Stochastic dynamic response and reliability assessment of controlled structures with fractional derivative model of viscoelastic dampers

Viscoelastic dampers, where fractional derivatives are involved, are often considered for use to mitigate dynamic response of structures. However, it is not an easy task to obtain the probabilistic dynamic response and the reliability of controlled structures with fractional terms. For this purpose, an efficient methodology based on the probability density evolution method is proposed, where the generalized density evolution equation is present to capture the instantaneous probabilistic dynamic response and the dynamic reliability can be evaluated from the standpoint of probability dissipation. Numerical solution is of practical necessity, where a deterministic procedure to solve the equation of motion with fractional derivatives is embedded. Therefore, the precise integration method (PIM) is extended to numerically integrate the equation of motion with fractional terms, which offers high accuracy. The numerical results verify the effectiveness of the advocated methodology, but also indicate the viscoelastic dampers can enhance the seismic performance of structures significantly.