Non‐Normal Stochastic Response of Linear Systems

Conventional analysis of mean squared values is extended to calculation of the fourth moment of the response of a linear system. This provides a way to investigate the non‐normality of structural response, due to a non‐normal excitation. Studies are made for a linear SDF structure subjected to fairly simple non‐normal forces, which include a “white noise” process and filtered processes. Each filtered non‐normal process is generated by passing a “white noise” non‐normal process through a linear second‐order filter. The non‐normality of the structural response is investigated by integration in both the time domain and the frequency domain and by a more efficient technique that is an extension of the Lyapunov equation. This latter method reduces the calculation of the fourth moment of the response to solving a set of simultaneous linear algebraic equations.