Wavenumber and natural frequency statistics of waveguides with spatially correlated material variability from finite element analysis

Todorovic Fabro, Adriano, Ferguson, Neil and Mace, Brian R. (2011) Wavenumber and natural frequency statistics of waveguides with spatially correlated material variability from finite element analysis. 18th International Congress on Sound and Vibration, Rio de Janeiro, Brazil. 10 - 14 Jul 2011. 8 pp .

Abstract

This paper concerns wave propagation in random waveguides and, in particular, when there is spatially correlated variability in the material and/or geometric properties. The one dimensional waveguide is modelled using a wave and finite element method to evaluate the wave-number. In the numerical examples presented the case of longitudinal motion in a thin rod is considered. The random field is discretized on the FE mesh and the element properties assumed piecewise constant. Analytical solutions for the wavenumbers are then found for each element of the random field mesh. When propagating over a finite distance, the total phase change of a wave is given by the summation of the phase changing in each element. Its statistics can be found by propagating the variability through an eigenvalue problem, by a sensitivity analysis or by Monte Carlo simulation. Spatial correlation is then seen to be important in determining the statistics of this phase (mean, variance, etc). This information can in turn be used to calculate the natural frequencies and forced response of finite structures. The statistics of the natural frequencies of rods of finite length are found by this wave approach are compared to those obtained by solving the full finite element problem.

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Contributors

Author: Neil Ferguson

Author: Brian R. Mace

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