Circular Plates on Elastic Foundations Modelled with Annular Plates

2009 ◽  
Author(s):  
M. Utku ◽  
C. Citipitioglu ◽  
I. Inceleme
Keyword(s):  
Circular Plates ◽  
Elastic Foundations ◽  
Annular Plates

Circular plates on elastic foundations modelled with annular plates

2000 ◽  
Vol 78 (1-3) ◽  
pp. 365-374 ◽  
Author(s):  
Mehmet Utku ◽  
Ergin Çıtıpıtıoğlu ◽  
İlker İnceleme
Keyword(s):  
Circular Plates ◽  
Elastic Foundations ◽  
Annular Plates

scholarly journals INVESTIGATION OF THE DYNAMIC BEHAVIOUR OF NON-UNIFORM THICKNESS CIRCULAR PLATES RESTING ON WINKLER AND PASTERNAK FOUNDATIONS

2020 ◽  
Vol 60 (2) ◽  
pp. 127-144
Author(s):  
Saheed Salawu ◽  
Gbeminiyi Sobamowo ◽  
Obanishola Sadiq
Keyword(s):  
Natural Frequency ◽  
Circular Plate ◽  
Analytical Solutions ◽  
Dynamic Behaviour ◽  
Circumferential Stress ◽  
Thickness Variation ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Weighted Residuals ◽  
Elastic Foundations

The study of the dynamic behaviour of non-uniform thickness circular plate resting on elastic foundations is very imperative in designing structural systems. This present research investigates the free vibration analysis of varying density and non-uniform thickness isotropic circular plates resting on Winkler and Pasternak foundations. The governing differential equation is analysed using the Galerkin method of weighted residuals. Linear and nonlinear case is considered, the surface radial and circumferential stresses are also determined. Thereafter, the accuracy and consistency of the analytical solutions obtained are ascertained by comparing the existing results available in pieces of literature and confirmed to be in a good harmony. Also, it is observed that very accurate results can be obtained with few computations. Issues relating to the singularity of circular plate governing equations are handled with ease. The analytical solutions obtained are used to determine the influence of elastic foundations, homogeneity and thickness variation on the dynamic behaviour of the circular plate, the effect of vibration on a free surface of the foundation as well as the influence of radial and circumferential stress on mode shapes of the circular plate considered. From the results, it is observed that a maximum of 8.1% percentage difference is obtained with the solutions obtained from other analytical methods. Furthermore, increasing the elastic foundation parameter increases the natural frequency. Extrema modal displacement occurs due to radial and circumferential stress. Natural frequency increases as the thickness of the circular plate increases, Conversely, a decrease in natural frequency is observed as the density varies. It is envisioned that; the present study will contribute to the existing knowledge of the classical theory of vibration.

Nonlinear Axisymmetric Static Analysis of Shallow Spherical Shells on Winkler-Pasternak Foundation

1987 ◽  
Vol 109 (1) ◽  
pp. 28-34 ◽  
Author(s):  
R. K. Jain ◽  
Y. Nath
Keyword(s):  
Static Analysis ◽  
Nonlinear Static Analysis ◽  
Normal Displacement ◽  
Pasternak Foundation ◽  
Chebyshev Series ◽  
Circular Plates ◽  
Spherical Shells ◽  
Linear Elastic ◽  
Annular Plates ◽  
Edge Conditions

In the present investigation nonlinear static analysis of thin axisymmetric circular plates, annular plates and shallow spherical shells resting on linear elastic Winkler-Pasternak foundation under uniformly distributed normal loads, has been carried out. Donnell-type governing differential equations expressed in terms of normal displacement and stress function have been employed and solved using Chebyshev series. A convergence study for Chebyshev series has been conducted. The influence of foundation stiffness parameters (K and G) on the response of circular plates, annulus and spherical shells has been studied for both the clamped and simply supported immovable edge conditions. A few typical snap-through results for shells are also included.

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