TITLE:
Effects of Residual Stress on the Hydro-Elastic Vibration of Circular Diaphragm
AUTHORS:
Junfeng Zhao, Song Yu
KEYWORDS:
Circular Diaphragm; Residual Stress; Hankel Transform; Frequency Parameter; Mode Shape; NAVMI
JOURNAL NAME:
World Journal of Mechanics,
Vol.2 No.6,
December
31,
2012
ABSTRACT: 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.