SUMMARYThis paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Uniÿed features of the DSC algorithm for solving di erential equations are explored. It is demonstrated that di erent methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and ÿnite di erence, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of di erent plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet.

Despite much e!ort in the past few decades, the numerical prediction of high-frequency vibrations remains a challenging task to the engineering and scienti"c communities due to the numerical instability of existing computational methods. However, such prediction is of crucial importance to certain problems of pressing practical concern, as pointed out by Langley and Bardell (1998 ¹he Aeronautical Journal 102, 287}297). This paper introduces the discrete singular convolution (DSC) algorithm for the prediction and analysis of high-frequency vibration of structures. Both a beam and two-span plates are employed as test examples to demonstrate the capability of the DSC algorithm for high-frequency vibration analysis. A completely independent approach, the Levy method, is employed to provide exact solutions for a cross validation of the proposed method. The reliability of the DSC results is also validated by convergence studies. Remarkably, extremely accurate and stable results are obtained in this work, e.g., the relative DSC errors for the "rst 7100 modes of the beam and the "rst 4500 modes of the two-span plates are all (1%. No numerical instability is encountered in the present study.

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