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Large amplitude free flexural vibration of arbitrary thin plates using superparametric element

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Abstract

The large amplitude free flexural vibration of arbitrarily shaped thin plates is presented using finite element method. The formulation uses superparametric element which consists of an ACM plate element along with in-plane displacements for defining the displacement field and cubic serendipity element for geometry. This element avoids the inherent disadvantages of isoparametric elements when applied to thin plates. Von Karman’s large deflection theory is used, and the formulation is performed in the total Lagrangian coordinate system. The nonlinear equation is solved by direct iteration technique that uses the linear mode shape as starting vector. Nonlinear frequencies are obtained for different geometries and boundary conditions. Various numerical examples are shown to proof the versatility of the formulation, and its efficacy is shown by validating with published results. The results can be used in the field of aerospace, civil and naval engineering fields.

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Authors and Affiliations

  1. Department of Civil Engineering, NIT, Rourkela, 769008, India

    Saleema Panda & Manoranjan Barik

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  1. Saleema Panda
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  2. Manoranjan Barik
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Correspondence to Saleema Panda.

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Panda, S., Barik, M. Large amplitude free flexural vibration of arbitrary thin plates using superparametric element. Int. J. Dynam. Control 5, 982–998 (2017). https://doi.org/10.1007/s40435-016-0275-5

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  • DOI: https://doi.org/10.1007/s40435-016-0275-5

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