# Eigenproblem for an ocean acoustic waveguide with random depth dependent sound speed

06 Jul 2014-pp 226-226

TL;DR: In this article, a Rayleigh-Ritz approximation for the depth eigenproblem with random sound speed was proposed, where the authors used the deterministic waveguide model for range and depth dependent acoustic waveguides.

Abstract: A recently developed deterministic FE model for range and depth dependent acoustic waveguides (Vendhan et al, J. Acoust. Am., 126, 3319–3326, 2010) may be extended to a medium with random properties. Such a model would require the eigensolution for a depth dependent waveguide at the far field of the FE domain. The aim of the present paper is to study the depth eigenproblem with random sound speed, which may be written as d2Z/dz2 + (1/k1 z )Z = 0 (1) where z denotes the depth coordinate, Z(z) the depth function and k z the depth wavenumber given by k2 z = (ω2/c2(z)-k1 r ) (2) In Eq.2, r k denotes the radial wavenumber of a cylindrically symmetric waveguide and c(z) the sound speed which is assumed to be random variable in the form c(z) = c (z) (1+a) where a denotes a small random fluctuation of the sound speed with c(z)as the mean value. The depth eigenmodes of a deterministic isovelocity waveguide are adopted to set up a Rayleigh-Ritz approximation for the depth eigenproblem (see Eq.1) in the form [K]{ψ} = λ [M]{ψ} (3) Choosing a perturbation approach (Nakagiri and Hisada, Proc. Intl. Conf. on FEM, 206–211, 1982; Ghanem and Spanos, Stochastic Finite Elements: A Spectral Approach, Springer Verlag, 1991) an approximate solution may be written in the form of a Taylor series as [M] = [M] + α [M 1 ] + α2/2[M 2 ] (4a)λ = λ + αλ 1 + (α2/2)λ 2 (4b){ψ} = {ψ} + α{ψ 1 } + α2/2{ψ 2 } (4c) where an over bar denotes deterministic quantity.

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21 Oct 2016

TL;DR: In this article, a finite element model for elastic scattering by axisymmetric bodies submerged in a heterogeneous ocean acoustic waveguide was developed, and the primary aim of this work was to develop an elastic scattering model.

Abstract: : The primary aim of this study is to develop a finite element model for elastic scattering by axisymmetric bodies submerged in a heterogeneous ocean acoustic waveguide.