Stability and subcritical dynamics of structures with spatially disordered travelling parametric excitation

Abstract Spatially periodic travelling loading may lead sometimes to parametric excitation of structures. However, random spatial nonuniformity of the loading pattern, which leads in time domain to fluctuations of the excitation frequency, makes this phenomenon less severe. This effect is considered for the case of a single-mode resonant response. Using stochastic averaging, stability boundaries are found both with respect to probability and in the mean square; subcritical response to an external broadband random excitation is also obtained.