High-frequency vibration analysis of thin plate based on b-spline wavelet on interval finite element method

For the dynamic analysis of thin plate bending problems, the Finite Element Methods (FEMs) are the most commonly used numerical techniques in engineering. However, due to the deficiency of low computing efficiency and accuracy, the FEMs can't be directly used to effectively evaluate dynamic analysis of thin plate with high modal density within low-high frequency domain. In order to solve this problem, the Wavelet Finite Element Methods (WFEMs) has been introduced to solve the problem by improving the computing efficiency and accuracy in this paper. Due to the properties of multi-resolution, the WFEMs own excellently high computing efficiency and accuracy for structure analysis. Furthermore, for the destination of predicting dynamic response of thin plate within high frequency domain, this paper introduces the Multi-wavelet element method based on c1 type wavelet thin plate element and a new assembly procedure to significantly promote the calculating efficiency and accuracy which aim at breaking up the limitation of frequency domain when using the existing WFEMs and traditional FEMs. Besides, the numerical studies are applied to certify the validity of the method by predicting state response of thin plate within 0~1000Hz based on a special numerical example with high modal density. According to the literature, the frequency domain between 0 to 1000Hz contains the low-high frequency domain aiming at the numerical example. The numerical results show excellent agreement with the reference solutions captured by FEM and analytical expressions respectively. Among these, it is noteworthy that the relative errors between the analytical solutions and numerical solution are less than 0.4% when the dynamic response involved with 1000 modes.