K. Suddalai Kannan, S. M. Abdul Kader, M. V. Sethumeenakshi, V. Chinnathambi, and S. Rajasekar
Nonlinear Response of a Position Dependent Mass System Driven by an Amplitude Modulated Force
Dynamic Systems and Applications 32 (2023) 18-32

https://doi.org/10.46719/dsa2023.32.02

ABSTRACT.
This paper highlights on the occurrence of vibrational resonance (VR), investigated in a double-well position-dependent mass (PDM)-Duffing oscillator system driven by an amplitude modulated (AM) force. The AM force consists of one low-frequency (ω) component and two high-frequencies (Ω + ω) and (Ω- ω) components with (Ω >> ω). In the PDM-Duffing oscillator with one low-frequency and one high-frequency forces, by applying a theoretical approach an analytical expression is obtained for the response amplitude at the low-frequency (ω). The system provides an interesting scenario where PDM function makes a significant contribution to the occurrence of VR. We examine the role played by PDM parameters (m_o, λ) and force parameters (g, ω, Ω ) on VR. We show the enhanced response amplitude Q at the low-frequency ω, showing more number of resonance peaks, a non-decay of response amplitude and hysteresis and a jump phenomenon on the response amplitude curve due to the amplitude modulated force. Results of analytical investigations are validated and complemented by numerical simulation.

AMS (MOS) Subject Classification. 34K18, 37C29, 65P20, 65P30, 74H65.

Key Words and Phrases. Position dependent mass system, Amplitude modulated force, Vibrational resonance,
Hysteresis, Chaos.