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TECHNICAL PAPERS

Transient Vibration Analysis of Open Circular Cylindrical Shells

[+] Author and Article Information
Selvakumar Kandasamy

Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada

Anand V. Singh1

Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canadaavsingh@eng.uwo.ca

1

Corresponding author.

J. Vib. Acoust 128(3), 366-374 (Nov 28, 2005) (9 pages) doi:10.1115/1.2172264 History: Received April 26, 2005; Revised November 28, 2005

Abstract

A numerical method based on the Rayleigh-Ritz method has been presented for the forced vibration of open cylindrical shells. The equations are derived from the three-dimensional strain-displacement relations in the cylindrical coordinate system. The middle surface of the shell represents the geometry, which is defined by an angle that subtends the curved edges, the length, and the thickness. The displacement fields are generated with a predefined set of grid points on the middle surface using considerably high-order polynomials. Each grid point has five degrees of freedom, viz., three translational components along the cylindrical coordinates and two rotational components of the normal to the middle surface. Then the strain and kinetic energy expressions are obtained in terms of these displacement fields. The differential equation governing the vibration characteristics of the shell is expressed in terms of the mass, stiffness, and the load consistent with the prescribed displacement fields. The transient response of the shell with and without damping is sought by transforming the equation of motion to the state-space model and then the state-space differential equations are solved using the Runge-Kutta algorithm.

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Figures

Figure 1

Open circular cylindrical shell

Figure 2

Circular cylindrical shell: (a) quarter segment of the shell with reference to the full geometry, (b) quarter shell showing geometric nodes, and (c) quarter shell showing displacement nodes for a fourth-order polynomial

Figure 3

Transient response of an open circular cylindrical shell: (a) load-type, uniformly distributed half-sine pulse and (b) response of the shell

Figure 4

Transient response of open cylindrical shells: (a) Load-type, uniformly distributed ramp function, (b) subtended angle θ0=20deg, (c) θ0=40deg, (d) θ0=60deg. Dotted line, undamped; dashed line, 5% damping; and solid line, 10% damping.

Figure 5

Transient response of open cylindrical shells: (a) load type, uniformly distributed triangular pulse with negative slope and (b) subtended angle θ0=20deg, (c) θ0=40deg, (d) θ0=60deg. Dotted line, undamped; dashed line, 5% damping; and solid line, 10% damping.

Figure 6

Transient response of open cylindrical shells: (a) load type, uniformly distributed rectangular pulse; (b) subtended angle θ0=20deg, (c) θ0=40deg, (d) θ0=60deg. Dotted line, undamped; dashed line, 5% damping; and solid line, 10% damping.

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