Abstract
The linear and geometrically nonlinear flexural vibration of simply supported simply supported free rectangular plates punctually supported at the free corner is investigated. First, the frequency parameters and mode shapes are calculated with the efficient Rayleigh-Ritz method (RRM). The RRM is used here to study the geometrically nonlinear vibrations occurring at large amplitudes of the plates examined. The test plate functions used are the products of beam functions with appropriate end conditions, i.e. simply supported-free beam functions, in each direction and the point support is modeled by a factious translational spring with a stiffness tending to infinity. The solutions obtained for various plate aspect ratios compare well with available solutions based on different approaches. The nonlinear vibrations have been then examined using spectral analysis and Hamilton’s principle to determine the backbone curves of SSFF plates with various aspect ratios via the so-called the second formulation in order to determine the fundamental nonlinear frequency parameter and its mode shape.
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Babahammou, A., Benamar, R. (2022). Linear and Geometrically Nonlinear Frequencies and Mode Shapes of Point Supported Rectangular Plates at the Free Corner Whose Opposite Edges Are Simply Supported. In: Bouraoui, T., et al. Advances in Mechanical Engineering and Mechanics II. CoTuMe 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-86446-0_47
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DOI: https://doi.org/10.1007/978-3-030-86446-0_47
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