Vibration of vertical rectangular plate in contact with water on one side

Abstract

SUMMARYIn this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain in"nite in the length direction. The e!ects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical-Ritz method is developed to analyse the interaction of the plate}water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh}Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The e!ects of some parameters such as the depth and width of water, the support sti!nesses, location and aspect ratio of the plate and the plate}water size and density ratios on the eigenfrequencies of the plate}water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also con"rmed by comparing the AVMI factor solutions with the analytical-Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of in"nite width and/or in"nite depth.

Natural vibration analysis of rectangular bottom plate structures in contact with fluid

“…An extensive literature survey up to 1998 on the vibration analysis of vertical and bottom plates in contact with fluid has been presented by Zhou and Cheung (2000). Accordingly, analytical methods (Bauer, 1981;Soedel and Soedel, 1994), semi analytical ones (Amabili, 1996;Cheung et al, 1985;Shafiee et al, 2014) and numerical methods (Kerboua et al, 2008;Kwak, 1996;Marcus, 1978) are distinguished.…”

“…Semi-analytical approaches using classical approximate methods for plates and analytical methods for fluid arise as an alternative since the analytical ones are limited to very special and simple models. Cheung and Zhou (2000) and Zhou and Cheung (2000) applied an analytical-Ritz method to analyse the dynamic characteristics of the fluid-structure interaction of vertical and horizontal rectangular plate, neglecting the free surface waves. A theoretical Rayleigh-Ritz dynamic model of the fuel assembly submerged in the coolant of research reactor, leading to free vibration analysis of a bundle of identical rectangular plates fully in contact with an ideal liquid is introduced by Jeong and Kang (2013).…”

Free vibration analysis of a functionally graded rectangular plate in contact with a bounded fluid

“…The boundary conditions for simply supported plates with movable edges (SSM) are: [6][7][8][9][10] where N x or N y and M x or M y are the normal force and the bending moment per unit length, respectively. The boundary conditions for simply supported plates with immovable edges (SSI) are: Three expansions of plate displacements are used to discretize the system for the different boundary conditions.…”

“…Numerous studies have been performed to investigate free and forced vibrations of thin isotropic plates in partial contact with a fluid. Some of the most complete reviews on the subject are presented by Khorshidi [1], Amabili [2,3], Pellicano and Amabili [4], Jeong and Kim [5], Jeong et al [6,7], Kwak [8], Zhou and Cheung [9], Chang and Liu [10], Ergin and Ugurlu [11], Zhou and Liu [12], Ugurlu et al [13] and Kerboua et al [14].…”

Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part I: Free Vibration

“…Amabili [16] and Amabili and Dalpiaz [17] studied the bulging modes of an elastic bottom in circular and annular cylindrical containers partially filled with liquid by using the Ritz method. Cheung and Zhou [18] and Zhou and Cheung [19] analyzed the hydro-elastic vibration of a rectangular container bottom plate and a vertical rectangular plate in contact with water on one side. Moreover, Zhou and Liu [20] studied the free vibration of elastic rectangular tanks partially filled with liquid by using a combination of analytical method and Ritz method.…”