湿-热-机耦合作用下多孔功能梯度梁的振动及屈曲特性
Vibration and buckling behaviors of porous functionally graded material beams subjected to hygro-thermal-mechanical effects

采用一种拓展的n阶广义梁理论（GBT），研究了轴向机械载荷作用下多孔功能梯度材料（FGM）梁在湿热环境中的振动及屈曲特性。考虑了材料的物性随温度变化，湿-热沿梁厚按三种不同类型分布，采用含孔隙率的修正Voigt混合率模型描述多孔功能梯度梁的材料属性，在宏-细观力学模型框架下应用Hamilton原理统一建立了系统的自由振动及屈曲方程，采用Navier法求解FGM简支梁的静动态响应。通过算例验证并讨论了GBT阶数n的理想取值，可用于丰富梁理论。探讨了湿热效应、湿-热-机耦合、孔隙率、材料梯度指标、跨厚比对FGM梁振动及屈曲特性的影响。结果表明：湿-热加剧降低了FGM梁的频率和临界载荷，且不同类型的湿热分布对其减小程度有显著差异；随着孔隙率增大，梁结构的整体刚度虽有所弱化，但在湿热环境中频率反而增大，稳定性增强；湿-热效应对多孔FGM细长梁频率和稳定性影响十分显著，但对短粗梁的影响比较有限。 The vibration and buckling behaviors of porous functionally graded material(FGM) beams under the action of axial mechanical load in hygrothermal environment were investigated by an extension of a n-th order generalized beam theory (GBT). The material properties were temperature-dependent and described by modified Voigt mixture rule with porosity. The free vibration and buckling equations of the system were obtained by using the macro-micro analytical approach and Hamilton principle, in which three types of hygro-thermal distribution through the thickness of a beam were assumed. Applying the Navier solution method, the solutions for the free vibration and buckling responses of FGM simply supported beams were presented. The availability and accuracy for the GBT were tested throughout the numerical results and herein the satisfactory values to n was proposed, which can also refine beam theories. The effects of three types of hygro-thermal distribution, coupling hygro-thermal-mechanical loads, porosity, material graded index and length-to-thickness ratio on the vibration and buckling behaviors of a FGM beam were discussed. The results show that frequency and buckling load of the structure decrease as both temperature and moisture rise, and different types of hygro-thermal distribution will lead to distinct effects on it. As the porosity of the material increases, the structural unitary stiffness will be weakened, while frequency and stability of the structure in hygro-thermal environment will increase. Hygro-thermal rise has a little effect for short and thick FGM porous beams but remarkable effect for long and thin ones on the frequency and stability. 国家自然科学基金（51978320；11962016）；兰州工业学院“启智”人才培养计划基金（2018QZ-05