Free Vibrations of a Circular Plate

1962 ◽  
Vol 10 (4) ◽  
pp. 668-674 ◽  
Author(s):  
Walter P. Reid
Keyword(s):  
Circular Plate ◽  
Free Vibrations

An Integral Equation Method for Free Vibration of Circular Plate with Concentrated Mass at Arbitrary Positions

2011 ◽  
Vol 255-260 ◽  
pp. 1830-1835 ◽  
Author(s):  
Gang Cheng ◽  
Quan Cheng ◽  
Wei Dong Wang
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Concentrated Mass

The paper concerns on the free vibrations of circular plate with arbitrary number of the mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green’s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

Free vibrations of an isotropic nonhomogeneous circular plate

AIAA Journal ◽  
1971 ◽  
Vol 9 (5) ◽  
pp. 963-964 ◽  
Author(s):  
D. M. MlSHRA ◽  
A. K. DAS
Keyword(s):  
Circular Plate ◽  
Free Vibrations

Free Vibration and Tension Buckling of Circular Plates With Diametral Point Forces

1990 ◽  
Vol 57 (4) ◽  
pp. 995-999 ◽  
Author(s):  
E. F. Ayoub ◽  
A. W. Leissa
Keyword(s):  
Circular Plate ◽  
Tensile Force ◽  
Ritz Method ◽  
Compressive Force ◽  
Free Vibrations ◽  
Plane Elasticity ◽  
Mode Shapes ◽  
Simply Supported ◽  
Symmetry Classes ◽  
Tensile Forces

This paper presents the first known results for the free vibrations of a circular plate subjected to a pair of static, concentrated forces acting on the boundary at opposite ends of a diameter. The closed-form exact solution of the plane elasticity problem is used to provide the in-plane stress distribution for the vibration problem. A proper procedure using the Ritz method is developed for solving the latter problem for clamped, simply supported, or free boundary conditions. Numerical results are given for the vibration frequencies of a simply supported circular plate, which separate into four symmetry classes of mode shapes. Compressive buckling loads for each symmetry class are determined as a special case as the frequencies decrease to zero with increasing compressive force. Tracking the frequency versus loading data with increasing tensile forces shows that buckling due to tensile force can also occur, and the critical value of the force is found.

A Theoretical Analysis of Transient Sound Radiation From a Clamped Circular Plate

1984 ◽  
Vol 51 (1) ◽  
pp. 41-47 ◽  
Author(s):  
A. Akay ◽  
M. Tokunaga ◽  
M. Latcha
Keyword(s):  
Theoretical Analysis ◽  
Circular Plate ◽  
Impulse Response ◽  
Sound Radiation ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Surface Integral ◽  
Pressure Impulse

A theoretical analysis of transient sound radiation from a clamped circular plate is given using a pressure impulse response method. The vibration response of the plate to a transient point force is obtained. The modal pressure impulse response functions for the plate are derived from the Rayleigh surface integral and numerically convoluted with the modal acceleration response of the plate. The impulse response functions are closely related to the mode shapes and the geometry of the problem. They relate the spatial domain to the temporal domain of the pressure waves. The pressure impulse response waveforms are given for a number of plate modes and the changes in the waveforms with distance from the plate are shown. Sound radiation due to forced and free vibrations of the plate are discussed.

scholarly journals Added Mass of Fluid and Fundamental Frequencies of a Horizontal Elastic Circular Plate Vibrating in Fluid of Constant Depth

2017 ◽  
Vol 64 (3-4) ◽  
pp. 163-186
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Fluid Motion ◽  
Added Mass ◽  
Free Vibrations ◽  
Constant Depth ◽  
Infinite Layer ◽  
Pressure Load ◽  
Fundamental Frequencies ◽  
Elastic Circular Plate

AbstractThe paper deals with free vibrations of a horizontal thin elastic circular plate submerged in an infinite layer of fluid of constant depth. The motion of the plate is accompanied by the fluid motion, and thus, the pressure load on this plate results from displacements of the plate in time. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the gap between the plate and the fluid bottom. In theoretical description of this phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. This coupling leads to the so-called co-vibrating (added) mass of fluid, which significantly changes the fundamental frequencies (eigenfrequencies) of the plate. In formulation of the problem, a linear theory of small deflections of the plate is employed. At the same time, one assumes the potential fluid motion with the potential function satisfying Laplace’s equation within the fluid domain and appropriate boundary conditions at fluid boundaries. In order to solve the problem, the infinite fluid domain is divided into sub-domains of simple geometry, and the solution of problem equations is constructed separately for each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.

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