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    Vibration Analysis of Arbitrarily Shaped Membranes

    S.Yu. Reutskiy1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

    Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇2w + k2q(x)w = 0, x∈ Ω⊂R2, B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of the maxima of… More >

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