机电工程技术2025，Vol.54Issue(8)：38-42,47,6.DOI:10.3969/j.issn.1009-9492.2025.08.008
分数阶微积分下粘弹性梁的振动分析
Vibration Analysis of Viscoelastic Beams under Fractional Calculus
王玉兰 1成建联1
作者信息
- 1. 长安大学工程机械学院,西安 710064
- 折叠
摘要
Abstract
In order to solve the problem of inaccurate analysis of the vibration characteristics of viscoelastic beams by integer order differential equations,a detailed vibration analysis of a viscoelastic material simply supported beam is presented using fractional calculus theory.Based on the Euler-Bernoulli beam theory,the dynamic model of the fractional order viscoelastic beam of axial motion is established,the differential equation is solved by the Galerkin method and the corresponding analytical solution is obtained,the mathematical model is numerically calculated by Matlab software,and the amplitude-frequency and phase-frequency curves of different fractional coefficient α(0<α<1)and different resonance frequencies are analyzed.The results show that the influence of fractional coefficient α on the resonance frequency of the beam is not significant,the smaller the α,the smaller the amplitude peak,with the increase of order α and frequency,the influence of fractional term on the attenuation of phase frequency curve gradually increases,and fractional calculus has a stronger ability to describe the dynamic characteristics of signals and systems in the case of high frequency and high order.The use of fractional differential equations to model system dynamics for viscoelastic materials can reduce the complexity of the differential equations by using fewer terms,which helps to simplify the model and reduce the amount of computation,while retaining sufficient accuracy.关键词
分数阶微积分/粘弹性梁/振动分析/Kelvin本构模型Key words
fractional calculus/viscoelastic beam/vibration analysis/Kelvin constitutive model分类
力学引用本文复制引用
王玉兰,成建联..分数阶微积分下粘弹性梁的振动分析[J].机电工程技术,2025,54(8):38-42,47,6.
