Bensoussan, Alain; Chandrasekharan, Keerthi; Turi, Janos Obtaining the critical excitation for elasto-plastic oscillators by solving an optimal control problem. (English) Zbl 1270.49022 Commun. Appl. Anal. 16, No. 4, 589-608 (2012). Summary: 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. MSC: 49M05 Numerical methods based on necessary conditions 49K15 Optimality conditions for problems involving ordinary differential equations 49J40 Variational inequalities 65K10 Numerical optimization and variational techniques 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) Keywords:critical excitation; elasto-plastic oscillators; variational inequality; optimal control; numerical approximation PDFBibTeX XMLCite \textit{A. Bensoussan} et al., Commun. Appl. Anal. 16, No. 4, 589--608 (2012; Zbl 1270.49022)