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用高阶剪切理论求双模量夹芯梁自由振动基频
Study on the fundamental frequency of free vibration of double modulus sandwich beams with higher - order shear theory
投稿时间:2023-11-01  修订日期:2023-11-27
DOI:
中文关键词:  高阶剪切  双模量  夹芯梁  自由振动  基频
英文关键词:higher-order shear  double modulus  sandwich beam  free vibration  fundamental frequency
基金项目:
作者单位邮编
吴晓* 湖南文理学院机械工程学院 415000
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中文摘要:
      基于高阶剪切理论研究了求解双模量夹芯梁的自由振动基频问题。首先假设双模量夹芯梁轴向位移为沿梁高方向变量的高阶函数,然后利用剪切应变与轴向位移、弯曲挠度微分关系确定了轴向位移表达式,推导出了双模量夹芯梁的弯曲微分方程,求出了均布载荷作用下的挠度曲线表达式。把该方法计算结果与有关试验结果进行比较可知,该方法的计算精度非常高。在此基础上把均布载荷作用下的挠度曲线表达式作为双模量夹芯梁自由振动的振型函数,利用Galerkin法研究了双模量夹芯梁的自由振动,求得了双模量夹芯梁自由振动的基频表达式。算例分析表明,双模量夹芯梁基频公式计算精度很高。
英文摘要:
      Based on high order shear theory, the free vibration fundamental frequency problems of double modulus sandwich beams were studied. Firstly, it was assumed that the axial displacement of double modulus sandwich beam was a high-order function with the variable along the beam height direction. Then, according to the differential relationship between shear strain and axial displacement and bending deflection, the expression of axial displacement was determined, the bending differential equation was derived, and the deflection curve expression of the double-mode sandwich beam under uniform load was obtained. Compared the calculation results of this method with relevant test results, it could be found that the method had high computational accuracy. On the basis of the study mentioned above, the expression of the deflection curve under uniform load was considered as the mode function of free vibration for the double modulus sandwich beam, the free vibration of the double-modulus sandwich beam was studied with Galerkin method, and the fundamental frequency expression of the free vibration was obtained. Example analysis shown that it had high precision in calculating the fundamental frequency of the double modulus sandwich beam.
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