Obtaining the critical excitation for elasto-plastic oscillators by solving an optimal control problem

We consider the problem of finding the "critical excitation" for the variational inequality describing an elasto-plastic oscillator. This is essentially an optimal control problem for a nonsmooth system. Using Pontryagin's necessary condition for optimality we obtain the critical excitation as the solution of a two point boundary value problem for the state and adjoint variables with additional jump conditions on the adjoint variables at instances of phase changes. Applying the appropriate governing equations inside the elastic and plastic phases, respectively, and continuity and jump conditions between consecutive phases we define an algorithm which leads to the critical excitation. Numerical case studies are included. © Dynamic Publishers, Inc.