A Comprehensive Study of the Free Vibration of Rectangular Plates Resting on Symmetrically-Distributed Uniform Elastic Edge Supports

1989 ◽  
Vol 56 (4) ◽  
pp. 893-899 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Comprehensive Treatment ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Rapid Convergence ◽  
Linear Elastic ◽  
Modes Of Vibration ◽  
Elastic Edge ◽  
Comprehensive Study

An analytical-type solution is developed for the free vibration analysis of rectangular plates with uniform elastic edge support symmetrically distributed about the plate central axes. Both linear elastic rotational and translational support are considered to act simultaneously. Rapid convergence is encountered. Because of the symmetry of the problem, the free vibration modes fall into three distinct families. Eigenvalues are tabulated for the first four modes of vibration of a square plate with identical stiffnesses on each edge and with various ratios of translational to rotational stiffnesses. This represents, to the author’s knowledge, the first comprehensive treatment of this problem.

Free Vibration Analysis of Rectangular Plates with Nonuniform Lateral Elastic Edge Support

1993 ◽  
Vol 60 (4) ◽  
pp. 998-1003 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Elastic Supports ◽  
Proper Frequency ◽  
Elastic Edge ◽  
Edge Stiffness

The method of superposition is utilized to obtain a solution for the free vibration of thin rectangular plates resting on non-uniform lateral elastic edge supports. The stiffness of the elastic supports may have any desired distribution along the edges, including discontinuities and local concentrations. Convergence is found to be rapid. Graphical results are plotted for square plates in order to verify that proper frequency limits are approached as the edge stiffness approach limits of zero and infinity. Results are tabulated for square and nonsquare plates in order that other researchers will have data against which they can compare their results.

scholarly journals Free Vibration of Sandwich Plates and Shells by Using Zig-Zag Function

2009 ◽  
Vol 16 (5) ◽  
pp. 495-503 ◽  
Author(s):  
S. Brischetto ◽  
E. Carrera ◽  
L. Demasi
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Sandwich Plates ◽  
Vibration Modes ◽  
Fundamental Vibration ◽  
First Derivative ◽  
The Core ◽  
Sandwich Plates And Shells ◽  
Plates And Shells ◽  
Free Vibration Response

This paper analyses the free vibration response of sandwich curved and flat panels by introducing the zig-zag function (—1)kζk(ZZF) in the displacement models of classical and higher order two-dimensional shell theories. The main advantage of ZZF is the introduction of a discontinuity in the first derivative, zig-zag effect, of the displacements distribution with correspondence to the core/faces interfaces. Results including and discarding ZZF are compared. Several values of face-to-core stiffness ratio (FCSR) and geometrical plate/shell parameters have been analyzed. Both fundamental vibration modes and those corresponding to high wave numbers are considered in the analysis. It is concluded that: (1) ZZF is highly recommended in the free vibration analysis of sandwich plates and shells; (2) the use of ZZF makes the error almost independent by FCSR parameter; (3) ZZF is easy to implement and its use should be preferred with respect to other `more cumbersome' refined theories.

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