Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation

2020 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty ◽  
Mohammad Malikan
Keyword(s):  
Chebyshev Polynomial ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Functionally Graded ◽  
Shifted Chebyshev Polynomial

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

Free Vibration Analysis of Functionally Graded Cylindrical Shells Stiffened by Uniformly and Non-Uniformly Disturbuted Ring Stiffeners

2009 ◽  
Author(s):  
S. A. Moeini ◽  
M. Rahaeifard ◽  
M. T. Ahmadian ◽  
M. R. Movahhedy
Keyword(s):  
Free Vibration ◽  
Functionally Graded Materials ◽  
Vibration Analysis ◽  
Strain Energy ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Graded Materials ◽  
Energy Evaluation

Free vibration analysis of a transversely stiffened circular thin hollow cylinder made of functionally graded materials (FGMs) is analytically evaluated. Functionally graded materials are inhomogeneous composites which are usually made from a mixture of metal and ceramic. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses induced when two dissimilar materials with large differences in material properties are bonded. In this paper, application of an FGM made of two different materials is investigated by applying Ritz method. While cylinder is assumed to be thin, strain energy evaluation is performed by Sander’s theorem. Stiffeners which are not necessarily in the same uniform shape are treated as discrete elements and can be placed on both sides of the cylinder or concentrate in the middle wall. Bending, stretching and wrapping effects of stiffeners are considered in calculation of strain energy. Evaluation of kinetic energy of stiffeners is performed by taking into account rotary and translational inertia. To apply Ritz method, polynomial functions are used and natural frequencies and mode shapes of ring stiffened thin cylinder are investigated. Results are compared and verified with previous theoretical and experimental studies of stiffened thin cylinders. Comparison indicates a good agreement between results.

Three-dimensional vibration analysis of functionally graded thick, annular plates with variable thickness via polynomial-Ritz method

2011 ◽  
Vol 18 (11) ◽  
pp. 1698-1707 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Solution Procedure ◽  
Functionally Graded ◽  
Thickness Variation ◽  
Power Law Distribution ◽  
Annular Plates

In this paper, free vibration analysis of functionally graded thick, annular plates with linear and nonlinear thickness variation along the radial direction is investigated by using the polynomial-Ritz method. The material properties of the functionally graded plates are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The solution procedure is based on the linear, small strain, three-dimensional elasticity theory. Potential (strain) and kinetic energies of the plates are formulated, and the polynomial-Ritz method is used to solve the eigenvalue problem. In this analysis method, a set of orthogonal polynomial series for three displacement components in a cylindrical polar coordinate are used to extract an eigenvalue equation yielding natural frequencies. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant digits is demonstrated. Numerical results are presented and compared with the available literature. The vibration frequencies are given in several examples for various boundary conditions for the first time.

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