Non-Iterative Rauscher Method for 1-DOF System: a New Approach to Studying Non-Autonomous System via Equivalent Autonomous One
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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
In the paper a new non-iterative variant of Rauscher method is considered. In its current statement the method
can be used in analysis of forced harmonic oscillations in 1-DOF nonlinear system.
It is shown that three different types o f equivalent authonomous dynamical systems can be built for a given
1-DOF non-autonomous one. Two of them (1st and 2nd type) have wider set of solutions than that of the initial
system. These solutions correspond to various values of amplitude and phase of external excitation. Solutions
of the equivalent system of 3rd type are exclusively periodic ones.
Based on the equivalent system of 3rd type such a function W(x,x') can be constructed that its level curves
correspond to periodic orbits of the initial non-autonomous system. This function can be built a priori via
computation of the invariant manifold of the equivalent system of 1st type. Using the same approach the
Rauscher expansions cos(Qt)=C(x,x'), sin(Qt)=S(x,x') can also be constructed.
It is also shown that equivalent systems can be investigated by means of harmonic balance method which
allows construction o f W(x,x'), C(x,x') andS(x,x') in semi-analytical manner.
Опис
Ключові слова
rauscher method, equivalent autonomous system, periodic solutions, invariant manifolds methodology, continuation tecniques, harmonic balance method
Бібліографічний опис
Perepelkin N. V. Non-Iterative Rauscher Method for 1-DOF System: a New Approach to Studying Non-Autonomous System via Equivalent Autonomous One/ N. V. Perepelkin // 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. 173-182.