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

### Significance

Generally, advanced equipment such as the airfoil are susceptible to various failures due to extreme heat and high frequency during operations. Thus, accurate prediction of the dynamic response in the high-frequency domain will be of significant importance in the design and optimization of such equipment. Among the available dynamic analysis techniques, statistical energy analysis and traditional finite element methods are commonly used for vibration and sound analysis. The former is based mainly on statistics and energy theory while the latter is based on polynomials. Unfortunately, traditional finite element methods are associated with low computing efficiency due to uncertain parameters and thus cannot be relied on in high-frequency domain analysis.

Even though statistical energy analysis is deemed suitable for high-frequency domain analysis as compared to the traditional finite element methods, its use is still limited due to its worse universality. Consequently, the dynamic response predicted by traditional finite element methods will be distorted in the high-frequency domain due to the uncertain parameters. Thus, it is necessary to avoid the uncertain parameters by constructing accurate numeric models. The uncertain parameters indicate uncertain structural properties like uncertain mass distribution and boundary conditions thus must be taken into consideration during finite element analysis.

To this end, researchers have been looking for alternative methods of efficiently predicting high-frequency domain responses based on finite element methods and have identified the average wavelet finite element method as a promising solution. This is attributed to the fact that it is capable of dealing with uncertain parameters and low computational efficiency distinctly.

Recently, Xi’an Jiaotong University scientists from the School of Mechanical Engineering: Dr. Jia Geng, Dr. Xingwu Zhang and Professor Xuefeng Chen developed an average wavelet finite element method for performing dynamic analysis in the high-frequency domain. The formulas of the proposed algorithm were derived based on the average statistic algorithm and wavelet finite element method.

Furthermore, the frequency domain index was constructed based on the resonant mode to divide the wide frequency domain into low and high-frequency domains. Eventually, the proposed algorithm was investigated in the high-frequency domain. They purposed to overcome the challenges of low computational efficiency and uncertain parameters. Their work is published in the journal, Mechanical Systems and Signal Processing.

The research team observed that the proposed average wavelet finite element method could be efficiently used to predict the dynamic response in the high-frequency domain just like in the statistic energy analysis. Furthermore, it took the CPU less than 5 minutes to predict each velocity response. However, it was noted that the numerical solution in the higher frequency domain agreed well with the results obtained for the statistic energy analysis.

The study successfully developed an average wavelet finite element method for efficient dynamic analysis in the high-frequency domain. This is attributed to the fact that it overcomes the effects of uncertain parameters and low computational efficiency. Therefore, it will enable engineers in different fields to pre-design and optimize equipment in the high-frequency domain at low costs thus enhancing their functionality.

### About the author

Jia Geng is an assistant research fellow in School of Mechanical Engineering, Xi’an Jiaotong University. He received the Ph.D degree from Xi’an Jiaotong University, Xi’an, China, 2018, and then joined in Xi’an Jiaotong University as an assistant research fellow. His research interests are wavelet finite element method, dynamic system modeling and analysis. He has published about 10 academic papers.

### About the author

Xingwu Zhang is an associate professor in School of Mechanical Engineering, Xi’an Jiaotong University. He received the Ph.D. degree from Xi’an Jiaotong University, Xi’an, China, 2012. His research interests are dynamic system modeling and analysis, structural health monitoring and active vibration control. He is the PI of over 4 projects, including National Natural Science Foundation of China etc..

He holds more than 30 patents and published over 50 academic papers with H index of 16. Dr. Zhang is the member of IEEE Instrument and Measurement, the technical committee member of IEEE Instruments and Measurement Society TC-7 Signals and Systems in Measurement.

### About the author

Xuefeng Chen is a professor and the dean of School of Mechanical Engineering, Xi’an Jiaotong University. He received the Ph.D degree from Xi’an Jiaotong University, Xi’an, China, in 2004. His research interests include finite element method, fault diagnosis and prognosis, active vibration control and optimization.

Dr. Chen has published over 200 papers in refereed journals, with SCI indexed citation > 6000 and H index of 42. He is the Chapter Chairman of the Xi’an and Chengdu Joint Section of the IEEE Instrumentation and Measurement Society. He was a recipient of the National Excellent Doctoral Dissertation of China in 2007, the Second Awards of Technology Invention of China in 2009, The China National Funds for Distinguished Young Scientists in 2012, and a Chief Scientist of the National Key Basic Research Program of China (973 Program) in 2015.

### Reference

Geng, J., Zhang, X., & Chen, X. (2018). High-frequency dynamic response of thin plate with uncertain parameter based on average wavelet finite element method (AWFEM). Mechanical Systems and Signal Processing, 110, 180-192.