AXISYMMETRIC VIBRATION OF A CIRCULAR PLATE WITH EXPONENTIAL THICKNESS VARIATION

1996 ◽  
Vol 192 (1) ◽  
pp. 35-42 ◽  
Author(s):  
B. Singh ◽  
V. Saxena
Keyword(s):  
Circular Plate ◽  
Thickness Variation ◽  
Axisymmetric Vibration

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.

scholarly journals Axisymmetric Vibration for Micropolar Porous Thermoelastic Circular Plate

2017 ◽  
Vol 22 (3) ◽  
pp. 583-600 ◽  
Author(s):  
R. Kumar ◽  
P. Kaushal ◽  
R. Sharma
Keyword(s):  
Circular Plate ◽  
Axisymmetric Problem ◽  
Volume Fraction ◽  
Hankel Transform ◽  
Specific Model ◽  
Axisymmetric Vibration ◽  
Physical Domain ◽  
Special Cases ◽  
Eigen Value ◽  
Field Temperature

AbstractThe present investigation is concerned with a two dimensional axisymmetric problem in a homogeneous isotropic micropolar porous thermoelastic circular plate by using the eigen value approach. The Laplace and Hankel transform are used to solve the problem. The expression of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain subjected to thermomechanical sources. A computer algorithm is developed for numerical computations. To obtain the resulting quantities in a physical domain, a numerical inversion technique is used. The resulting quantities are depicted graphically for a specific model. Some special cases are also deduced.

Axisymmetric vibration analysis of isotropic circular plate with attached annular piezoceramic plate

2012 ◽  
Vol 8 (4) ◽  
pp. 302 ◽  
Author(s):  
Syed Noh Syed Abu Bakar ◽  
Mostafa M. Abdalla ◽  
Waleed F. Faris ◽  
Sany Izan Ihsan
Keyword(s):  
Circular Plate ◽  
Vibration Analysis ◽  
Axisymmetric Vibration ◽  
Piezoceramic Plate

scholarly journals Theoretical and Numerical Estimation of Vibroacoustic Behavior of Clamped Free Parabolic Tapered Annular Circular Plate with Different Arrangement of Stiffener Patches

2018 ◽  
Vol 8 (12) ◽  
pp. 2542 ◽  
Author(s):  
Abhijeet Chatterjee ◽  
Vinayak Ranjan ◽  
Mohammad Azam ◽  
Mohan Rao
Keyword(s):  
Circular Plate ◽  
Acoustic Radiation ◽  
Power Level ◽  
Radiation Efficiency ◽  
Thickness Variation ◽  
Sound Power ◽  
The Finite Element Method ◽  
Acoustic Response ◽  
Sound Power Level ◽  
Design Options

This paper compares the vibroacoustic behavior of a tapered annular circular plate having different parabolic varying thickness with different combinations of rectangular and concentric stiffener patches keeping the mass of the plate and the patch constant for a clamped-free boundary condition. Both numerical and analytical methods are used to solve the plate. The finite element method (FEM) is used to determine the vibration characteristic and both Rayleigh integral and FEM is used to determine the acoustic behavior of the plate. It is observed that a Case II plate with parabolic decreasing–increasing thickness variation for a plate with different stiffener patches shows reduction in frequency parameter in comparison to other cases. For acoustic response, the variation of peak sound power level for different combinations of stiffener patches is investigated with different taper ratios. It is investigated that Case II plate with parabolic decreasing–increasing thickness variation for an unloaded tapered plate as well as case II plate with 2 rectangular and 4 concentric stiffeners patches shows the maximum sound power level among all variations. However, it is shown that the Case III plate with parabolically increasing–decreasing thickness variation with different combinations of rectangular and concentric stiffeners patches is least prone to acoustic radiation. Furthermore, it is shown that at low forcing frequency, average radiation efficiency with different combinations of stiffeners patches remains the same, but at higher forcing frequency a higher taper ratio causes higher radiation efficiency, and the radiation peak shifts towards the lower frequency and alters its stiffness as the taper ratio increases. Finally, the design options for peak sound power actuation and reduction for different combinations of stiffener patches with different taper ratios are suggested.

On Axisymmetric Vibration of Annular Plate of Parabolic Thickness Variation by Factorization of Differential Equation

2001 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Annular Plate ◽  
Poisson's Ratio ◽  
Thickness Variation ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
Fourth Order Differential Equation

Abstract In the present paper an analytic solution of free axisymmetric vibration of a class of annular plates of parabolic thickness variation is obtained by factorization of the fourth-order differential equation. Poisson’s ratio is taken v = 1/3, applicable to many materials.

scholarly journals Analytical Solutions To Boundary Value Problem Of Free Vibration Of Sandwich Thin Circular Plates With Discrete Elements

2015 ◽  
Vol 20 (3) ◽  
pp. 617-627
Author(s):  
K.K. Żur ◽  
J. Jaroszewicz ◽  
Ł. Dragun
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Analytical Investigation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Discrete Elements ◽  
Classical Plate Theory ◽  
Influence Matrix ◽  
The Core ◽  
Variable Distribution

Abstract In the paper the influence function and the method of partial discretization in free axisymmetric vibration analysis of multilayered circular plates of constant and linearly variable thickness were presented. The effects of shear deformation and rotary inertia for the core as well as the facings were neglected. An analytical investigation based on the classical plate theory was made for the multilayered plate which satisfies Sokołowski’s condition. Discretization of mass and replacing stiffness of a fixed circular plate were presented. Formulas of influence matrix and Bernstein-Kieropian’s estimators for different steps of discretization were defined. The influence of variable distribution of parameters on the value of double estimators of natural basic and higher frequency of a sandwich circular plate was investigated.

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