Modal-interaction approach to the strong structural–acoustic coupling of an elastic Helmholtz resonator and an acoustic cavity containing a heavy fluid

Abstract

This paper focuses on the development of a method for the accurate representation of the strong structural–acoustic coupling between an elastic Helmholtz resonator, a heavy fluid and an impedance tube. The Helmholtz resonator has an elastic wall and is connected to the impedance tube, yielding a system with two acoustic cavities coupled through a neck and the fluid–structure interaction between a liquid medium and a plate. The proposed analytical formulation is based on the modal superposition method in combination with a lumped parameter model of the neck. The effect of the evanescent waves is taken into account in the form of both the inertial attached length of the neck and the terms of the evanescent pressure modes in the governing equations, which are omitted in other methods. The formulation of the evanescent pressure field is redefined to include the reflected waves, thus expanding the application to the acoustic cavity of an arbitrary shape. Strong coupling between the heavy fluid and the plate is accomplished with the implementation of the non-resonant acoustic modes. Furthermore, the improved performance of the model for moderately thick plates is achieved with the combined approach of the Mindlin–Reissner theory mode shapes and the Kirchhoff–Love theory governing equations. The proposed model is validated with FEA simulations of three different resonator configurations and compared to other applicable methods. The results demonstrate substantially increased accuracy in the predicted response of the coupled structural–acoustic system.