Nonlinear Response of a Position Dependent Mass System Driven by an Amplitude Modulated Force

Abstract

. This paper highlights on the occurrence of vibrational resonance (VR), investigated in a double-well position-dependent mass (PDM)-Du–ng oscillator system driven by an amplitude modulated (AM) force. The AM force consists of one low-frequency ( ! ) component and two high-frequencies (› + ! ) and (› ¡ ! ) components with (› (cid:192) ! ). In the PDM-Du–ng 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 ( ! ). The system provides an interesting scenario where PDM function makes a signiflcant contribution to the occurrence of VR. We examine the role played by PDM parameters ( m 0 ; ‚ ) and force parameters ( g; !; ›) on VR. We show the enhanced response amplitude Q at the low-frequency ! , 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.