Effects of Residual Stress on the Hydro-Elastic Vibration of Circular Diaphragm

Abstract

<p class="MsoNormal" style="text-align:justify;"> <span lang="EN-US">The effects of residual stress on the hydro-elastic vibration of circular diaphragm are theoretically investigated by using the added mass approach. The Kirchhoff theory of plates is used to model the elastic thin circular diaphragm on an aperture of an infinite rigid wall and in contact with a fluid on one side. The fluid is assumed to be incompressible and inviscid and the velocity potential is used to describe its irrotational motion. A non-dimensional tension parameter is defined, and the effects of the tension parameter on the frequency parameters and mode shapes of the diaphragm in the air are presented. The Hankel transform is applied to solve the fluid-diaphragm coupled system; boundary conditions are expressed by integral equations. Finally, the effects of residual stress on the non-dimensional added virtual mass incremental (NAVMI) factors of the diaphragm contact with a fluid on one side are investigated. It is found that the effects of the residual stress cannot be neglected when the edges of the circular diaphragm are clamped. The effects of residual stress for NAVMI factors can be increases 11% when the non-dimensional tension parameter is 1000.</span><span lang="EN-US"><o:p></o:p></span> </p&gt

The forced vibration of the system consisting of an elastic plate, compressible viscous fluid and rigid wall

“…Fu and Price (1987) studied the vibration of a cantilevered plate partially or totally immersed within the fluid and the effect of the free surface on the resonance frequencies of the plate was established. The effect of the initial stretching of the circular plate with clamped edge on its hydroelastic vibration was studied in a paper by Zhao and Yu (2012). This effect is taken into account through the influence of the initial stretching on the NAVMI factors.…”

“…It is evident that in many cases (for instance, in the cases where the wave length is less significant than the thickness of the plate) more accurate results in the qualitative and quantitative sense, can be obtained by employing the exact equations for describing the plate motion. Moreover, in the foregoing investigations (except the paper by Zhao and Yu (2012)) the initial strains (or stresses) in plates, which can be one of their characteristics, are not taken into account. These two characteristics, namely the use of the exact equations of plate motion and the existence of initial stresses in the plate are taken into consideration in a paper by Bagno et al (1994) and others, a review of which is given in a survey paper by Bagno and Guz (1997).…”

The influence of the rheological parameters of a hydro-viscoelastic system consisting of a viscoelastic plate, viscous fluid and rigid wall on the frequency response of this system

“…On the basis of this assumption the Rayleigh quotient is employed to determine the natural frequencies of such a hydro-elastic system. Later, the NAVMI approach was also employed in investigations by Kwak and Kim (1991), Fu and Price (1987), Zhao and Yu (2012) and many others reviewed therein. At the same time, there are also investigations, such as Tubaldi and Armabili (2013), Charman and Sorokin (2005) and others listed therein, that were made without employing the NAVMI approach.…”