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Abstract
In this work, a new separation-of-variable (nSOV) method for the free vibration of Kirchhoff rectangular thin plates is developed based on the Rayleigh quotient variational principle. Using this nSOV method, all closed-form solutions can be obtained as long as not both directions include free edge, and the solution accuracy is improved compared with the separation-of-variable (SOV) method proposed previously by the present authors. In addition, as a natural extension of the nSOV method, an iterative SOV (iSOV) method is developed, which is suitable for rectangular thin plates with any kinds of homogeneous boundary conditions. Moreover, all closed-form solutions are presented in explicit forms, and the proposed methods and results are validated via theoretical and numerical comparisons.
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