Outer isolated detached resonance curve and its implications of a two-stage nonlinear dynamic system

Abstract

This paper presents an innovative study of a two-stage nonlinear dynamic system, providing insights into the occurrence of Large-Amplitude Long-Duration Vibration State (LALDVS) and outer isolated detached resonance curves (OIDRCs). The Lagrange equations and the incremental harmonic balance method (IHBM) are used to uncover the fundamental mechanism of OIDRCs and to discover two and three OIDRCs that have not been previously reported. Multiple OIDRCs could have significant practical implications in engineering, as they indicate the possibility of unpredictable and potentially hazardous vibrations under certain operating conditions. The existence of OIDRCs depends on the jump frequency point being a Neimark-Sacker bifurcation, and the resulting phase diagram provides vital insights into the stability and bifurcation behaviors of the system. This work also explores the effect of stiffness on the nonlinear response behavior of the system and identifies the range of stiffness values that lead to LALDVS. The correctness of the theoretical calculation results is validated by comparing them with vibration experiment and simulation calculations. These results have practical implications for engineering and energy harvesting research, including identifying potential hazards associated with vibration and designing systems that maximize energy harvesting efficiency. Overall, these findings are innovative and have significant implications for predicting potentially hazardous vibrations in engineering and the design of energy harvesting systems.