基于Legendre多项式对变分数阶粘弹性微梁数值模拟  

Numerical Simulation of Variable-Fractional Viscoelastic Microbeams Based on Legendre Polynomials

作　　者：刘芸辰 屈静国 杨爱民 韩阳 LIU Yunchen;QU Jingguo;YANG Aimin;HAN Yang(College of Science,North China University of Science and Technology,Tangshan Hebei 063210,China;Department of Discipline Construction,North China University of Science and Technology,Tangshan Hebei 063210,China)

机构地区：[1]华北理工大学理学院,河北唐山063210 [2]华北理工大学学科建设处,河北唐山063210

出　　处：《华北理工大学学报(自然科学版)》2025年第2期114-124,共11页Journal of North China University of Science and Technology:Natural Science Edition

基　　金：唐山市科技计划项目(22130201G):融合大数据深度学习的高炉炉况智能研判机理研究;河北省高等学校自然科学研究项目(QN2023153):基于转炉炉口火焰光谱调制的烟气分析动态矫正模型研究。

摘　　要：微梁是工程领域中常见结构之一,因此对微梁进行深入研究至关重要。本文对可变分数阶粘弹性微梁的控制方程进行深入的变分数阶建模与数值求解,并进行一系列动力学分析和讨论。采用一种新的数值算法,直接在时域内求解变分数阶非线性粘弹性微梁的控制微分方程,并研究微梁在不同参数下的位移情况。进行均布载荷和阶跃载荷条件下微梁挠度的数值模拟。结果表明研究结果可以为未来研究和工程应用提供可靠的数值计算方法。Microbeams are one of the common structures in the field of engineering,so it is essential to conduct an in-depth study of microbeams.In this paper,the governing equations of variable fractional viscoelastic microbeams are modeled and numerically solved,and a series of dynamic analyses and discussions are carried out.A new numerical algorithm is used to solve the controlling differential equation of the variable fractional nonlinear viscoelastic microbeams directly in the time domain,and the deflection and displacement of the microbeams under different parameters are studied.Numerical simulation of the deflection of microbeams under uniform load and step load is carried out.The results show that the results can provide a reliable numerical method for future research and engineering applications.

关 键 词：移位Legendre多项式算法 阶跃载荷 随机力 数值模拟 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]