Coupled vibration analysis of acoustic field including flexible structures

Abstract

This paper describes vibration analysis methods using modal analysis for coupled vibration between an acoustic field and flexible structures. In particular, the case where flexible structures are installed inside of an acoustic field is described in this paper. Numerical analysis methods such as finite element method and finite-difference time-domain method have been used to analyze coupled vibrations. Spatial discretization is used in these numerical analyses; however, the proposed analysis methods can analyze coupled vibrations without using spatial discretization because the proposed methods use the superposition of the vibration modes of the original acoustic field as a continuous system. Mathematically, superposition of vibration modes is a kind of series. The coupled vibration is expressed by the series that corresponds to the superposition of the vibration modes in the proposed methods. Based on this concept, two methods are proposed in this paper: one is referred to as built-in method, and the other is referred to as binding method in this research. The characteristics of the flexible structures are built in the acoustic field in the built-in method. In contrast, the acoustic field and flexible structures are bound by sufficiently stiff elastic bodies in the binding method. The equations of motion of the analytical models were derived, and the effectiveness of the proposed method was verified through simulations.