Coupled vibratory characteristics of a rectangular container bottom plate

The natural frequencies of an elastic thin plate placed into a rectangular hole and connected to the rigid bottom slab of a rectangular container filled with fluid having a free surface are studied. The fluid is assumed to be incompressible, inviscid and irrotational, and the effect of surface waves is neglected. An analytical-Ritz method is developed to study the vibratory characteristics of the plate in contact with the fluid. First of all, the exact expression of the motion of the fluid is obtained, in which the unknown coefficients are determined by using the method of separation of variables and the method of Fourier series expansion. Then, the Ritz approach is used to obtain the frequency equation of the system. The vibrating beam functions are adopted as the admissible functions for the wet-mode expansion of the plate, and the added virtual mass incremental (AVMI) matrices are obtained for plates with arbitrary boundary conditions. Finally, a convergence study is carried out and some numerical results are given. The accuracy of AVMI factor solutions is discussed by comparing with the more accurate analytical-Ritz solutions presented in this paper. Furthermore, It is seen that the present method is also suitable for the vibration analysis of rectangular plates in contact with infinite fluid by taking the finite, but larger size fluid domain as an approximation in the computation.

[1]  Marco Amabili,et al.  VIBRATIONS OF BASE PLATES IN ANNULAR CYLINDRICAL TANKS: THEORY AND EXPERIMENTS , 1998 .

[2]  W S Vorus,et al.  THE ADDED MASS MATRIX IN SHIP VIBRATION, USING A SOURCE DISTRIBUTION RELATED TO THE FINITE ELEMENT GRID OF THE SHIP STRUCTURE , 1982 .

[3]  W. G. Price,et al.  Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid , 1987 .

[4]  Moon K. Kwak,et al.  Vibration of Circular Plates in Contact With Water , 1991 .

[5]  Kosuke Nagaya,et al.  Vibration of a plate with arbitrary shape in contact with a fluid , 1984 .

[6]  Moon K. Kwak,et al.  Hydroelastic vibration of rectangular plates , 1996 .

[7]  M. Amabili,et al.  NATURAL FREQUENCIES AND MODES OF FREE-EDGE CIRCULAR PLATES VIBRATING IN VACUUM OR IN CONTACT WITH LIQUID , 1995 .

[8]  M. Chiba,et al.  Axisymmetric Free Hydroelastic Vibration of a Flexural Bottom Plate in a Cylindrical Tank Supported on an Elastic Foundation , 1994 .

[9]  Y. K. Cheung,et al.  Dynamic analysis of prismatic structures surrounded by an infinite fluid medium , 1985 .

[10]  Helmut F. Bauer,et al.  Hydroelastic vibrations in a rectangular container , 1981 .

[11]  Horace Lamb,et al.  On the Vibrations of an Elastic Plate in Contact with Water , 1920 .

[12]  W.Kay Meyerhoff.  Added Masses of Thin Rectangular Plates Calculated from Potential Theory , 1970 .

[13]  M. Chiba,et al.  Nonlinear Hydroelastic Vibration of a Cylindrical Tank with an Elastic Bottom, Containing Liquid. Part II: Linear Axisymmetric Vibration Analysis , 1993 .

[14]  Marco Amabili,et al.  FREE VIBRATIONS OF ANNULAR PLATES COUPLED WITH FLUIDS , 1996 .

[15]  M S Marcus.  A FINITE-ELEMENT METHOD APPLIED TO THE VIBRATION OF SUBMERGED PLATES , 1978 .

[16]  Marco Amabili,et al.  FREE VIBRATIONS OF CIRCULAR PLATES COUPLED WITH LIQUIDS: REVISING THE LAMB PROBLEM , 1996 .

[17]  Hisao Kondo,et al.  Axisymmetric Free Vibration Analysis of a Circular Cylindrical Tank , 1981 .

[18]  M. Amabili,et al.  EFFECT OF FINITE FLUID DEPTH ON THE HYDROELASTIC VIBRATIONS OF CIRCULAR AND ANNULAR PLATES , 1996 .

[19]  W. Soedel,et al.  On the Free and Forced Vibration of a Plate Supporting a Freely Sloshing Surface Liquid , 1994 .