Abstract
Spatial statistics of the modes in an elastic body plays a useful role in predicting certain average elastodynamic responses of complex structures, such as transmitted power or nonlinear spectral energy redistribution. For single wave-speed fields, extensive evidence exists that high-frequency modes in the interior of a generic ray-chaotic body resemble a superposition of plane waves with random amplitudes and phases. This implies centered Gaussian statistics for the field amplitude and a specific form for the two-point correlation function. The former can also be linked to the imaginary part of the Green’s function averaged over a frequency band or over a characteristic ensemble of body realizations, which allows extension to the boundaries and inclusion of effects of finite body size. In the present study we analyze and compare theoretical expressions for a number of spatial statistics, such as intensity distribution, wave-type energy equipartition, and two-point correlation function, with numerical results for an ensemble of 2D plane-strain elastic bodies with rough boundaries.
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