Analysis of the free vibration of a coupled plate/fluid interacting system and interpretation using sub-system modal energy

Abstract

This paper describes a method for describing and quantifying the vibratory behaviour of interacting structural/fluid systems based upon reference to the relative energy associated with each of the sub-systems. The particular case selected is that of a circular plate in interaction with a cylindrical fluid cavity. A theoretical analysis is performed, based upon the Euler Bernoulli and Helmholtz equations combined through a Galerkin technique, from which the natural frequencies and associated mode functions of the interacting system are calculated. The convergence of the analysis is investigated and the opportunity is taken to investigate the sensitivity of the coupled natural frequencies to different assumed mode shapes of the plate in vacuo. Subsequently the coupled mode functions are used to describe details of the energy associated with the plate and the fluid. It is found that presentation of these relative energies renders a satisfactory insight into the vibration behaviour of the coupled system

Measurement and mathematical simulation of acoustic characteristics of an artificially lengthened vocal tract

“…Following our previous studies of acoustic structural interaction (see, for example, [19,20]), we can explain the influence of yielding walls in the vocal tract cavity on the acoustic frequencies by using a simplified model of a coupled mechanicalacoustical system. Similarly, Rabiner and Schaffer [21] considered the effect of yielding walls on acoustical resonances in a simple cylindrical cavity (compliant shell) simulating the vocal tract.…”

Pressure-Based and Potential-Based Differential Quadrature Procedures for Free Vibration of Circular Plates in Contact with Fluid

“…They also solved the problem using the finite element method and studied the effects of fluid compressibility on natral frequencies of the coupled system. Chiba (1994), Amabili et al (1995), Kwak (1997), Kwak and Han (2000), Jeong (2003), Ergin and Ugurlu (2004), Kim and Lee (2005), Gorman and Horáček (2007), Gorman et al (2008), Jeong et al (2009), Askari and Daneshmand (2010), Askari et al (2013), Tariverdilo et al (2013), and Shafiee et al (2014) also solved various circular plate-fluid interaction problems using various analytical or approximate methods.…”