黏弹性胶合铁木辛柯梁的力学性能分析  

Analysis of mechanical properties of glued Timoshenko beams with a viscoelastic interlayer

作　　者：王林 吴鹏 周叮[1] 张建东[1] 

机构地区：[1]南京工业大学土木工程学院,江苏南京211800

出　　处：《南京工业大学学报（自然科学版）》2017年第5期85-91,114,共8页Journal of Nanjing Tech University(Natural Science Edition)

基　　金：国家重点基础研究发展计划(973计划)(2012CB026205);国家自然科学基金(51478107);江苏省交通运输科技项目(2014Y01)

摘　　要：研究任意荷载作用下黏弹性胶合铁木辛柯梁的力学性能,用标准线性固体模型描述胶层黏弹性。基于一阶剪切变形理论建立铁木辛柯梁的基本方程,将两端简支铁木辛柯梁的位移和转角表示为系数与时间相关的傅里叶级数,代入通过能量法导出的位移和转角平衡方程求解确定待定系数,从而得到任意荷载作用下黏弹性胶合铁木辛柯梁应力和位移随时间变化的解析表达式。以正弦荷载和均布荷载为例验证本研究解的正确性,数值比较显示本研究解与有限元解吻合良好。研究表明:当梁跨高比较小时,铁木辛柯梁理论解的精度明显高于欧拉-伯努利梁理论解;胶层剪应力随时间的延长而减小;梁跨中挠度随时间的延长而增大,但最终趋于常值,该值受胶层厚度和剪切模量的影响较为显著。The mechanical properties of glued Timoshenko beams with a viscoelastic interlayer subjected to any kinds of loads are studied by using the standard linear solid model to describe the viscoelasticity of the glue. The basic equations of Timoshenko beams are established based on the first-order shear deformation theory.The displacement and rotation angle functions of simply supported Timoshenko beams are expressed as Fourier series with time-dependent coefficients. Substitute the Fourier series into equilibrium equations of displacement and rotation angle obtained by energy method to solve the undetermined coefficients. Then the time-dependent analytic expressions of stress and displacement of glued Timoshenko beams with a viscoelastic interlayer subjected to any kinds of loads can be obtained.Taking sinusoidal and distributed loads as the examples to prove the correctness of the present results.Numerical comparison shows that the present results have a good agreement with the finite element solutions.It shows that results based on the Timoshenko beam theory have a better accuracy than those based on the Euler-Bernoulli beam theory when the length-to-thickness ratio of the layered beams is small.And the shear stress of the glue decreases with time.The mid-span deflection of the beams increases with time and tends to constant,which is significantly affected by the thickness and shear modulus of theglue,after a certain time.

关 键 词：层合梁 黏弹性层 一阶剪切变形理论 标准线性固体模型 解析解 

分 类 号：O345[理学—固体力学] TU311.1[理学—力学]