Non-Linear Beam-Type Vibrations of Long Cylindrical Shells
This paper presents a closed-form solution of the problem of free beam-type vibration of a long cylindrical shell subject to uniform axial tension, uniform internal pressure, and elastic axial restraint. The shell is assumed to be clamped at the ends. The bending moment-curvature relationship employed in this paper is non-linear due to the effect of ovalization (flattening) of initially circular cross sections. Another non-linear effect taken into account is the stretching of the shell axis which is caused by the axial restraint. The analysis results in a cubic differential equation; the frequency of the solution of this equation is found exactly using elliptic integrals. © 1987.
V. Birman and C. W. Bert, "Non-Linear Beam-Type Vibrations of Long Cylindrical Shells," International Journal of Non-Linear Mechanics, Elsevier, Jan 1987.
The definitive version is available at https://doi.org/10.1016/0020-7462(87)90025-4
Mechanical and Aerospace Engineering
Article - Journal
© 1987 Elsevier, All rights reserved.