This paper presents a theoretical analysis of the dynamic response of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial biaxial stress and subjected to a radial point force that moves uniformly either along the axial direction or the circumferential direction. The analytical solutions are obtained in explicit form for the transient response of the first problem and the steady-state response of the latter problem. Critical speeds are given for both problems. Numerical results for both problems show the effects of the various relevant parameters. The effects of initial biaxial stress on the radial displacement and the critical velocities are presented. The behavior of cylinders beyond the lowest critical velocity is also pointed out.
This paper presents general solutions for both Flu¨gge’s and Donnell’s equations governing the displacements of the midsurface of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial twoway stress and subjected to general time-dependent surface loads. Analytical solutions are presented to the specific problems of a stationary radial point force and a stationary point couple. A numerical comparison of Donnell’s and Flu¨gge’s theories is made for these specific problems for a wide variety of shell parameters including initial stress. It is found for the case of a dynamic point force or point couple that Donnell’s theory is satisfactory for thin and very short shells (h/a ≤ 0.01 and l/a ≤ 2).
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