Abstract
AbstractLarge amplitude free vibration behavior of thin, isotropic square plate configurations resting on Winkler type of elastic foundation are expressed in the form of simple closed‐form solutions by using the Rayleigh‐Ritz (R‐R) method based on coupled displacement fields (CDF). Geometric non‐linearity of von‐Kármán type is taken into consideration. The in‐plane displacement field variations used in the formulation of the R‐R (CDF) method are derived by using the governing in‐plane static differential equations of the plate which in turn simplifies the difficulty of assuming an in‐plane displacement field variations of the plate. Accuracy and robustness of proposed closed‐form solutions is compared to the available finite element formulation results. Proposed closed‐form solutions are corrected for the simple harmonic motion (SHM) assumption using the well established harmonic balance method (HBM) which is applicable for the homogeneous form of cubic non‐linear Duffing equation.
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