轴向运动分数阶粘弹性梁的动力学模型及振动问题研究  

Study on Dynamic Model and Vibration of Axially Moving Fractional Order Viscoelastic Beams

作　　者：殷凯琳 欧志英[1] Yin Kailin;Ou Zhiying(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《黑龙江科学》2023年第18期48-51,55,共5页Heilongjiang Science

基　　金：国家自然科学基金(11862014)。

摘　　要：基于Euler-Bernoulli梁理论,在位移应变关系前提下建立了轴向运动分数阶粘弹性梁的动力学模型并对其振动问题进行分析。考虑粘弹性梁微单元的受力情况,利用牛顿第二定律与Euler-Bernoulli假设推导出梁非线性振动的偏微分方程。在此类非线性模型中,梁的轴向应力在梁的整个轴上是与轴向坐标有关的一个变量,由此分析其在不同条件下的变化情况。在轴向运动梁的振动分析中考虑了梁材料的粘弹性,这种粘弹性阻尼的存在对运动梁振动的幅频响应及受某种激励下运动梁的稳定性有非常明显的影响。利用直接多尺度法分析轴向运动梁的振动问题,根据可解性条件求解梁的控制偏微分方程。利用所建模型分析其他参数,如阻尼比与固有频率对梁振动的影响,通过数值算例对模型进行比较得出结论。在研究过程中,分数阶模型具有更高的精度及更广的研究范围,进一步体现了分数阶模型的优越性。Based on Euler-Bernoulli beam theory,the study establishes a dynamic model of an axially moving fractional-order viscoelastic beam,and analyzes its vibration on the premise of displacement and strain relation.Then the study derives partial differential equation of nonlinear vibration of a viscoelastic beam with Newton’s second law and Euler-Bernoulli hypothesis.In this kind of nonlinear model,the axial stress of the beam is a variable related to the axial coordinates on the whole axis of the beam;analyzes its variation under different conditions.The viscoelasticity of the beam material is considered in the vibration analysis of the axially moving beam.The existence of the viscoelastic damping has a very obvious influence on the amplitude-frequency response of the moving beam and the stability of the moving beam under certain excitation.The study analyzes the vibration problem of axially moving beam with direct multi-scale method,and solves the control partial differential equation of beam according to the condition of solvability.The effects of other parameters,such as damping ratio and natural frequency,on the vibration of the beam are analyzed by using the model,and a numerical example is given to compare the model.In the research process,the fractional-order model has higher precision and wider research scope,which further embodies the superiority of fractional-order model.

关 键 词：分数阶 粘弹性梁 振动 HPM 

分 类 号：TB53[理学—物理]