The Response of a Thin Cylindrical Shell to Transient Surface Loading
Solutions are presented in explicit form for elastic flexural displacements and stresses of a simply supported, thin circular cylindrical shell of finite length subjected to transient surface loading. Williams' method, introduced here for the first time as applicable to the vibration problem of a shell, is utilized in the analytical treatment based on Donnell-type equations. The method differs from that of ordinary normal-mode solutions in that the response is considered in two constituent portions, namely, the static portion obtainable in a closed form by direct integration, and the remaining dynamic portion, expressible in series involving terms of normal modes of vibration. The advantage of this approach is in the convergence-accelerating ability of the series for the dynamic portion during the time when the transient load is being applied. The analysis is general in that it may be used to solve either transient or steady surface loading problems. A numerical example is employed for illustration.