Indexed on: 07 Jul '18Published on: 03 Jul '18Published in: Applied Mathematical Modelling
Publication date: October 2018 Source:Applied Mathematical Modelling, Volume 62 Author(s): Jia Geng, Xingwu Zhang, Xuefeng Chen, Chenxi Wang, Jiawei Xiang Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c1 type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c1 type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c1 type WFEMs. On the other hand, the method combining c1 type B-spline wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.