Abstract
In this work the problem of targeted energy transfer (TET) from a linear medium to a nonlinear attachment is studied in the presence of stochasticity. Using a Green's function formulation, complexification-averaging technique and diffusion approximation we derive a complex, nonlinear, Ito stochastic differential equation that governs the slow dynamics of the system. Through the numerical solution of the corresponding FokkerPlanckKolmogorov (FPK) equation we study the optimal regime of TET and its robustness to stochasticity for the case of nonlinear interactions of the nonlinear attachment with a single mode of the linear system. The probabilistic analysis reveals that in the presence of stochasticity the optimal TET regime, predicted in the deterministic theory, is not only preserved but also is enhanced due to the interaction of nonlinearity and stochasticity.
Original language | English (US) |
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Pages (from-to) | 119-133 |
Number of pages | 15 |
Journal | Probabilistic Engineering Mechanics |
Volume | 26 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2011 |
Keywords
- Diffusion approximation
- Energy harvesting
- FokkerPlanckKolmogorov equation
- Random nonlinear vibrations
- Stochastic targeted energy transfer
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Civil and Structural Engineering
- Nuclear Energy and Engineering
- Condensed Matter Physics
- Aerospace Engineering
- Ocean Engineering
- Mechanical Engineering