Explicit time-domain method for sensitivity analysis of nonstationary random vibration of systems with fractional derivatives

Fractional derivative models are capable of describing the constitutive behaviors of viscoelastic materials. This paper is devoted to the sensitivity analysis of nonstationary random vibration of linear systems comprising fractional derivative terms. The explicit time-domain expressions of dynamic responses are firstly established for the system with fractional derivatives. The sensitivities of dynamic responses are then derived using the direct differentiation method (DDM) or the adjoint variable method (AVM). On the basis of the explicit expressions of dynamic responses and their sensitivities, an explicit time-domain method (ETDM) is proposed for efficient calculation of the sensitivities of statistical moments of responses. The proposed DDM- and AVM-based ETDM are applicable to the scenarios with less and more design variables, respectively. A numerical example involving a shear-type structure under nonstationary seismic excitations and with viscoelastic dampers modelled by fractional derivatives is presented to validate the computational accuracy and efficiency of the proposed method. © 2022, Editorial Board of Journal of Vibration Engineering. All right reserved.