Affiliation:
1. Department of Applied Mechanics and Engineering, Sun Yat-sen University , Guangzhou 510275, China
2. Department of Mechanical Engineering, University of Maryland , Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250
Abstract
AbstractPeriodic and period-doubling vibrations in a gear transmission system subjected to forced excitations with multipiecewise linear functions are investigated in this work by using the incremental harmonic balance (IHB) method. The nonlinear ordinary differential equations that govern vibration of the gear transmission system are formulated by employing the Newton's second law. Analytical results reveal abundant interesting phenomena, including jumps, bifurcations, softening-spring behaviors, and primary, super-harmonic, and subharmonic resonances, which have not been exhibited in existing investigations on nonlinear vibrations of gear transmission systems. Nonlinear phenomena and resonances of the gear transmission system are revealed by considering different numbers of degrees-of-freedom of the system. The bifurcations containing saddle-node, period-doubling, and Hopf bifurcations are observed in frequency response curves. The period-doubling phenomena are characterized by phase-plane diagrams and Fourier spectra. Further, analytical results obtained by the IHB method match very well with those from numerical integration.
Funder
Guangdong Science and Technology Department
National Natural Science Foundation of China
Subject
Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,General Medicine