Open Access

ARTICLE

Position and Velocity Time Delay for Suppression Vibrations of a Hybrid Rayleigh-Van der Pol-Duffing Oscillator

by Y. A. Amer, A. T. El-Sayed, M. N. Abd El-Salam

1 Mathematics Department, Science Faculty, Zagazig University, Zagazig, Egypt
2 Basic Sciences Department, Modern Academy for Engineering and Technology, Cairo, Egypt
3 Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City, Egypt

* Corresponding Author: M. N. Abd EL-Salam. Email:

Sound & Vibration 2020, 54(3), 149-161. https://doi.org/10.32604/sv.2020.08469

Received 28 August 2019; Accepted 15 May 2020; Issue published 31 August 2020

Abstract

In this paper, we used time delay feedback to minimize the vibrations of a hybrid Rayleigh–van der Pol–Duffing oscillator. This system is a one-degree-offreedom containing the cubic and fifth nonlinear terms and an external force. We applied the multiple scales method to get the solution from first approximation. Graphically and numerically, we studied the system before and after adding time delay feedback at the primary resonance case (Ω ≌ ω). We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.

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