Evolutionary earthquake response of uncertain structure with bounded random parameter

The evolutionary earthquake response problem of an uncertain structure with bounded random parameters is solved in a unified way. Bounded random parameters, modelled by the λ-PDF, are more reasonable for engineering structures than the unbounded Gaussian random ones. The earthquake excitation is modelled as an evolutionary random process. The random structure is first transformed into an equivalent deterministic one by the Gegenbauer polynomial approximation. Then the evolutionary random response problem of the equivalent deterministic structure is solved by a unified approach formerly suggested by the last author. The essence of the orthogonal polynomial approximation is clearly explored. Numerical examples show that the proposed method is effective and practical.