基于n阶GBT热-机载荷作用下FGM梁的振动特性和稳定性分析

研究了热-机载荷耦合作用下弹性地基FGM梁的振动特性与稳定性。考虑到材料的物性依赖于温度变化且组分沿梁厚按幂律分布。首先,基于一种扩展的n阶广义剪切变形梁理论(n-th GBT),应用Hamilton原理,统一建立了系统自由振动及屈曲问题力学模型的控制方程,采用一种改进型广义微分求积法(MGDQ)获得FGM梁静动态响应的数值解。其次,通过算例验证GBT的有效性并给出阶次n的理想取值,在丰富梁理论的同时,也可验证或改进其他各种剪切变形梁理论。最后,讨论并分析了升温、边界条件、初始轴向机械载荷、梯度指标、地基刚度、跨厚比等诸多参数对FGM梁振动特性和稳定性的影响。

Vibration and stability characteristics of FGM beams under thermal-mechanical loads based on a n-th generalized shear beam theory

The vibration and stability behaviors of FGM beams on an elastic foundation under the coupled action of thermal-mechanical loads are studied.The material properties are assumed to be temperature-dependent and vary according to power-law along the thickness of the beam.Firstly,according to an extension of a n-th order generalized shear beam theory and applying Hamilton′s principle,the model of the free vibration and buckling governing equations are obtained as a unity.The static and dynamic responses for FGM beams are obtained by using a MGDQ method.Then,the accuracy of the GBT is tested throughout several numerical examples and herein the satisfactory values to n is proposed.It also refined the beam theories and can be used as a benchmark to verify other various shear deformation beam theories.Finally,the effect of temperature rise,boundary conditions,initial axial mechanical load,material graded index,elastic foundation stiffness,and length-to-thickness ratio on the vibration behaviors and stability of FGM beams are mainly discussed.