Feedback linearization and semilinearization for smart elastic structures

This paper shows how the geometrically exact quasilinear equations of motio n of nonlinearly elastic and viscoelastic rods and shells whose response is sensitive to ambient magnetic, electric, or thermal fields can be converte d to semilinear or linear equations by suitable feedback controls of the am bient fields. Indeed, in certain cases, the feedback can make the response of a nonhomogeneous structure be like that of a homogenous structure, enlar ge or diminish the isotropy group of the structure, increase or decrease th e internal dissipation in the structure, and cause naturally different wave speeds to be the same. The availability of such controls indicates that th e shocks to which quasilinear hyperbolic partial differential equations for nonlinear elastic structures are susceptible need cause no difficulty in c ontrol problems. In particular, if the structure is subject to additional c ontrols that cause it to perform specific tasks, then these additional cont rols are treated by the theory for (semi)linear partial differential equati ons, for which there is an extensive development.