摘要
对于初始几何缺陷的功能梯度梁的振动问题,基于功能梯度材料的细观结构模型,采用幂函数模拟材料组分沿梁厚度方向的变化规律;基于Euler-Bernoulli梁理论,从几何方程和Marguerre应变得到了轴向应变的表达式,利用Hamilton原理推导了初始几何缺陷的功能梯度梁的运动微分方程,并进行无量纲化;运用微分求积法对无量纲振型微分方程以及边界条件进行离散,得到了特征方程;最后,分析了初始几何缺陷的功能梯度梁的梯度指标、初始的几何曲率、边界约束对其无量纲固有频率和振型的影响。
For the vibration problem of a functionally graded beam with initial geometric defect,based on the meso-structure model of functionally graded materials,the power function is used to simulate the variation of material composition along the direction of beam thickness.Based on the Euler-Bernoulli beam theory,the axial strain expression was obtained from the geometric equation and Marguerre strain,the differential equation of motion for the functionally graded beam with initial geometric defect was derived by using the Hamilton principle in the dimensionless form.The dimensionless differential equations of mode and boundary conditions are discretized by differential quadrature method,and the eigen-equation is obtained.Finally,the effects of gradient index,initial geometric curvature,boundary constraints on the dimensionless natural frequency and modes of the beam with initial geometric defects are analyzed.
作者
田婷婷
王忠民
王清波
TIAN Tingting;WANG Zhongmin;WANG Qingbo(School of Civil Engineering and Architecture,Xi’an University of Technology,Xi’an 710048,China;Huanghe S&T University,Zhengzhou 450006;Department of Civil Engineering,Sichuan College of Architectural Technology,Deyang 618000,Sichuan,China)
出处
《力学与实践》
北大核心
2022年第5期1151-1158,共8页
Mechanics in Engineering
基金
国家自然科学基金资助项目(11972286)。
关键词
功能梯度梁
初始几何缺陷
振动特性
微分求积法
functionally graded beam
initial geometric defect
vibration characteristics
differential quadrature method
