High-frequency dynamic response of thin plate with uncertain parameter based on average wavelet finite element method (AWFEM)

Due to the limitation caused by the low computational efficiency and parameters uncertainty, the Traditional Finite Element Methods (TFEMs) based on the general polynomials cannot provide reliable numerical solutions in the high-frequency domain. To this end, the Average Wavelet Finite Element Method (AWFEM) is proposed in this paper for dealing with the low computational efficiency and uncertain parameters at one time. Thus, the essential formulas of the AWFEM are derived based on the Wavelet Finite Element Methods (WFEMs) and average statistic algorithm. Besides, to divide the wide-frequency domain into the low and high-frequency domain, the Frequency Domain Index (FDI) is constructed based on the resonant mode number in bandwidth. Later, to investigate the proposed method's prediction ability in the high-frequency domain, the dynamic response of the numerical models under various classical boundary conditions and non-uniform mass distributions are computed by AWFEM and Statistical Energy Analysis (SEA), respectively. And, the numerical results show that the AWFEM can be applied for predicting dynamic response in the high-frequency domain as same as SEA. Besides, the CPU time is less than 5 min to capture the numerical solutions based on personal computer. Most notably, it gives us an optional choice to predict dynamic response in the high-frequency domain only based on finite element models.