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Plate vibration under irregular internal supports. (English) Zbl 1090.74603
Summary: This paper studies the problem of plate vibration under complex and irregular internal support conditions. Such a problem has its widely spread industrial applications and has not been addressed in the literature yet, partially due to the numerical difficulties. A novel computational method, discrete singular convolution (DSC), is introduced for solving this problem. The DSC algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries, boundary conditions and internal support conditions. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. Case studies are considered to the combination of a few different boundary conditions and irregular internal supports. The latter are generated by using an image processing algorithm. Completely independent verifications are conducted by using the established pb-2 Ritz method, which is available for two relatively simpler support patterns. The morphology of the first few eigenmodes is found to be localized to largest support-free spatial regions.

74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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