Study On Nonlinear Vibration Of Axially Moving Systems

The multiple dimension Lindstedt-Poincaré(L-P) method and the incremental harmonic balance (IHB) method are employed for nonlinear vibration analysis of axially moving systems.Firstly, the modified Lindstedt-Poincarémethod is used to study the strongly nonlinear vibrations of beams without axially moving. The free vibration, the fundamental resonance, subharmonic resonance, supharmonic resonance are studied respectively. All the results are compared with those obtained by the IHB method to show the effectiveness and accuracy.Secondly, the multiple dimension Lindstedt-Poincarémethod is used to study the nonlinear vibration of axially moving beams. The equation of motion of axially moving beams are derived by using Hamilton principle and discretized by using Galerkin method. Various resonance such as fundamental harmonic resonance, subharmonic resonance, supharmonic resonance, supharmonic resonance, combination harmonic resonance, are studied in detail, which occurred when the excitation frequencyΩis near to the first natural frequencyω₁₀, the second frequencyω₂₀, the one third of first frequency 1/3ω₁₀, the one half ofω₁₀ +ω₂₀, respectively. From which, many varied and interesting nonlinear phenomenon are revealed. The differences between the results with and without the model damping are analyzed at the same time.Thirdly, the IHB method is employed to study every resonance mentioned above. The results obtained by the IHB method and the multiple dimension L-P method are compared one by one to show the accuracy and effectiveness of both methods. Finally, the conclusion and recommendation are given.Parts of this work have been or will be published in several international and national journals.