An asymptotic analysis for the coupled dispersion characteristics of a structural acoustic waveguide

Abstract

Analytical expressions are derived, using asymptotics, for the fluid–structure coupled wavenumbers in a one-dimensional (1-D) structural acoustic waveguide. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation with an added term due to the fluid–structure coupling. As a result of this coupling, the prior uncoupled structural and acoustic wavenumbers, now become coupled structural and acoustic wavenumbers. A fluid-loading parameter ε, defined as the ratio of mass of fluid to mass of the structure per unit area, is introduced which when set to zero yields the uncoupled dispersion equation. The coupled wavenumber is then expressed in terms of an asymptotic series in ε. Analytical expressions are found as ε is varied from small to large values. Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. This systematic derivation helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Though the asymptotic expansion used is limited to the first-order correction factor, the results are close to the numerical results. A general trend is that a given wavenumber branch transits from a rigid-walled solution to a pressure-release solution with increasing ε. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency.