Oscillator with variable mass excited with non-ideal source
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In this paper dynamics of a non-ideal mechanical system which contains a motor, which is a non-ideal source, and an oscillator with slow time variable mass is investigated. Due to the insufficient energy of the energy source the one degree-of-freedom oscillator has an influence on the motion of the motor. The system is modeled with two coupled second order equations with time variable parameters where the motor torque is assumed as a linear function of angular velocity. The equations are transformed into four first order differential equations. An analytical procedure for obtaining the approximate averaging equations is developed. Based on these equations the amplitude-frequency relations are determined. In the paper the equations of motion of the non-ideal mass variable oscillatory system are solved numerically, too. The approximate analytical solutions are compared with numerically obtained ones. The difference is negligible. In the paper the qualitative analysis of the model is done. It is shown that due to mass variation the number and the position of the ‘almost’ steady-state positions are varying. By increasing or decreasing of mass the number of almost steady-state positions is varying. Based on the obtained results it is suggested to develop the control method for motion in the non-ideal mass variable oscillatory system.
KeywordsSommerfeld effect ‘Almost’ steady-state position Oscillator with variable mass Non-ideal system
The investigation has been supported by the Ministry of Science of Serbia (Proj. Nos. ON174028 and IT41007).
- 5.Xie, G.Q., Qian, S.W., Gu, Z.Y.: Separation of variables treatment of the time-dependent damped harmonic oscillator with an arbitrary varying mass and with a force quadratic in the velocity under the action of an arbitrary time-varying force. Phys. Lett. A 207, 11–16 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
- 13.Nayfeh, A.H., Mook, D.T.: Nonlinear Oscilltions. Wiley, New York (1979)Google Scholar
- 14.Kononenko, V.O.: Vibrating Systems with Limited Excitation. Nauka, Moscow (1964)Google Scholar
- 16.Balthazar, J.M., Brasil, R.M.L.R.F., Weber, H.I., Fenili, A., Belato, D., Felix, J.L.P., Garzeri, F.J.: A review of new vibrating issues due to non-ideal energy sources. In: Udwadia, F., Weber, H.I., Leitmann, G. (eds.) Dynamics Systems and Control, Stability and Control Theory. Methods and Applications, vol. 22, pp. 237–258. Chapman & Hall, London (2004)Google Scholar