Discrete singular convolution for the prediction of high frequency vibration of plates.

*(English)*Zbl 1090.74604Summary: Theoretical analysis of high-frequency vibrations is indispensable in a variety of engineering designs. Much effort has been made on this subject in the past few decades. However, there is no single technique which can be applied with confidence to various engineering structures for high-frequency predictions at present. This paper introduces a novel computational approach, the discrete singular convolution (DSC) algorithm, for high-frequency vibration analysis of plate structures. Square plates with six distinct boundary conditions are considered. To validate the proposed method, a completely independent approach, the Levy method, is employed to provide exact solutions for a comparison. The proposed method is also validated by convergence studies. We demonstrate the ability of the DSC algorithm for high frequency vibration analysis by providing extremely accurate frequency parameters for plates vibrating in the first 5000 modes.

##### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74K20 | Plates |

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |