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热环境下弹性地基上多孔FGM圆板的自由振动特性
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Free Vibration Characteristics of Porous FGM Circular Plates on Elastic Foundations under Thermal Environment
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    摘要:

    基于一阶剪切变形理论,研究了热环境下弹性地基上多孔功能梯度材料(Functionally Graded Materials,FGM)圆板的自由振动特性.首先,考虑含孔隙的Voigt修正混合幂律模型,并给出统一温度场描述材料受温度依赖,利用Hamilton原理,推导热环境下弹性地基上多孔FGM圆板自由振动的控制微分方程并进行无量纲化;然后,应用微分变换法对无量纲控制微分方程和边界条件进行变换,得到计算无量纲固有频率和临界温升值的代数特征方程.将问题退化后并与已有文献结果进行对比以验证其有效性;最后,计算并分析了梯度指数、孔隙率、边界条件、厚度与半径比、温升值和Winkler 弹性刚度系数对多孔FGM圆板无量纲固有频率的影响以及各相关参数对临界温升值的影响.结果表明,梯度指数影响频率,反映材料从陶瓷向金属过渡的特点,孔隙率削弱刚度进而影响固有频率大小,Winkler地基对刚度有着增强的作用,温度增大使结构发生热屈曲而失稳等.

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    Based on the first-order shear deformation theory, the free vibration characteristics of a circular plate of porous Functionally Gradient Material (FGM) on an elastic foundation in a thermal environment are studied. First, Voigt modified mixed power law model with pores is considered, and a unified temperature field is given to describe the temperature dependence of materials. Using Hamilton’s principle, the governing differential equation of free vibration of porous FGM circular plate on elastic foundation under thermal environment is derived and dimensionless. Then the dimensionless governing differential equation and boundary conditions are transformed by using the differential transformation method, and the algebraic characteristic equations for dimensionless natural frequencies and critical temperature rise are obtained. The problem is degenerated and compared with the existing literature results to verify its effectiveness. Finally, the influence of gradient index, porosity, boundary conditions, thickness radius ratio, temperature rise, and Winkler elastic foundation coefficient on the dimensionless natural frequency of porous FGM circular plate as well as the influence of relevant parameters on the critical temperature rise is calculated and analyzed. The results show that the gradient index affects the frequency, reflecting the characteristics of the transition of materials from ceramics to metals. Porosity weakens the stiffness and then affects the natural frequency. Winkler foundation has a role in strengthening the stiffness, and the increase in temperature causes thermal buckling and instability of the structure.

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TENG Zhaochun?,WANG Weibin, XUE Gang.热环境下弹性地基上多孔FGM圆板的自由振动特性[J].湖南大学学报:自然科学版,2023,(10):193~202

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  • 在线发布日期: 2023-11-13
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