Dynamic Steady-State Analysis of Structures under Uncertain Harmonic Loads via Semidefinite Program

In this paper we present an optimization-based method for finding confidential bounds for the dynamic steady-state response of a damped structure subjected to uncertain driving loads. The amplitude of harmonic driving loads is supposed to obey a non-probabilistic uncertainty model. We formulate a semidefinite programming problem, whose optimal value corresponds to a confidential bound for the characteristic amount of dynamic steady-state response, e.g. the modulus and phase angle of the complex amplitude of the displacement. Numerical examples demonstrate that sufficiently tight bounds can be obtained by solving the presented semidefinite programming problems.