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.  

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 Forced Response of Polar Orthotropic Tapered Circular Plates Resting on Elastic Foundation

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. H. Ansari
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Ritz Method ◽  
Forced Response ◽  
Bending Moments ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Different Types ◽  
Foundation Parameter ◽  
Polar Orthotropic

Forced axisymmetric response of polar orthotropic circular plates of linearly varying thickness resting on Winkler type of elastic foundation has been studied on the basis of classical plate theory. An approximate solution of problem has been obtained by Rayleigh Ritz method, which employs functions based upon the static deflection of polar orthotropic circular plates. The effect of transverse loadings has been studied for orthotropic circular plate resting on elastic foundation. The transverse deflections and bending moments are presented for various values of taper parameter, rigidity ratio, foundation parameter, and flexibility parameter under different types of loadings. A comparison of results with those available in literature shows an excellent agreement.

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

Computing Buckling Characteristics of Double-Layered Graphene Film Embedded in an Elastic Foundation

2019 ◽  
Vol 19 (06) ◽  
pp. 1950065
Author(s):  
Zhengtian Wu ◽  
Yang Zhang ◽  
Weicheng Ma
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Graphene Film ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Type Model ◽  
Classical Plate Theory ◽  
Buckling Behavior ◽  
Small Scale Effect ◽  
Simulation Results

Given the unique and extremely valuable properties, research has significantly focussed on graphene sheets (GSs). To premeditate the small-scale effect, the present work applies the nonlocal theory to study the buckling behavior of a double-layered GS (DLGS) embedded in an elastic foundation. To derive the equation, classical plate theory is adopted. For the elastic foundation, Pasternak-type model is used. In terms of buckling response, a meshless method is utilized to compute simulation results. Accordingly, we examine the effects of aspect ratio, geometry, boundary conditions and nonlocal parameters on the buckling responses of DLGSs.

Static and Dynamic Analyses of Beam-Columns on Winkler Foundation

1991 ◽  
Author(s):  
T. W. Lee ◽  
W. L. Cleghorn ◽  
B. Tabarrok
Keyword(s):  
Elastic Foundation ◽  
Axial Load ◽  
Natural Frequencies ◽  
Homogeneous Solution ◽  
Time History ◽  
Element Model ◽  
Free Vibrations ◽  
Winkler Foundation ◽  
Static Case ◽  
Minimum Number

Abstract A finite element model is developed for static, free and forced vibration analyses of a compressed beam resting on a Winkler-type elastic foundation and subjected to transverse loads. The homogeneous solution of the governing differential equation of static equilibrium is used as shape functions when deriving the load vector, the stiffness and mass matrices. For the static case, a procedure is outlined for improving the internal distributions of deflections, rotations, bending moments and shear forces of the structure. In this procedure, exact results are obtained for concentrated, uniform and ramp distributed loads with a minimum number of elements. When considering free vibrations, natural frequencies converge rapidly with increasing numbers of elements, and are shown to agree with results obtained by other analytical methods. The effects of the axial load and elastic foundation on the natural frequencies are also illustrated. For forced vibrations, the Newmark β Method is employed for obtaining the time history response of a beam-column on an elastic foundation subjected to lateral time-dependent excitations and constant axial load.

Maximization of Natural Frequencies for Functionally Graded Rectangular Plates

2021 ◽  
Vol 891 ◽  
pp. 116-121
Author(s):  
Aleksander Muc
Keyword(s):  
Analytical Methods ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Optimization Techniques ◽  
Point Of View ◽  
Rectangular Plates ◽  
Classical Plate Theory ◽  
Arbitrary Boundary

In this paper optimal design of free vibrations for functionally graded plates is studied using the analytical methods. The analytical methods can be employed for the solution of six of 21 arbitrary boundary conditions (the combinations of clamped, simply supported and free). The influence of various models of porosity and forms of different reinforcements with nanoplatelets and carbon nanotubes are investigated, including variations of stiffness/density along the thickness of a plate. The analysis is carried out for the classical plate theory. Parametric studies illustrate the possibility of increasing natural frequencies and the necessity of implementing the optimization techniques to find the best solutions from the engineering point of view.

scholarly journals Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
Author(s):  
Krzysztof Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

Sign in / Sign up

Export Citation Format

Share Document