Reliability analysis of structures controlled by external fractional viscoelastic dampers with interval parameters

Seismic performance of structures controlled by external viscoelastic dampers with uncertain properties is investigated. The behaviour of the energy dissipation devices is described by a fractional constitutive law where both the fractional derivative order and the damping coefficient are modelled as interval variables with assigned lower bound and upper bound. Ground motion acceleration is modelled as a zero-mean stationary Gaussian random process. Under these assumptions, the motion of the controlled structure is governed by a set of interval fractional differential equations. All response quantities are described by interval zero-mean stationary Gaussian random processes, fully characterized in the frequency domain by their power spectral density function which depends on the interval parameters of the viscoelastic devices. Reliability analysis is carried out by extending the classical first-passage problem to the interval framework. The bounds of the interval-valued reliability function are computed by an efficient approximate procedure. A case-study, involving viscoelastic devices with interval properties defined based on experimental results available in the literature, is presented.