Reliability sensitivity analysis of frame structures controlled by external fractional viscoelastic dampers

Installing seismic devices, such as energy dissipation devices and seismic isolators, is one of the most effective approaches to protect new and existing structures against earthquake effects in seismic areas. An efficient strategy to improve the calibration of the main parameters of seismic devices is the design sensitivity analysis (DSA). Design sensitivity relies on a linear approximation of the selected performance measure in terms of the design variables. It provides a quantitative estimate of design changes due to variations in the available design variables. This paper focuses on frame structures connected to much more rigid walls (the exoskeleton) by means of a set of linear energy dissipation devices with fractional viscoelastic behaviour, subjected to seismic excitation modelled as a zero-mean stationary Gaussian random process. To assess the seismic performance of the controlled structure, the reliability function of the extreme value response process is evaluated by adopting Vanmarcke's approximation. Then, explicit analytical expressions of the sensitivities of the reliability function to the main parameters of fractional viscoelastic devices are derived. Numerical results demonstrate that such expressions are highly valuable in the context of the DSA of controlled structures, as they may assist engineers in the optimal placement and design of seismic devices.