TY - JOUR

T1 - Vibration characteristics of rectangular plate in compressible inviscid fluid

AU - Liao, Chan Yi

AU - Ma, Chien Ching

N1 - Publisher Copyright:
© 2015 Elsevier Ltd. All rights reserved.

PY - 2016/2/3

Y1 - 2016/2/3

N2 - This paper presents a mathematical derivation of the vibration characteristics of an elastic thin plate placed at the bottom of a three dimensional rectangular container filled with compressible inviscid fluid. A set of beam functions is used as the admissible functions of the plate in a fluid-plate system, and the motion of the fluid induced by the deformation of the plate is obtained from a three-dimensional acoustic equation. Pressure from the fluid over the fluid-plate interface is integrated to form a virtual mass matrix. The frequency equation of the fluid-plate system is derived by combining mass, stiffness, and the virtual mass matrix. Solving the frequency equation makes it possible to obtain the dynamic characteristic of the fluid-plate system, such as resonant frequencies, corresponding mode shapes, and velocity of the fluid. Numerical calculations were performed for plates coupled with fluids with various degrees of compressibility to illustrate the difference between compressible and incompressible fluids in a fluid-plate system. The proposed method could be used to predict resonant frequencies and mode shapes with accuracy compared to that of incompressible fluid theory (IFT). The proposed method can be used to analyze cases involving high value of sound velocity, such as incompressible fluids. When the sound velocity approaches infinity, the results obtained for compressible fluids are similar to those of incompressible fluids. We also examined the influence of fluid compressibility on vibration characteristics in which a decrease in sound velocity was shown to correspond to a decrease in resonant frequency. Additional modes, not observed in incompressible fluids, were obtained in cases of low sound velocity, particularly at higher resonant frequencies. Fluid velocity plots clearly reveal that the additional resonant modes can be attributed to the compressible behavior of the fluid.

AB - This paper presents a mathematical derivation of the vibration characteristics of an elastic thin plate placed at the bottom of a three dimensional rectangular container filled with compressible inviscid fluid. A set of beam functions is used as the admissible functions of the plate in a fluid-plate system, and the motion of the fluid induced by the deformation of the plate is obtained from a three-dimensional acoustic equation. Pressure from the fluid over the fluid-plate interface is integrated to form a virtual mass matrix. The frequency equation of the fluid-plate system is derived by combining mass, stiffness, and the virtual mass matrix. Solving the frequency equation makes it possible to obtain the dynamic characteristic of the fluid-plate system, such as resonant frequencies, corresponding mode shapes, and velocity of the fluid. Numerical calculations were performed for plates coupled with fluids with various degrees of compressibility to illustrate the difference between compressible and incompressible fluids in a fluid-plate system. The proposed method could be used to predict resonant frequencies and mode shapes with accuracy compared to that of incompressible fluid theory (IFT). The proposed method can be used to analyze cases involving high value of sound velocity, such as incompressible fluids. When the sound velocity approaches infinity, the results obtained for compressible fluids are similar to those of incompressible fluids. We also examined the influence of fluid compressibility on vibration characteristics in which a decrease in sound velocity was shown to correspond to a decrease in resonant frequency. Additional modes, not observed in incompressible fluids, were obtained in cases of low sound velocity, particularly at higher resonant frequencies. Fluid velocity plots clearly reveal that the additional resonant modes can be attributed to the compressible behavior of the fluid.

UR - http://www.scopus.com/inward/record.url?scp=84947710242&partnerID=8YFLogxK

U2 - 10.1016/j.jsv.2015.09.031

DO - 10.1016/j.jsv.2015.09.031

M3 - 期刊論文

AN - SCOPUS:84947710242

VL - 362

SP - 228

EP - 251

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

ER -