This paper deals with a new method for solving dynamics problems of arbitrarily shaped plates. The method consists in cross approximation of functions satisfying solely an equation of motion and functions satisfying solely boundary conditions on irregular plate edges. This approach is applied in the paper to the case of free and forced vibration of homogeneous and sandwich plates with edges of various shapes. Functions satisfying boundary conditions are determined by the Rvachev’s R-function method. The validity of the method is discussed.

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