On the Determination of the Fundamental Frequency of Vibration of Clamped Rectangular Plates of Variable Thickness

1978 ◽  
Vol 100 (4) ◽  
pp. 703-705 ◽  
Author(s):  
P. A. A. Laura ◽  
L. E. Luisoni
Keyword(s):  
Fundamental Frequency ◽  
Variable Thickness ◽  
Variational Approach ◽  
Practical Interest ◽  
Rectangular Plates ◽  
Polynomial Approximations ◽  
Plates Of Variable Thickness

It is shown that use of polynomial approximations and a variational approach allows for a very simple determination of the fundamental frequency of vibration in two cases of practical interest and results are obtained for several values of width to length ratios.

scholarly journals Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
Dongyan Shi ◽  
Qingshan Wang ◽  
Xianjie Shi ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Practical Interest ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Solution Algorithms ◽  
Wide Range

A generalized Fourier series solution based on the first-order shear deformation theory is presented for the free vibrations of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions, a class of problem which is of practical interest and fundamental importance but rarely attempted in the literatures. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures. Under the current framework, the one displacement and two rotation functions are generally sought, regardless of boundary conditions, as an improved trigonometric series in which several supplementary functions are introduced to remove the potential discontinuities with the displacement components and its derivatives at the edges and to accelerate the convergence of series representations. All the series expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. The effectiveness and reliability of the presented solution are demonstrated by comparing the present results with those results published in the literatures and finite element method (FEM) data, and numerous new results for moderately thick rectangular plates with nonuniform thickness and elastic restraints are presented, which may serve as benchmark solution for future researches.

scholarly journals To Calculation of Rectangular Plates on Periodic Oscillations

2018 ◽  
Vol 245 ◽  
pp. 01003 ◽  
Author(s):  
Rustamkhan Abdikarimov ◽  
Dadakhan Khodzhaev ◽  
Nikolay Vatin
Keyword(s):  
Variable Thickness ◽  
Dynamic Instability ◽  
Rheological Parameters ◽  
Problem Solution ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Weakly Singular Kernel ◽  
Parametric Oscillations ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

Geometrically nonlinear mathematical model of the problem of parametric oscillations of a viscoelastic orthotropic plate of variable thickness is developed using the classical Kirchhoff-Love hypothesis. The technique of the nonlinear problem solution by applying the Bubnov-Galerkin method at polynomial approximation of displacements (and deflection) and a numerical method that uses quadrature formula are proposed. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Parametric oscillations of viscoelastic orthotropic plates of variable thickness under the effect of an external load are investigated. The effect on the domain of dynamic instability of geometric nonlinearity, viscoelastic properties of material, as well as other physical-mechanical and geometric parameters and factors are taken into account. The results obtained are in good agreement with the results and data of other authors.

Deflection and Moment Data for Rectangular Plates of Variable Thickness

1972 ◽  
Vol 39 (3) ◽  
pp. 814-815 ◽  
Author(s):  
P. Petrina ◽  
H. D. Conway
Keyword(s):  
Variable Thickness ◽  
Rectangular Plates ◽  
Direction Parallel ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Plates Of Variable Thickness

Numerical values of deflections and moments are given for uniformly loaded rectangular plates with a pair of opposite sides simply supported and the others either simply supported or clamped. The plates are tapered in a direction parallel to the simply supported sides. Data are given for two tapers and for plate aspect ratios equal to 1 (square plates), 1.5 and 2.

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