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 sector of distinct nonlinear strength move in mechanical and structural structures. this idea was once first and foremost found through the 2 best authors in 1999, and was once additional constructed solely by means of the total writer team within the final 6 years. on account that then, extra teams of researchers within the united states, Russia, united kingdom and France have set to work in this inspiration and using it. it's predicted that during the future years, the concept that of precise nonlinear strength move should be thought of and utilized by way of a number of teams of researchers and practitioners the world over. This monograph provides theoretical tools, computational effects and experimental demonstrations of this idea utilized to discrete and non-stop coupled nonlinear oscillators. additionally, it demonstrates the extensive applicability of distinctive nonlinear power move to quite a lot of difficulties, together with: (1) Vibration and surprise isolation in mechanical platforms; (2) Seismic mitigation; (3) Aeroelastic and structural instability suppression; (4) Drilling operations; (5) Packaging units. this can be a groundbreaking and exact quantity, delivering new layout paradigms in quite a few fields.
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Extra resources for Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems (Solid Mechanics and Its Applications)
Acoust. 120, 579–587, 1998. , The calculation of strongly nonlinear systems close to vibration-impact systems, Prikl. Mat. Mech. (PMM) 49, 572–578, 1985. , A transformation for vibrating systems based on a non-smooth periodic pair of functions, Dokl. AN Ukr. SSR Ser. A 4, 37–40, 1988 [in Russian]. , Analytic study of vibrating systems with strong nonlinearities by employing sawtooth time transformations, J. Sound Vib. 192(1), 43–64, 2006. , Study of a class of subharmonic motions using a non-smooth temporal transformation (NSTT), Physica D 100, 145–164, 1997.
When no resonances exist, the NNM invariant manifolds of a MDOF discrete oscillator are two-dimensional, and the NNMs are uncoupled from each other. When internal resonances exist, there occur strongly nonlinear interactions between NNMs which couple them; this causes an increase of the dimensionality of the corresponding NNM invariant manifold. NNMs and NNM damped invariant manifolds will play a central role in our discussion of TET and related strongly nonlinear transient dynamical phenomena.
For additional works on localized NNMs in nonlinear chains we refer to Manevitch (2001) and Manevitch and Pervouchine (2003). 12) provided that H < ∞ (this holds for stationary localized wave solutions of the type considered in our analysis). 14a) x→±∞ By the first of the above relations we require spatial localization of the envelope, and by the second time-periodicity. 14b) It follows that we only need to confine our analysis to x ≥ 0 and u0 (t) ≥ 0. 13) represents a modal function for the sought NNM oscillation in functional space, and, viewed in that context, it may be regarded as an infinite-dimensional extension of modal relations satisfied by NNMs of finitedimensional oscillators.