Effect of Initial Geometric Imperfections on Nonlinear Vibration of Thin Plate by an Asymptotic Numerical Method

Springer Science and Business Media LLC - 2020
Lahcen Benchouaf1, El Hassan Boutyour2
1Hassan First University of Settat, Higher School of Education and Training, Berrechid, Morocco
2Hassan First University of Settat, Faculty of Sciences and Technologies, Department of Applied Physics, Settat, Morocco

Tóm tắt

In this work, the influence of initial geometric imperfections on geometrically nonlinear free vibrations of thin elastic plates has been investigated by an asymptotic numerical method. The nonlinear strain displacement relationship of von Karman theory is adopted to calculate the elastic strain energy. The harmonic balance approach and Hamilton’s principle are used to convert the equation of motion into an operational formulation. The nonlinear problem is transformed into a sequence of linear ones having the same stiffness matrix, which can be solved by a classical finite-element method. To improve the validity range of the power series, Padé approximants are incorporated and a continuation technique is also used to get the whole solution. Numerical results are discussed and compared to those available in the literature and convergence of the solution is shown for various amplitudes of imperfection.

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