Flexural Wave Propagation in Slowly Varying Random Waveguides Using a Finite Element Approach

13th International Conference on Motion and Vibration Control; 12th International Conference on Recent Advances in Structural Dynamics

Fabro, A.T.^1 ; Ferguson, N.S.^2 ; Mace, B.R.^3

Department of Mechanical Engineering, University of Brasília, Brasília- DF

70910-900, Brazil^1

ISVR, University of Southampton, Highfield Campus, SO17 1BJ, United Kingdom^2

Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland

1142, New Zealand^3

关键词: Finite-element approach;    Flexural vibrations;    Gauss Legendre quadrature;    Integration points;    Karhunen Loeve Expansion;    Random waveguides;    Wave amplitudes;    Wave based method;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/744/1/012198/pdf
DOI  :  10.1088/1742-6596/744/1/012198

来源: IOP

【 摘 要 】

This work investigates structural wave propagation in waveguides with randomly varying properties along the axis of propagation, specifically when the properties vary slowly enough such that there is negligible backscattering. Wave-based methods are typically applied to homogeneous waveguides but the WKB (after Wentzel, Kramers and Brillouin) approximation can be used to find a suitable generalisation of the wave solution in terms of the change of phase and amplitude, but is restricted to analytical solutions. A wave and finite element (WFE) approach is proposed to extend the applicability of the WKB method to cases where no analytical solution is available. The wavenumber is expressed as a function of the position along the waveguide and a Gauss-Legendre quadrature scheme is used to obtain the phase change while the wave amplitude is calculated using conservation of power. The WFE method is used to evaluate the wavenumbers at each integration point. The flexural vibration example is considered with random field proprieties being expressed by a Karhunen-Loeve expansion. Results are compared to a standard FE approach and to the WKB analytical solution. They show good agreement and require only a few WFE evaluations, providing a suitable framework for spatially correlated randomness in waveguides.