Novel Discrete Singular Convolution for High-Frequency Vibration Analysis of Structural Elements

The prediction and control of high-frequency vibrations is of crucial importance to aerostructures. However, developing accurate and numerically stable methods for the analysis of high-frequency vibration is an extremely challenging task. In this paper, a novel discrete singular convolution algorithm is presented for efficient analysis of high-frequency vibration of structural elements. A nonregularized Lagrange's delta sequence kernel based on harmonic functions is adopted. Taylor series expansion method is used to eliminate the degrees of freedom at fictitious points outside the physical domain, and thus various combinations of boundary conditions can be applied rigorously. Free vibration of beams and rectangular plates with and without two adjacent free edges is solved, and the results are compared with either exact solutions or results obtained by the differential quadrature method using much larger number of grid points. It is demonstrated that the performance of the proposed method for predicting high mode frequencies is excellent and better than existing algorithms. For the beam with both ends simply supported, all mode frequencies obtained by proposed method are very accurate. Such excellent feature of the algorithm was never reported before.