The stability problem is studied for a system of stochastic Volterra integrodifferential equations. The system describes the mechanical behaviour of viscoelastic structural members driven by random forces. Some restrictions on kernels of the Volterra integral operators are imposed, and their mechanical meaning is discussed. New explicit sufficient conditions of the the mean square stability are developed. These conditions are derived by constructing the Lyapunov stability functionals. As examples, stability problems for a viscoelastic bar under stochastic loads are considered. Some conditions are developed, which ensure the bar stability for an arbitrary relaxation measure of material and for various types of end supports.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics