Stable Intrinsic Localized Modes in Microelectromechanical Cantilever Structures
Technical Report,15 May 2014,14 Feb 2015
State University of New York (SUNY) at Buffalo Amherst United States
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Protection of humans from large, finite time perturbations is an important area of research. Hence it is of interest to develop systems that arethin, light-weight and capable of absorbing large accelerations. An area of special interest concerns highly nonlinear systems which possessa rich variety of dynamical responses. This study focused on whether it is possible to convert any incident perturbation into localizedexcitations. The study explored the dynamics of a weakly nonlinear system with quadratic and quartic on-site and inter-site potentials wherethe linear pieces are significantly stronger than the nonlinear pieces that has been introduced by Sievers and coworkers. The system isrealized by a micromechanical cantilever structure. We showed that the Sievers system can trap excitations that are in a specific amplitudeand frequency window. We have studied whether breathers form from noisy perturbations in the Fermi-Pasta-Ulam system which consists ofmasses interacting via a quadratic and a quartic potentials. Turns out that only weak breathers form from such perturbations. Our worksuggests the emergence of highly localized excitations when synchronized or nearly synchronized perturbations from two ends meet ingranular chains with soft centers. Similar physics is also seen in preliminary studies on Fermi-Pasta-Ulam chains.
- Numerical Mathematics
- Electrical and Electronic Equipment