Theoretical and numerical study of vibrational resonance in a damped softening Duffing oscillator

We study the possibility of occurrence vibrational resonance in a softening Duffing oscillator underdamped and overdamped cases both theoretically as well numerically. The is driven by two periodic forces. Numerically we find that case oscillatory solutions are obtained limited range parameters considered (damping coefficient amplitude high frequency force) for fixed low force depending on initial conditions. These have distinct response to force. When damping gradually increased, only one solution observed. Vibrational observed regions oscillation. analytical approximation yields all values. Analytically, peak area bounded phase portrait function connected resonance. Also, values forcing at which found occur obtained. In case, not thus showing marked contrast bistable oscillator. • (VR) studied (SDO). VR SDO. Area peaks with high-frequency