A numerical method for the time-domain dynamic analysis of buildings equipped with viscoelastic dampers

A novel numerical scheme for the time-domain dynamic analysis of buildings incorporating energy dissipation devices of viscoelastic type is presented. Two alternative state-space representations are considered for the frequency-dependent behaviour of the viscoelastic dampers, namely generalized Maxwell’s (GM) model and Laguerre’s polynomial approximation (LPA) technique. The computational burden is dramatically reduced by using a convenient modal transformation of coordinates, where the equilibrium modulus of the viscoelastic devices is included in the evaluation of modal shapes and undamped modal frequencies. Both GM model and LPA technique lead to closed-form expressions for the parameters characterizing the modal relaxation functions of the building, which in turn are exploited in deriving the exact integration operators for the modal oscillators. Importantly, all the matrices required in the proposed cascade scheme are directly computable from the exact transition matrices of traditional state variables (displacements and velocities) and additional internal variables (for either GM model or LPA technique). A simple application to a Single-DoF oscillator demonstrates the unconditional stability of the numerical method; the numerical efficiency is proved with the dynamic analysis of a discretized structural system with a large number of degrees of freedom; the accuracy is confirmed by the seismic response analysis of a realistic 10-storey building equipped with viscoelastic dampers.