A novel approach for the analysis of high-frequency vibrations

Despite much effort in the past few decades, the numerical prediction of high-frequency vibrations remains a challenging task to the engineering and scientific 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 The Aeronautical Journal102, 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 first 7100 modes of the beam and the first 4500 modes of the two-span plates are all