The dynamics of thin elastic plates have been studied using various theoretical and experimental methods. In the context of acoustics, the primary interest is in the sound propagation from one side of the plate to the other. This paper shows how to compute the vibration of rectangular single- and double-plates that have inhomogeneous material properties. One of the inhomogeneities is the elasticity modulus of the plates, which is continuously and smoothly varying over the plates. The elasticity modulus is simulated as a random function with a pre-assigned probability density at any given position on the plate and power spectral density over the plate. The method of simulating such random functions is adopted from the theories of signal processing. In the case of the double-plate, the inhomogeneities in the junctions between the plate and the reinforcement beams are also considered. The behaviour of the plates is numerically analysed using the root-mean-square velocity and the transmission loss factor. The vibration field of the plates is represented using the Fourier series by taking advantage of the rectangular shape. Furthermore the random functions are represented by the series of cosine functions with random phases, wavelengths and amplitudes. As a result, the computation of the solution does not require discretization of the object, and thus the computational cost is low compare to typical finite element methods. Effects of the random inhomogeneities are compared to those of the deterministic inhomogeneities. Several probability density functions for the elasticity are also tried. In addition to numerical simulations, theoretical studies on the single-plate are presented using the analytical formulas for the Fourier coefficients.