基于n阶GBT初始轴向载荷影响下FGM梁的振动特性

Vibration characteristics of FGM beams under the action of initial axial load based on a n-th generalized shear beam theory

研究了初始轴向载荷影响下弹性地基功能梯度材料(FGM)梁的振动特性。基于一种拓展的n阶广义剪切变形梁理论(n-GBT),以轴向位移、剪切变形挠度与弯曲变形挠度为基本未知函数,应用Hamilton原理,建立了该系统自由振动问题力学模型的控制方程。引入边界控制参数,采用一种改进型广义微分求积(MGDQ)法获得了FGM梁的静动态响应。通过算例验证并给出了GBT阶次n的理想取值,丰富梁理论的同时,可供验证或改进其它各种剪切变形梁理论;提供的数值分析方法切实可行,拓展了GDQ法的使用范围。最后,着重讨论并分析了初始轴向载荷、边界条件、梯度指标、地基刚度、跨厚比等参数对FGM梁振动特性的影响。

The vibration behavior of functional gradient material(FGM)beams on elastic foundation under the action of initial axial load was investigated.Based on an extended n-th generalized shear deformation beam theory and applying Hamilton’s principle,the free vibration governing equations of the mechanical model for the system was developed,in which the unknown basic functions are the axial displacement,shear and bending components of deflection.Introducing boundary condition coefficients and applying a modified generalized differential quadrature(MGDQ)method,the static and dynamic responses of FGM beams were obtained.The availability and accuracy of the extended theory and the method were verified through numerical examples and herein the ideal value of n was proposed.The study refines the beam theories and the result can be used as a benchmark to verify or modify other various shear deformation beam theories.The numerical solution by using MGDQ was validated and the process can expand its applicable scope.The effects of the initial axial load,boundary conditions,material graded index,elastic foundation stiffness,and length-to-thickness ratio on the vibration characteristics of FGM beams were mainly analyzed.