Nonlinear Sonic Vacua
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Дата
2016
Автори
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
NTU "KhPI"
Анотація
We will present recent results on a special class of dynamical systems designated as nonlinear sonic vacua.
These systems are non-linearizable, and have zero speed of sound (in the sense of classical acoustics).
Accordingly, their dynamics and acoustics are highly degenerate and tunable with energy, enabling new and
highly complex nonlinear phenomena. Two examples of sonic vacua will be discussed. The first is uncompressed
ordered granular media, which, depending on their local state, behave either as strongly nonlinear
and non-smooth dynamical systems (in the absence of strong local compression), or as almost linear coupled
oscillators (under strong local compression, e.g., in the primary fronts of propagating solitary pulses) [1,2].
The second example concerns a spring-mass lattice in the plane. In the small energy limit this seemingly simple
system is 'transformed' by geometric nonlinearity to a nonlinear sonic vacuum with surprising properties, such
as strong nonlocality (despite o f only next-neighbor interactions in the lattice!), orthogonal nonlinear normal
modes, and accelerating propagating fronts [3,4]. Interesting applications of nonlinear sonic vacua will be
discussed, including intense energy cascading from low-to-high frequencies and long-to-short wavelengths,
resembling “mechanical turbulence ”. We will discuss the implications of these findings on the design of
dynamical systems for predictive passive energy management.
Опис
Ключові слова
nonlinear sonic vacuum
Бібліографічний опис
Vakakis A. Nonlinear Sonic Vacua / A. Vakakis // Nonlinear Dynamics–2016 (ND-KhPI2016) : proceedings of 5th International Conference, dedicated to the 90th anniversary of Academician V. L. Rvachev, September 27-30, 2016 = Нелінійна динаміка–2016 : тези доп. 5-ї Міжнар. конф., 27-30 вересня 2016 р. – Kharkov : NTU "KhPI", 2016. – P. 45.