A stochastic analysis method of transient responses using harmonic wavelets, Part 1: Time-invariant structural systems

Abstract The transient response components have significant impacts on the stochastic response analysis of structural systems subjected to nonstationary stochastic excitations. However, available stochastic analysis methods focus on the steady-state response components. This paper proposes a novel stochastic analysis method of the transient responses for multi-degree-of-freedom (MDOF) structural systems subjected to nonstationary stochastic excitations based on periodic generalized harmonic wavelets (GHW). Firstly, the importance of transient response components on structural systems is discussed in detail. The equations of motion of the MDOF structural systems are established by using the periodic GHW with considering the rigid displacement components. The linear algebraic equations with respect to the wavelet coefficients of responses and excitations are established, respectively. Then the connection equations of wavelet coefficients in all scales are established to include the transient components in the responses. A stochastic analysis method of transient responses for structural systems is proposed based on the periodic GHW, and the time-varying power spectral density functions of the structural responses are obtained in a semi-analytical form. The proposed method is validated by two numerical examples, which illustrate the high efficiency and high accuracy of the novel method.