Free vibrations of rectangular plates of exponentially varying thickness and with a free edge

1990 ◽  
Vol 140 (3) ◽  
pp. 513-522 ◽  
Author(s):  
V.E. Sonzogni ◽  
S.R. Idelsohn ◽  
P.A.A. Laura ◽  
V.H. Cortinez
Keyword(s):  
Free Edge ◽  
Free Vibrations ◽  
Rectangular Plates ◽  
Varying Thickness

scholarly journals Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates

2002 ◽  
Vol 9 (4-5) ◽  
pp. 193-201 ◽  
Author(s):  
Sergio Ferreira Bastos ◽  
Lavinia Borges ◽  
Fernando A. Rochinha
Keyword(s):  
Experimental Approach ◽  
Natural Frequencies ◽  
Free Edge ◽  
Free Vibrations ◽  
Elastic Parameter ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Elastic Parameters ◽  
Non Destructive ◽  
Parameter Problem

This article deals with the identification of elastic parameters (engineering constants) in sandwich honeycomb orthotropic rectangular plates. A non-destructive method is introduced to identify the elastic parameters through the experimental measurements of natural frequencies of a plate undergoing free vibrations. Four elastic constant are identified. The estimation of the elastic parameter problem is solved by minimizing the differences between the measured and the calculated natural frequencies. The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. The analysis of the results indicates the efficiency of the method.

VIBRATION AND BUCKLING OF SS-F-SS-F RECTANGULAR PLATES LOADED BY IN-PLANE MOMENTS

2001 ◽  
Vol 01 (04) ◽  
pp. 527-543 ◽  
Author(s):  
JAE-HOON KANG ◽  
ARTHUR W. LEISSA
Keyword(s):  
Beam Theory ◽  
Free Edge ◽  
Free Vibrations ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
One Dimensional ◽  
Simply Supported ◽  
Free Vibration Frequency ◽  
Edge Conditions

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon the Poisson's ratio (ν), results are shown for 0≤ν≤0.5, valid for isotropic materials.

Free vibrations of rectangular plates of exponentially varying thickness and with two free edges

1992 ◽  
Vol 19 (4) ◽  
pp. 405-408 ◽  
Author(s):  
P.M. Belles ◽  
M.J. Maurizi ◽  
P.A.A. Laura ◽  
H.C. Sanzi
Keyword(s):  
Free Vibrations ◽  
Rectangular Plates ◽  
Varying Thickness ◽  
Free Edges

Numerical analysis of free vibrations of rectangular plates based on different approaches

2019 ◽  
pp. 33-41
Author(s):  
Oleksandr Grigorenko ◽  
◽  
Maksym Borysenko ◽  
Olena Boychuk ◽  
Volodymyr Novytskyi ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Free Vibrations ◽  
Rectangular Plates
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