Stability of Cylindrical Shells under Random Excitation

A Lyapunov-type approach is used in the investigation, and the formulation of the problem is perfectly general in terms of the dynamic system input-output statistical correlation as well as the degree of stochastic interdependency of the excitation processes. The dynamic motion of the system considered can be described by a Hill-type equation with two stochastic parameters. Sufficient conditions are developed to ensure mean-square global stability in terms of statistical parameters of the excitation processes and physical system parameters. Stochastic convergence and mean-square global stability are defined and examined. The shell is considered to be subjected to simultaneous axial and radial stochastic loadings. The results obtained are more general than those formerly available since the present results permit any degree of system input-output correlation as well as any degree of stochastic interdependency between the simultaneous excitation processes. In addition, the techniques utilized in this analysis are capable of being extended to systems involving more than two simultaneous excitations.