Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid
ABSTRACT An analytical method for the linear free vibration of a circular plate submerged in a fluid was developed by the Rayleigh–Ritz method based on the Fourier–Bessel series expansion. It is assumed that the plate is clamped at an offcenter location of a rigid cylindrical container and the fluid bisected by the plate in the container is non-viscous and compressible. Since a combination of the dry modal functions of the circular plate can approximate the wet vibration modes, the functions were used to form a set of linearly independent functions of the Rayleigh–Ritz method. It was found that the theoretical results could predict well the fluid-coupled natural frequencies with excellent accuracy compared with the finite element analysis results. The effects of the fluid compressibility and the offcenter distance on the natural frequencies were also observed.
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ABSTRACT: Dynamics of mechanical system can be analyzed with obtaining motion equations of systems. These equations are provided with various methods, which are proposed and accepted by community. Every system cannot be simplify unless negligible boundary condition has exist. In this article, Rayleigh-Ritz Solution Method are explained. For demonstration of the method, longitudinal vibration of a beam is chosen. Discretization has been applied with Rayleigh-Ritz Method and Finite Element Direct Method. After obtaining rigidity and mass matrix, Sweeping Method is applied for eigensolution. Then Solutions are compared with exact solution. In result, discretization ability has been demonstrated.3rd International Scientific Conference on Engineering ”Manufacturing and Advanced Technologies” MAT 2014, Mostar Bosnia and Herzegovina; 09/2014
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ABSTRACT: An analytical method for the hydroelastic vibration of a vessel composed of an upper annular plate and a lower circular plate is developed by the Rayleigh-Ritz method. The two plates are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies comparing with the finite element analysis resultTransactions of the Korean Society for Noise and Vibration Engineering. 01/2005; 15(8).
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ABSTRACT: Vibration of circular plates in contact with fluid has extensive applications in the industry. This paper derives added mass and frequencies for asymmetric free vibration of coupled system including clamped circular plate in contact with incompressible bounded fluid. Considering small oscillations induced by the plate vibration in the incompressible and inviscid fluid, velocity potential function is used to describe the fluid motion. Derivation uses Kirchoff’s thin plate theory. Two approaches are used to derive the free vibration frequency of the system. The solutions include an analytical solution employing Fourier–Bessel series and a variational formulation applied simultaneously on the plate and fluid. Strong correlation is found between free vibration frequencies of the two solutions. Finally the effect of fluid depth on the added mass and free vibration frequencies of the coupled system is investigated.Applied Mathematical Modelling 01/2013; 37(s 1–2):228–239. · 2.16 Impact Factor