By Alexander F. Vakakis, Oleg V. Gendelman, Lawrence A. Bergman, D. Michael McFarland, Gaëtan Kerschen, Young Sup Lee
This monograph is the 1st within the new region of designated nonlinear strength move in mechanical and structural structures. this idea used to be at first stumbled on through the 2 top authors in 1999, and used to be additional built solely through the whole writer workforce within the final 6 years. on the grounds that then, extra teams of researchers within the united states, Russia, united kingdom and France have set to work in this idea and making use of it. it really is anticipated that during the future years, the idea that of specified nonlinear strength move might be thought of and utilized by way of a number of teams ofresearchers and practitioners across the world. This monograph provides theoretical equipment, computational effects and experimental demonstrations of this idea utilized to discrete and non-stop coupled nonlinear oscillators. in addition, it demonstrates the broad applicability of specified nonlinear power move to a variety of difficulties, together with:
- Vibration and surprise isolation in mechanical structures
- Seismic mitigation
- Aeroelastic and structural instability suppression
- Drilling operations
- Packaging units
This is a groundbreaking and exact quantity, delivering new layout paradigms in quite a few fields.
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Additional resources for Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems
Example text
Indeed a NNM-based approach seems to be natural for the study of TET and the associated strongly nonlinear phenomena discussed in this work. , 2005a). In an additional series of works (King and Vakakis, 1993, 1994, 1995a; Vakakis and King, 1995; Andrianov, 2008) methodologies for analysing the NNMs (and their bifurcations) of nonlinear elastic and continuous systems have been developed. In King and Vakakis (1994) stationary and traveling solitary waves (breathers) in a class of nonlinear partial differential equations are regarded as localized NNMs over domains of infinite spatial extent and are studied analytically.
1996). 6). , 1997) has been investigated. A review of mode localization in systems governed by nonlinear partial differential equations was given in Vakakis (1996). We will demonstrate some aspects of nonlinear mode localization in coupled oscillators by considering two examples, one involving a low-dimensional cyclic system, and a second one with a nonlinear medium of infinite spatial extent. The latter example will underline the theoretical link between NNMs and solitary waves. , 1993): y¨i + yi + εµyi3 + εk(yi − yi+1 ) + εk(yi − yi−1 ) = 0, y0 ≡ yN , yN+1 ≡ y1 i = 0, .
The ranges of system parameters, external excitations and initial conditions) for the realization of TET in the dissipative system. The topological structure and bifurcations of the NNMs of the underlying non-dissipative systems will be carefully studied in this work – especially in the frequency-energy domain, since the energy dependencies of NNMs (and damped NNM invariant manifolds) play a key role regarding TET; this holds especially for NNMs whose spatial distributions change from non-localized to localized with decreasing energy.