（1 广州市市政工程设计研究总院， 广州 510060； 2 同济大学土木工程学院， 上海 200092；

3 武汉交通职业学院交通工程学院， 武汉 430065）

 ［摘要］混凝土梁在振捣作用下，其弹性模量会沿梁高变化。如果假设其他材料参数保持不变，根据各向异性体弹性理论，推导出了弹性模量随梁高度梯度变化的Timoshenko型剪切梁的自由振动方程；在此基础上，通过算例数值分析了Timoshenko型剪切梁的动力特性，主要得到了弹性模量按指数函数变化时Timoshenko型剪切梁的自振频率及其相应阶段的模态图以及不同高跨比条件下的梯度功能梁的梯度变化时，梁的自振频率变化图。

［关键词］梯度功能材料； Timoshenko剪切梁； 自由振动； 固有频率； 高跨比

中图分类号： TU375 文献标识码： A文章编号：  1002-848X(2016)S2-0466-05

Vibration analysis of functionally graded Timoshenko shear beam

Shi Yuhua1, Li Jingjun1，2 , Chen Yanping3

（1 Guangzhou Municipal Engineering Design & Research Institute, Guangzhou 510060, China;

2 Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;

3 Wuhan Technical College of Communications, Wuhan 430065, China）

Abstract: Under the action of vibration ,elastic modulus of concrete beam will change along the beam high. If other material parameters are assumed to remain constant, based on anisotropic theory of elasticity, the free vibration equation of Timoshenko shear beam with elastic modulus of the beam height gradient were investigated. On this basis, frequency results and some mode shapes of FGM beam were given under certain exponential gradient function condition through a numerical example by assuming that variation of elasticity modulus in the thickness direction was taken in different exponential form. The dynamic characteristic of FGM beam was also researched according to results of the numerical example. And the change of FGM beam with different height span ratio and the gradient. The dynamic characteristic of FGM beam was also researched according to results of the numerical example.

Keywords: functionally graded material(FGM); Timoshenko shear beam; free vibration; vibration frequency; depthspan ratio

作者简介： 石玉华，硕士，高级工程师，Email：347617854@qq.com。