温度变化对不同边界梁非线性振动及特性影响

发布时间：2018-07-25 16:02

【摘要】：温度变化有可能导致工程结构产生温度应力,引起结构振动特性发生改变.因此针对工程中常见的受轴力作用梁,基于Hamilton变分原理,在梁的应力-应变关系中引入温度变化,推导其非线性运动微分方程.针对三类边界条件(铰支-铰支、铰支-固支和固支-固支),开展特征值分析及模态离散.利用摄动法求解系统非线性自由振动和主共振响应的近似解,并得到其幅频响应方程.通过算例研究温度变化对梁非线性振动特性影响.研究结果表明:梁固有频率和温度变化呈现出反比例关系;温度变化与梁非线性振动时硬弹簧特性的程度呈正比例关系;温度变化对小幅和大幅振动时的响应幅值影响恰恰相反;相同温度变化条件对不同边界梁的振动特性影响有定量差异;温度变化会导致梁的位移场曲线发生定量改变.总之梁结构的线性和非线性振动特性受温度响明显,且需特别关注其边界条件.
[Abstract]:The change of temperature may lead to the thermal stress of the engineering structure and the change of the vibration characteristics of the structure. Based on the Hamilton variational principle, the temperature change is introduced into the stress-strain relation of the beam, and the nonlinear differential equation of motion is deduced. The eigenvalue analysis and modal discretization are carried out for three kinds of boundary conditions (hinge-hinge support, hinge-fixed support and clamped support). The perturbation method is used to solve the approximate solutions of the nonlinear free vibration and the principal resonance response of the system, and the amplitude-frequency response equation is obtained. The effect of temperature change on nonlinear vibration characteristics of beam is studied by an example. The results show that the natural frequency and temperature of the beam are inversely proportional, and the change of temperature is proportional to the degree of the characteristics of the hard spring in the nonlinear vibration of the beam. The effect of temperature change on the response amplitude of small and large vibration is the opposite; the effect of the same temperature change conditions on the vibration characteristics of different boundary beams has quantitative difference; the temperature change will lead to the quantitative change of displacement field curve of the beam. In a word, the linear and nonlinear vibration characteristics of beam structure are obviously affected by temperature response, and special attention should be paid to its boundary conditions.
【作者单位】：华侨大学土木工程学院;湖南大学土木工程学院;
【基金】：国家自然科学基金青年项目(11602089,11402085) 福建省自然科学基金青年创新项目(2016J05011) 福建省中青年教师教育科研项目(JAT160025) 华侨大学高层次人才科研启动项目(15BS409)
【分类号】：O327

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