FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES

2002 ◽  
Vol 252 (3) ◽  
pp. 429-442 ◽  
Author(s):  
E. PAN ◽  
P.R. HEYLIGER
Keyword(s):  
Free Vibrations ◽  
Elastic Plates ◽  
Simply Supported

On nonlinear free vibrations of simply supported uniform beams

1992 ◽  
Vol 159 (3) ◽  
pp. 527-531 ◽  
Author(s):  
S.R.R. Pillai ◽  
B. Nageswara Rao
Keyword(s):  
Free Vibrations ◽  
Simply Supported

On the Singularities in Reissner’s Theory for the Bending of Elastic Plates

1986 ◽  
Vol 53 (1) ◽  
pp. 220-222 ◽  
Author(s):  
W. S. Burton ◽  
G. B. Sinclair
Keyword(s):  
Plate Theory ◽  
Elastic Plates ◽  
Singular Behavior ◽  
Simply Supported ◽  
Reissner’S Theory

Wedge-shaped elastic plates under bending, with the edges forming the wedge vertex being either stress-free, clamped or simply supported, are characterized as to possible singular behavior within the context of Reissner’s plate theory.

Nonlinear Vibration of Thin Elastic Plates, Part 2: Internal Resonance by Amplitude-Incremental Finite Element

1984 ◽  
Vol 51 (4) ◽  
pp. 845-851 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
S. Y. Wu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Internal Resonance ◽  
Harmonic Excitation ◽  
Plate Element ◽  
Elastic Plates ◽  
Simply Supported ◽  
Speed Up ◽  
Numerical Process ◽  
Thin Elastic Plates

The simple amplitude-incremental triangular plate element derived in Part 1 of this paper is applied to treat the large-amplitude periodic vibrations of thin elastic plates with existence of internal resonance. A simply supported rectangular plate with immovable edges (b/a = 1.5) and having linear frequencies ω13 = 3.45 ω11 is selected as a typical example. The frequency response of free vibration as well as forced vibration under harmonic excitation are computed. To the best knowledge of the authors, these very interesting results for such plate problems have not appeared in literature previously. Some special considerations to simplify and to speed up the numerical process are also discussed.

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.

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