平面薄膜结构耦合动力学特性研究与无量纲分析

Coupling dynamics and dimensionless analysis of a planar membrane structure

  • 摘要: 利用固定界面的模态综合法建立了平面薄膜结构耦合动力学模型,精确得到了薄膜结构发生耦合振动的临界条件,分析了其耦合动力学特性。结果表明,与薄膜结构耦合基频有关的参数主要有薄膜预应力、框架弹性模量、截面惯性矩、长宽比、边长、框架横截面积、框架密度、薄膜密度和薄膜厚度。当薄膜预应力小于临界值时,薄膜结构的振动由薄膜来主导,当薄膜预应力大于临界值时,薄膜与框架发生耦合振动,此时薄膜结构的振动特性由薄膜与框架共同影响,并且随着薄膜预应力的增大,薄膜与框架发生耦合振动的阶数也随之增多并会出现振型顺序后移的现象。对薄膜结构的动力学特性进行了无量纲分析,推导了薄膜结构的小尺寸模型和大尺寸实物之间的相似准则.

     

    Abstract: The coupling dynamics model of a planar membrane structure is established by the modal synthesis method of the fixed interface. The critical conditions for the coupling vibration of the membrane structure are accurately obtained,and the coupling dynamics characteristics are analyzed. The results show that the parameters related to the fundamental frequency of the membrane structure coupling mainly include membrane prestress,frame elastic modulus,moment of inertia,aspect ratio,side length,frame cross-sectional area,frame density,membrane density,and membrane thickness. When the membrane prestress is less than the critical value,the vibration of the membrane structure is dominated by the membrane. When the membrane prestress is greater than the critical value,the membrane and the frame are coupled in vibration. At this time,the vibration characteristics of the membrane structure are jointly affected by the membrane and the frame. With the increase of the prestress of the film,the order of the coupled vibration between the membrane and the frame also increases and the order of the mode shapes will shift backward. Dimensionless analysis of the dynamic characteristics of the membrane structure is carried out,and the similarity criterion is derived between the small-size and the large-size of the membrane structures.

     

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