Analysis of nonlinear autonomous conservative oscillators by a time transformation method. (English) Zbl 0562.70024

Burton, T. D.; Hamdan, M. N.

J. Sound Vib. 87, 543-554 (1983).

Summary: The problem considered is that of the free vibration of the class of strongly nonlinear oscillators \(\ddot u+mu+\alpha f(u)=0\), where \(m=1,0\), or \(-1,\) \(f(u)\) is a nonlinear function of the displacement \(u(t)\), and \(\alpha\) is not small. Through a continuous stretching of the time \(t\) a new time \(T\) is found in whose domain the response is simple harmonic. This time transformation method allows the response \(u(t)\) and period \(\tau\) to be calculated to any desired degree of accuracy; however, the primary objective is to developed reasonably simple, accurate approximations for the oscillators considered.

MSC:

70K99

Nonlinear dynamics in mechanics

Keywords:

free vibration; strongly nonlinear oscillators; time transformation method