Vibration energy transfer in nonlinear coupled near-identical systems

This study investigates the dynamic response and vibrational energy transfer characteristics of coupled near-identical systems, with a focus on coupled discrete oscillators and coupled cantilever beams. Using analytical approximations based on the averaging method and harmonic balance-alternating frequency time (HB-AFT), alongside numerical integration, the dynamic responses and vibration transfer behaviour are analysed. The influence of both linear and nonlinear coupling stiffness is thoroughly examined. Comprehensive experimental results and finite element analysis (FEM) are conducted, focusing on mode shape and frequency response under motion excitation. For the motion excitation analysis, our findings reveal that even minor variations in mass can disrupt symmetry, resulting in the emergence of an additional resonant peak and illustrating the unique frequency response behaviours of near-identical systems. Notably, power flow analysis indicates that energy is transferred from the lighter oscillator to the heavier one across different frequency ranges, with distinct patterns observed during both in-phase and out-of-phase oscillations. For the power transfer curves, both linear and nonlinear cubic coupling stiffness ratio controls the location of the second resonance frequencies. It is also shown that the second resonance peak bends to a higher frequency when the cubic stiffness ratio increases. The results offer valuable implications for the design and optimization of coupled systems in various engineering applications.