Analysis of Primary Resonance in Damped Duffing-Helmholtz Oscillator Excited by an Amplitude-Modulated Signal

Chaudhary Anunay Kumar (Sri Venkateswara College, University of Delhi South Campus)
Das Saureesh (Institute of Informatics and Communication, University of Delhi South Campus)
Narang Pankaj (A. R. S. D. College, University of Delhi South Campus)
Das Mrinal Kanti (Institute of Informatics and Communication, University of Delhi South Campus)

Journal of the Indonesian Mathematical Society
Vol. 32 No. 3 (2026): SEPTEMBER

The effect of amplitude modulated signal on the primary resonance on a Duffing-Helmholtz oscillator has been investigated using ($i$) a multiple time scale perturbation method involving two different time scales i.e., regular time ($T_0$) and a slow time, ($T_1$), to analyze the system response and ($ii$) its modified version which is valid for larger values of expansion parameter viz., asymptotic ordering parameter, incorporating Lindstedt-Poincare transformation method that allows the interaction of the amplitude and frequency of the response. The modification of the amplitude- frequency plots, exhibiting bi-stable behavior, caused by different values of modulation amplitude and damping has been obtained both analytically and numerically for various parameters of the system near the primary resonance. The peak amplitude of the response is shown to get lowered in strongly nonlinear Duffing-type system. Phase plane trajectories of stable and unstable manifolds are presented in different instances.