The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

1991 ◽  
Vol 12 (9) ◽  
pp. 871-879
Author(s):  
Ji Zhen-yi
Keyword(s):  
General Solution ◽  
Elastic Foundation ◽  
Circular Plates

AXISYMMETRIC VIBRATION OF POLAR ORTHOTROPIC CIRCULAR PLATES OF QUADRATICALLY VARYING THICKNESS RESTING ON ELASTIC FOUNDATION

2005 ◽  
Vol 05 (03) ◽  
pp. 387-408 ◽  
Author(s):  
N. BHARDWAJ ◽  
A. P. GUPTA
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Three Dimensional ◽  
Normal Modes ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Varying Thickness ◽  
Edge Conditions ◽  
Polar Orthotropic

This paper is concerned with the axisymmetric vibration problem of polar orthotropic circular plates of quadratically varying thickness and resting on an elastic foundation. The problem is solved by using the Rayleigh–Ritz method with boundary characteristic orthonormal polynomials for approximating the deflection function. Numerical results are computed for frequencies, nodal radii and mode shapes. Three-dimensional graphs are also plotted for the first four normal modes of axisymmetric vibration of plates with free, simply-supported and clamped edge conditions for various values of taper, orthotropy and foundation parameters.

A State Space Solution Approach for Problems of Cylindrical Tubes and Circular Plates

2015 ◽  
Vol 31 (5) ◽  
pp. 557-572 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
General Solution ◽  
State Space ◽  
Eigenfunction Expansion ◽  
Separation Of Variables ◽  
Transversely Isotropic ◽  
Circular Plates ◽  
Solution Approach ◽  
Space Solution ◽  
Cylindrical Tubes ◽  
Space Formalism

AbstractWe present a general solution approach for analysis of transversely isotropic cylindrical tubes and circular plates. On the basis of Hamiltonian state space formalism in a systematic way, rigorous solutions of the twisting problems are determined by means of separation of variables and symplectic eigenfunction expansion.

scholarly journals Effect of elastic foundation on vibrational behavior of graphene based on first-order shear deformation theory

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881462
Author(s):  
Mohsen Motamedi ◽  
Amirhossein Naghdi ◽  
Ayesha Sohail ◽  
Zhiwu Li
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Circular Plates ◽  
First Order ◽  
Special Case ◽  
Good Agreement

In this study, an investigation of “the free vibrations of hollow circular plates’’ is reported. The study is based on elastic foundation and the results depicted are further extended to study the special case of “graphene sheets.’’ The first-order shear deformation theory is applied to study the elastic properties of the material. A hollow circular sheet is modeled and the vibrations are simulated with the aid of finite element method. The results obtained are in good agreement with the theoretical findings. After the validation, a model of graphene is presented. Graphene contains a layer of honeycomb carbon atoms. Inside a layer, each carbon atom C is attached to three other carbon atoms and produces a sheet of hexagonal array. A 25 nm × 25 nm graphene sheet is modeled and simulated using the validated technique, that is, via the first-order shear deformation theory. The key findings of this study are the vibrational frequencies and vibrational mode shapes.

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