Frequencies of Circular Plates Weakened Along an Internal Concentric Circle and Elastically Restrained Edge Against Translation

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Lokavarapu Bhaskara Rao ◽  
Chellapilla Kameswara Rao
Keyword(s):  
Natural Frequencies ◽  
Radial Crack ◽  
Concentric Circle ◽  
Outer Edge ◽  
Circular Plates ◽  
Plate Vibrations ◽  
Rotational Restraint ◽  
Method Of Solution ◽  
Elastically Restrained Edge ◽  
Elastically Restrained

The present study deals with the derivation of an exact solution for the problem of obtaining the natural frequencies of the vibration of circular plates weakened along an internal concentric circle due to the presence of a radial crack and elastically restrained along the outer edge of the plate against translation. The frequencies of the circular plates are computed for varying values of the elastic translational restraint, the radius of the radial crack, and the extent of the weakening duly simulated by considering the radial crack as a radial elastic rotational restraint on the plate. The results for the first six modes of the plate vibrations are computed. The effects of the elastic edge restraint, the radius of the weakened circle, and the extent of the weakening represented by an elastic rotational restraint on the vibration behavior of thin circular plates are studied in detail. The internal weakening due to a crack resulted in decreasing the fundamental frequency of the plate. The exact method of solution and the results presented in this paper are expected to be of specific use in analyzing the effect of a radial crack on the fundamental natural frequency of the circular plate in the presence of a translational restraint existing along the outer edge of the plate. These exact solutions can be used to check the numerical or approximate results.

scholarly journals Influence of boundary constraints on the appearance of asymmetrical equilibrium states in circular plates under normal pressure

2020 ◽  
pp. 38-46
Author(s):  
Svetlana M. Bauer ◽  
Eva B. Voronkova
Keyword(s):  
Radial Direction ◽  
Elasticity Modulus ◽  
Normal Pressure ◽  
Outer Edge ◽  
Buckling Load ◽  
Circular Plates ◽  
Boundary Constraints ◽  
Angular Coordinate ◽  
Elastically Restrained Edge ◽  
Elastically Restrained

Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. The effect of material heterogeneity and boundary on the buckling load is examined. It is shown that if the outer edge of a plate is elastically restrained against radial deflection, the buckling load for unsymmetrical buckling is larger than for a plate with a movable edge. The elasticity modulus decrease away from the center of a plate leads to sufficient lowering of the buckling pressure if the outer edge can move freely in the radial direction.

Bending of Circular Plates Under a Uniform Load on a Concentric Circle—Part II

1968 ◽  
Vol 90 (2) ◽  
pp. 279-293
Author(s):  
J. C. Heap
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Concentric Circle ◽  
Outer Edge ◽  
Circular Plates ◽  
Uniform Load ◽  
Simply Supported ◽  
Basic Equations

The basic equations of deflection, slope, and moments for a thin, flat, circular plate subjected to a uniform load on a concentric circle were derived for four generalized cases. From these generalized cases, six simplified cases were deduced. The four generalized cases have the uniform load acting on a concentric circle of the plate between the inner and outer edges, with the following boundary conditions: (a) Outer edge supported and fixed, inner edge fixed; (b) outer edge simply supported, inner edge free; (c) outer edge simply supported, inner edge fixed; and (d) outer edge supported and fixed, inner edge free.

scholarly journals Vibrations of Circular Plates with Elastically Restrained Edge against Translation and Resting on Elastic Foundation

2016 ◽  
Vol 13 (2) ◽  
pp. 187
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates elastically restrained against translation and resting on Winkler-type elastic foundation based on the classical plate theory. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates. 

scholarly journals On non-axisymmetric buckling modes of inhomogeneous circular plates

2021 ◽  
Vol 8 (2) ◽  
pp. 204-211
Author(s):  
Svetlana M. Bauer ◽  
◽  
Eva B. Voronkova ◽  
Keyword(s):  
Elasticity Modulus ◽  
Normal Pressure ◽  
Mode Number ◽  
Circular Plates ◽  
Plate Edge ◽  
Buckling Modes ◽  
Axisymmetric Buckling ◽  
Flexibility Coefficient ◽  
Elastically Restrained Edge ◽  
Elastically Restrained

Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The asymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value at which waves in the circumferential direction can appear. The effect of material heterogeneity and boundary on the buckling load is examined. For a plate with elastically restrained edge, the buckling pressure and mode number increase with a rise of spring stiffness. Increasing of the elasticity modulus to the plate edge leads to increasing of the buckling pressure, but the mode number does not change. If the translational flexibility coefficient is small, decreasing of the elasticity modulus to the shell (plate) edge leads to sufficient lowering of the buckling pressure.

scholarly journals Vibrations of Circular Plates Resting on Elastic Foundation with Elastically Restrained Edge Against Translation

2018 ◽  
Vol 13 (1) ◽  
pp. 14
Author(s):  
L.B. Rao ◽  
C.K. Rao
Keyword(s):  
Elastic Foundation ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Vibration Characteristics ◽  
Graphical Form ◽  
Winkler Foundation ◽  
Stiffness Ratio ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Elastically Restrained

The present paper deals with exact solutions for the free vibration characteristics of thin circular plates resting on Winkler-type elastic foundation based on the classical plate theory elastically restrained against translation. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in the design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates.  

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