scholarly journals Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Muhmmad Nawaz Naeem ◽  
Shazia Kanwal ◽  
Abdul Ghafar Shah ◽  
Shahid Hussain Arshad ◽  
Tahir Mahmood
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Lagrangian Function ◽  
Dynamical Equations ◽  
Graded Materials ◽  
Present Technique ◽  
Circular Cylindrical Shells ◽  
Stiffened Cylindrical Shells

The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.

scholarly journals Vibrational Study of Fluid-Filled Functionally Graded Cylindrical Shells Resting on Elastic Foundations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Abdul Ghafar Shah ◽  
Tahir Mahmood ◽  
Muhammad Nawaz Naeem ◽  
Shahid Hussain Arshad
Keyword(s):  
Cylindrical Shells ◽  
Functionally Graded ◽  
Dynamical Equations ◽  
Graded Materials ◽  
Elastic Foundations ◽  
Present Technique ◽  
Vibrational Characteristics ◽  
Love’S Thin Shell Theory ◽  
Thin Shell Theory ◽  
Good Agreement

Vibrational characteristics of functionally graded cylindrical shells filled with fluid and placed on Winkler and Pasternak elastic foundations are investigated. Love's thin-shell theory is utilized for strain-displacement and curvature-displacement relationships. Shell dynamical equations are solved by using wave propagation approach. Natural frequencies for both empty and fluid-filled functionally graded cylindrical shells based on elastic foundations are determined for simply-supported boundary condition and compared to validate the present technique. Results obtained are in good agreement with the previous studies. It is seen that the frequencies of the cylindrical shells are affected much when the shells are filled with fluid, placed on elastic foundations, and structured with functionally graded materials. The influence of Pasternak foundation is more pronounced than that of Winkler modulus.

Relationship between Bending Solutions of FGM and Homogenous Circular Cylindrical Shells

2013 ◽  
Vol 353-356 ◽  
pp. 3236-3242
Author(s):  
Ze Qing Wan ◽  
Shi Rong Li
Keyword(s):  
Cylindrical Shell ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Continuous Functions ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Circular Cylindrical Shells

Based on the Loves shell theory, relationship between bending solutions of functionally graded materials (FGM) and homogenous circular cylindrical shells was studied. By comparing the displacement-type governing equations for axially symmetrically bending of FGM and homogenous circular cylindrical shells, an analogous transform relation between the deflections of FGM circular cylindrical shell and those of homogenous one was obtained. By giving the material properties of FGM circular cylindrical shell changing as continuous functions in the thickness direction, the corresponding transition factor between the solutions of the two kind circular cylindrical shells were derived, which reflect the non-uniform properties of the functionally graded material circular cylindrical shell. Numerical example shows that the numerical solutions of the maximum of non-dimensional deflections are almost in agreement with the transformational solutions whennequals approximately 5, wherenis the volume fraction index. As a result, solutions for axially symmetrically bending of a non-homogenous circular cylindrical shell can be reduced to that of a homogenous one and the calculation of the transformation factors.

Aerothermoelastic Stability of Functionally Graded Circular Cylindrical Shells

2010 ◽  
Author(s):  
Farhad Sabri ◽  
Aouni A. Lakis
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Shell Thickness ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Aerodynamic Pressure ◽  
Circular Cylindrical Shells

In this work, a hybrid finite element formulation is presented to predict the flutter boundaries of circular cylindrical shells made of functionally graded materials. The development is based on the combination of linear Sanders thin shell theory and classic finite element method. Material properties are temperature dependent, and graded in the shell thickness direction according to a simple power law distribution in terms of volume fractions of constituents. The temperature field is assumed to be uniform over the shell surface and along the shell thickness. First order piston theory is applied to account for supersonic aerodynamic pressure. The effects of temperature rise and shell internal pressure on the flutter boundaries of FG circular cylindrical shell for different values of power law index are investigated. The present study shows efficient and reliable results that can be applied to the aeroelastic design and analysis of shells of revolution in aerospace vehicles.

scholarly journals Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method

2012 ◽  
Vol 34 (3) ◽  
pp. 139-156 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Axial Compression ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Method Effects ◽  
Circular Cylindrical Shells

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection.  Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper  [13] which were solved by Ritz energy method.

Axisymmetric Buckling of Ring-Stiffened Cylindrical Shells Under Axial Compression

1965 ◽  
Vol 9 (02) ◽  
pp. 66-73
Author(s):  
Thein Wah
Keyword(s):  
Finite Difference ◽  
Axial Compression ◽  
Torsional Rigidity ◽  
Cylindrical Shells ◽  
Axisymmetric Buckling ◽  
Circular Cylindrical Shells ◽  
Stiffened Cylindrical Shells

The possibility of axisymmetric modes of buckling of ring-stiffened circular cylindrical shells under axial compression is investigated by the use of finite-difference calculus. The theory accounts for both the extensional as well as torsional rigidity of the rings.

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