An uncertainty model of acoustic metamaterials with random parameters

Abstract

Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully.

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Acknowledgements

The project is supported by the National Natural Science Foundation of China (Grant No. 51322502) and Project funded by China Postdoctoral Science Foundation. The authors also wish to thank Research Project of State Key Laboratory of Structural Analysis for Industrial Equipment (Grant No. GZ1403), the Science Fund of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (Grant No. 51375001), and Research Project of State Key Laboratory of Mechanical Systems and Vibration MSV201613.

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Correspondence to Eric Li.

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He, Z.C., Hu, J.Y. & Li, E. An uncertainty model of acoustic metamaterials with random parameters. Comput Mech 62, 1023–1036 (2018). https://doi.org/10.1007/s00466-018-1548-y

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Keywords

  • Acoustic metamaterials
  • Random parameters
  • Perturbation stochastic finite element method
  • Change-of-variable technique
  • Probability density function