Frequency response of rectangular plate structures in contact with fluid subjected to harmonic point excitation force

Abstract Numerical procedure for the forced vibration analysis of bottom and vertical rectangular plate structures in contact with fluid, subjected to internal point harmonic excitation force is developed. The procedure is based on the assumed mode method for free vibration calculation and mode superposition method for forced vibration analysis. Structural model covers Mindlin rectangular plates and stiffened panels. Lagrange's equation of motion is utilized to formulate the eigenvalue problem taking into account potential and kinetic energies of a plate and reinforcements, and fluid kinetic energy which is calculated according to potential flow theory, respectively. From the boundary conditions for the fluid and structure the fluid velocity potential is derived and it is utilized for the calculation of added mass using the assumed modes. The developed theoretical model and in-house code are verified with extensive numerical examples related to forced vibration of bare plates and stiffened panels in contact with different fluid domains. Comparisons of the results with those obtained by a general purpose finite element (FE) software confirmed high accuracy of the presented numerical procedure.

[1]  J. Mirzapour,et al.  Asymmetric free vibration of circular plate in contact with incompressible fluid , 2013 .

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

[3]  Y. K. Cheung,et al.  Coupled vibratory characteristics of a rectangular container bottom plate , 2000 .

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

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

[6]  Moon K. Kwak,et al.  HYDROELASTIC VIBRATION OF CIRCULAR PLATES , 1997 .

[7]  Yu Takeda,et al.  Fundamental Vibration Modes of Stiffened Tank Plate in Contac with Fluid , 2000 .

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

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

[10]  Wei-Hui Wang,et al.  Analysis and reversal of dry and hydroelastic vibration modes of stiffened plates , 2011 .

[11]  E D Schaefer.  A PRACTICAL GUIDE FOR DETERMINING THE VIBRATION CHARACTERISTICS OF PLATE STRUCTURES , 1979 .

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

[13]  Kyeong-Hoon Jeong,et al.  Free vibration of multiple rectangular plates coupled with a liquid , 2013 .

[14]  Y. K. Cheung,et al.  Vibration of vertical rectangular plate in contact with water on one side , 2000 .

[15]  Mojtaba Mahzoon,et al.  Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid , 2014 .

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

[17]  Hiroshi Nishino,et al.  Study on Vibration Characteristics of Stiffened Plates in Contact with Water by Use of Energy Method (1st Report) , 1995 .

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

[19]  Nikola Vladimir,et al.  Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method , 2015 .

[20]  Jong Hoon Chung,et al.  Vibration Analysis of Orthotropic Mindlin Plates with Edges Elastically Restrained against Rotation , 1993 .

[21]  Y. Kerboua,et al.  Vibration analysis of rectangular plates coupled with fluid , 2008 .

[22]  Nikola Vladimir,et al.  Natural vibration analysis of vertical rectangular plates and stiffened panels in contact with fluid on one side , 2016 .

[23]  M. Karimi,et al.  Vibration analysis of rectangular Mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method , 2010 .

[24]  Raymond D. Mindlin,et al.  FLEXURAL VIBRATIONS OF RECTANGULAR PLATES , 1955 .

[25]  F. Montero de Espinosa,et al.  On the resonance frequencies of water-loaded circular plates , 1984 .

[26]  Shahrokh Hosseini-Hashemi,et al.  Natural frequencies of rectangular Mindlin plates coupled with stationary fluid , 2012 .

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

[28]  Kookhyun Kim,et al.  Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method , 2012 .

[29]  N W McLachlan,et al.  The accession to inertia of flexible discs vibrating in a fluid , 1932 .

[30]  Nikola Vladimir,et al.  Natural vibration analysis of stiffened panels with arbitrary edge constraints using the assumed mode method , 2015 .

[31]  Nikola Vladimir,et al.  Approximate natural vibration analysis of rectangular plates with openings using assumed mode method , 2013 .

[32]  Y. K. Cheung,et al.  HYDROELASTIC VIBRATION OF A CIRCULAR CONTAINER BOTTOM PLATE USING THE GALERKIN METHOD , 2002 .