Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

Muhmmad Nawaz Naeem,Abdul Ghafar Shah,Tahir Mahmood,Shazia Kanwal,Shahid Hussain Arshad

doi:10.5402/2012/232498

Abstract

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.

Highlights

Circular cylindrical shells stiffened by rings are widely used in many structural applications such as airplanes, marine crafts, pressure vessels, silos, core barrels of pressurized water reactors, submarine hulls, offshore drilling rings, and construction buildings
Numerical technique known as the Rayleigh-Ritz method has been employed to study the vibration characteristics of functionally graded circular cylindrical shells with ringstiffeners
The axial model dependence has been approximated by the characteristic beam functions

Summary

Introduction

Circular cylindrical shells stiffened by rings are widely used in many structural applications such as airplanes, marine crafts, pressure vessels, silos, core barrels of pressurized water reactors, submarine hulls, offshore drilling rings, and construction buildings. Cylinders are stiffened by rings or strings to increase the stiffness and strength, reduce the weight structure to be designed In designing these shells, it is vital to know their resonant frequencies because excessive vibrations can lead to fatigue rupture. Sewall and Naumann [8] studied that stiffened cylindrical shells problem experimentally and analytically They approximated the shell displacement deformations by the beam functions and used Rayleigh-Ritz method to derive shell frequency equation in the eigenvalue form. Wang et al [9] transform vibration analysis of shell eigen-frequency equation in the general eigenvalue problem They used Ritz polynomial functions for the axial deformation displacements by considering boundary condition equations. They designed three types of shells by the locations of isotropic rings. Sharma and Johns [10] applied Rayleigh-Ritz method for theoretical analysis of vibrating clamped-free and clamped-stiffened shell using

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