Passive spatial confinement of impulsive responses in coupled nonlinear beams

A system of weakly coupled, geometrically nonlinear beams is examined. A Galerkin procedure is used to express the motions of the two beams in terms of their linearized flexural modes. Transient, impulsive excitations are considered, and the response of the system is analytically and numerically computed. For small values of a coupling nonlinear parameter, the vibrational energy injected into the system is proved to localize mainly at the directly forced beam, and only a small portion of this energy “leaks” to the unforced one. This passive, transient motion confinement is solely due to nonlinear localized modes of the unforced system, and it becomes more profound for stronger impulse excitations, and as the nonlinearity increases and/or the coupling stiffness connecting the two beams decreases. In the absence of nonlinearity, the injected vibrational energy is continuously transferred between the two beams, and thus no passive motion confinement is possible. Numerical integrations are used to verify the theoretical predictions. The implications of these findings on the passive and active isolation of flexible, nonlinear periodic structures are discussed.