Abstract

Vibration analysis of fluid-filled functionally graded material (FGM) cylindrical shells (CSs) is investigated with ring supports. The shell problem is formulated by deriving strain and kinetic energies of a vibrating cylindrical shell (CS). The method of variations of Hamiltonian principle is utilized to change the shell integral problem into the differential equation (DE) expression. Three differential equations (DE) in three unknown for displacement functions form a system of partial differential equations (PDEs). The shells are restricted along the thickness direction by ring supports. The polynomial functions describe the influence of the ring supports and have the degree equal to the number of ring supports. Fluid loaded terms (FLT) are affixed with the shell motion equations. The acoustic wave equation states the fluid pressure designated by the Bessel functions of first kind. Axial modal deformation functions are specified by characteristic beam functions which meet end conditions imposed on two ends of the shell. The Galerkin method is employed to get the shell frequency equation. Natural frequency of FGM cylindrical shell is investigated by placing the ring support at different position with fluid for a number of physical parameters. For validity and accuracy, results are obtained and compared with the data in open literature. A good agreement is achieved between two sets of numerical results.

Highlights

  • All over the word, applications of fluid-filled cylindrical shells have grown in engineering and science

  • It is seen that the influences of ring supports and fluid terms are converse to each other

  • The shell problem has been associated with investigation vibrations of cylindrical shells with ring supports

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Summary

Introduction

Applications of fluid-filled cylindrical shells have grown in engineering and science. Najafizadeh and Isvandzibaei [5] analyzed vibration characteristics of functionally graded cylindrical shells with ring supports. They based their analysis higher order shear deformation theory of shells. Zhang et al [4] studied vibrations of CSs and applied the wave propagation approach (WPA) to solve shell dynamical equations. This method depended on the eigenvalue of characteristic beam functions. This factor is expressed by the polynomial functions which carry the degree equal to the number of ring supports

Functionally graded shells
Theoretical investigation
Mx 7 6 B11 B12 0 D11 D12 0 76 κ1 7
Application of Galerkin technique
A12 ðI6 þ I7Þ À B11ðI8 þ 3I9Þ 3 R
Effective material
Numerical results
Frequency analysis of fluid-filled cylindrical shell
Frequency analysis of fluid-filled cylindrical shells with ring support
Summary
Full Text
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