- 摘 要
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（1 廣州市市政工程設(shè)計研究總院， 廣州 510060； 2 同濟大學土木工程學院， 上海 200092；
3 武漢交通職業(yè)學院交通工程學院， 武漢 430065）
［摘要］混凝土梁在振搗作用下，其彈性模量會沿梁高變化。如果假設(shè)其他材料參數(shù)保持不變，根據(jù)各向異性體彈性理論，推導(dǎo)出了彈性模量隨梁高度梯度變化的Timoshenko型剪切梁的自由振動方程；在此基礎(chǔ)上，通過算例數(shù)值分析了Timoshenko型剪切梁的動力特性，主要得到了彈性模量按指數(shù)函數(shù)變化時Timoshenko型剪切梁的自振頻率及其相應(yīng)階段的模態(tài)圖以及不同高跨比條件下的梯度功能梁的梯度變化時，梁的自振頻率變化圖。
［關(guān)鍵詞］梯度功能材料； Timoshenko剪切梁； 自由振動； 固有頻率； 高跨比
中圖分類號： TU375 文獻標識碼： A文章編號： 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; depthspan ratio
作者簡介： 石玉華，碩士，高級工程師，Email：347617854@qq.com。
