Abstract
The geometric nonlinearity due to the large elastic deformations of three flexible links is considered in setting up the dynamic equation of elastic linkages. It is shown that both the quadratic nonlinear terms and the cubic nonlinear terms are included in the model. The analyses with the method of multiple scales demonstrate that the superharmonic resonances caused by the quadratic and cubic nonlinearities, as well as the multi-frequency nature of the inertial force are the reasons causing the critical speed to take place. They also demonstrate that the combination resonances caused by the combined effects of internal resonance in the form of ω2 ≈ 2ω1, the cubic nonlinearity and the multi-frequency nature of the inertial forces is the reason causing the production of the nonsynchronism of the lower order harmonic resonances of elastic linkages. Meanwhile, the influences of important system parameters on the resonances are investigated.
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Wang, Y. Dynamics of an Elastic Four Bar Linkage Mechanism with Geometric Nonlinearities. Nonlinear Dynamics 14, 357–375 (1997). https://doi.org/10.1023/A:1008269731024
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DOI: https://doi.org/10.1023/A:1008269731024