【作者】 黄建亮；

【导师】 陈树辉；

【作者基本信息】 中山大学 ， 工程力学， 2004， 博士

【摘要】 本文应用多元Lindstedt-Poincaré（L-P）法及增量谐波平衡法（the incremental harmonic balance method, IHB）研究轴向运动体系的横向非线性振动。首先,研究无轴向运动的梁的强非线性振动,应用改进的L-P法分析了梁的自由振动和在外激励力作用下的基谐波响应、次谐波响应、超谐波响应,并与IHB法结果比较,证明改进的L-P法的有效性和正确性。其次,研究轴向运动梁的横向非线性振动,根据哈密顿原理建立轴向运动梁的横向运动微分方程,利用Galerkin方法离散方程,再应用多元L-P法分别研究当外激励力频率Ω接近于系统第一阶固有频率ω₁₀、第二阶固有频率ω₂₀、第一阶固有频率的1/3 (即1/3ω₁₀)和第一、第二阶固有频率的平均值1/2 (ω₁₀ +ω₂₀)时伴随内部共振的基谐波响应、次谐波响应、超谐波响应和组合谐波响应,同时也分析有和没有模态阻尼的差别,从中揭示了丰富多彩的非线性振动现象。接着,应用IHB法计算上述各种非线性振动响应问题,并与多元L-P法的计算结果进行比较,说明两种方法的有效性和正确性。最后,给出本文工作的结论和对今后工作的展望。本论文的部分研究成果已在国内外力学类核心期刊上发表或录用待发表。更多还原

【Abstract】 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.更多还原