两项激励下石墨环氧叠层板的组合共振特性研究
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study on combination resonances of a simply supported rectangular graphite-expoxy laminated plate excited by two-term harmonic forces
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    摘要:

    对两项激励下石墨环氧叠层板的非线性特性进行了研究.根据板的非线性运动方程,应用伽辽金法得出了矩形叠层板在两项均布简谐激励力作用下的无量纲化达芬型非线性振动微分方程,用多尺度法对层叠板组合共振微分方程求解,得出发生组合共振的各种情形,对组合共振的稳定性进行了分析,得到稳态运动下的幅频响应方程.代入有关参数,分析了不同参数对系统共振的影响,结果表明两项激励下层叠板表现出较复杂的动力学特性.

    Abstract:

    This paper studied the nonlinearity properties of a simply supported rectangular graphiteexpoxy laminated plate, excited by twoterm harmonic forces. The nondimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method from the vibration differential equation.The amplitude frequency response equation of the system steady motion under combination resonance was obtained by the method of multiple scales. Based on Lyapunov stable theory , the critical conditions of steadystate solutions stability were obtained .By examples, the influence of different parameters on nonlinear combination resonances properties of system was analyzed. Finally the conclusion of graphiteexpoxy laminated plate’s nonlinearity properties excited by twoterm forces were presented.

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任建华,吕书锋.两项激励下石墨环氧叠层板的组合共振特性研究[J].动力学与控制学报,2011,9(2):172~176; Ren Jianhua, Lv shufeng. study on combination resonances of a simply supported rectangular graphite-expoxy laminated plate excited by two-term harmonic forces[J]. Journal of Dynamics and Control,2011,9(2):172-176.

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  • 收稿日期:2010-12-10
  • 最后修改日期:2011-01-11
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