Free vibrations of periodically point-supported rectangular plates

1989 ◽  
Vol 132 (3) ◽  
pp. 491-509 ◽  
Author(s):  
A.V. Bapat ◽  
S. Suryanarayan
Keyword(s):  
Free Vibrations ◽  
Rectangular Plates

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

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.

Comments on “New exact solutions for free vibrations of thin orthotropic rectangular plates”

2014 ◽  
Vol 107 ◽  
pp. 745-746 ◽  
Author(s):  
Arian Bahrami ◽  
Mansour Nikkhah Bahrami ◽  
Mohammad Reza Ilkhani
Keyword(s):  
Exact Solutions ◽  
Free Vibrations ◽  
Rectangular Plates ◽  
New Exact Solutions

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.

scholarly journals EQUATION DECOMPOSITION METHOD FOR SOLVING OF PROBLEMS OF STATICS, VIBRATIONS AND STABILITY OF THIN-WALLED CONSTRUCTIONS

2020 ◽  
Vol 16 (2) ◽  
pp. 63-70
Author(s):  
Elena Koreneva ◽  
Valery Grosman
Keyword(s):  
Decomposition Method ◽  
Middle Surface ◽  
Free Vibrations ◽  
Rectangular Plates ◽  
Effective Equation ◽  
Transverse Loads ◽  
Approximate Analytical Solutions ◽  
Thin Walled ◽  
Definition Of ◽  
Elastically Supported

The work suggests the effective equation decomposition method (EDM) for solving of statics, vibrations and stability problems of thin-walled constructions. This method is based on the partition of the initial problem on the consideration of more simple auxiliary problems. The additional unknown functions are introduced for definition of the sought solutions. The paper shows the method’s advantages on the examples of the boundary value problems for rectangular areas. The problem of anisotropic plate resting on an elastic subgrade and subjected to an action of expanding forces acting in the middle surface and to transverse loads is under study. The plate’s edges are elastically supported. Also free vibrations of the rectangular plates of variable thickness with different boundary conditions were under consideration. The approximate analytical solutions with high exactness are obtained.

Exact Solutions for the Free Vibrations and Buckling of Rectangular Plates With Linearly Varying In-Plane Loading

2001 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jae-Hoon Kang
Keyword(s):  
Solution Procedure ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Buckling Loads ◽  
Simply Supported ◽  
Edge Conditions ◽  
Elastically Supported

Abstract An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.

Sign in / Sign up

Export Citation Format

Share Document