Vibration of Pressurized Thin-Walled Cylinder Induced by Pulsed Laser

摘要

Differential equations are presented that describe wall oscillations of a gas-pressurized thin-walled cylinder for cases where variations in the axial direction are negligible. A linear stress/strain relation is assumed. Harmonic solutions are obtained. Limiting forms of these solutions are given for cases where the mode number, n = 0, 1, 2,...,is moderate and for cases where the mode number is large. In the former case, curvature effects are important. In the latter case, the vibrations behave locally like those on a flat plate. The applicability of the harmonic solutions, for evaluating the hoop stress induced by a high energy pulsed laser beam, is discussed. The maximum stress induced during the initial transient is investigated. An estimate is given for the maximum stress perturbation induced by a 'slab' type (no axial variation) beam with uniform fluence and width equal to the cylinder diameter. In this case, the estimate for the maximum value of the laser induced hoop stress perturbation sigma sub m, is found from sigma sub m/sigma sub i = (CF/pa)(E'/p) sup 1/2 where sigma sub i, C, F, P, a, E', and p are initial pressure induced hoop stress, coupling coefficient, fluence, cylinder internal pressure, cylinder radius, effective wall modulus of elasticity, and wall density, respectively. The maximum stress perturbation induced by slab and circular cross-section laser beams, with non-uniform profiles and widths which are small compared with cylinder radius, are also estimated. For the case of a narrow slab beam, the upper bound on the laser induced hoop stress is found from sigma sub m/sigma sub i - 0.5(CF sub 0/pa) exp 2(E'/p) where F sub 0 is center line fluence.