Dynamic analysis of vibrating systems with nonlinearities. (English) Zbl 1247.34054

Yazdi, Kalami M.; Ahmadian, H.; Mirzabeigy, A.; Yildirim, A.

Commun. Theor. Phys. 57, No. 2, 183-187 (2012).

Summary: The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He’s max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.

MSC:

34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K20	Stability for nonlinear problems in mechanics

Keywords:

nonlinear oscillation; He’s max-min approach; dynamic analysis