广西师范大学学报（自然科学版） ›› 2025, Vol. 43 ›› Issue (6): 128-139.doi: 10.16088/j.issn.1001-6600.2024120304

• 数学与统计学 • 上一篇    下一篇

两种黏弹性运动板的数值模拟与稳定性分析

邓金娜1, 刘秋梅1*, 陈一鸣2, 杨爱民1   

  1. 1.华北理工大学 理学院,河北 唐山 063210;
    2.燕山大学 理学院,河北 秦皇岛 066000
  • 收稿日期:2024-12-03 修回日期:2025-01-15 发布日期:2025-11-19
  • 通讯作者: 刘秋梅(1981—),女,河北唐山人,华北理工大学副教授,博士。E-mail: liuqiumei@ncst.edu.cn
  • 基金资助:
    河北省自然科学基金(E2022209110)

Numerical Simulation and Stability Analysis of Two Kinds of Viscoelastic Moving Plates

DENG Jinna1, LIU Qiumei1*, CHEN Yiming2, YANG Aimin1   

  1. 1. College of Science, North China University of Science and Technology, Tangshan Hebei 063210, China;
    2. School of Science, Yanshan University, Qinhuangdao Hebei 066004, China
  • Received:2024-12-03 Revised:2025-01-15 Published:2025-11-19

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1

摘要： 为研究2种黏弹性轴向运动板的动态响应,采用变分数阶模型推导轴向运动板的控制方程,将移位Bernstein多项式作为基函数来求解变分数阶微分方程,导出移位Bernstein多项式的算子矩阵,控制方程用矩阵乘积的形式表示。通过数值算例验证算法的可行性。比较陶瓷(ceramic)板和聚对苯二甲酸乙二醇酯(PET)板在简谐载荷下的位移,分析轴向移动速度对轴向黏弹性板位移的影响,并比较不同材料板在不同厚度变化下的位移变化。研究结果初步突破求解黏弹性运动板的变分数阶模型,为黏弹性结构的研究提供理论依据。

关键词: 黏弹性轴向运动板, 变分数阶微分方程, 移位Bernstein多项式, 数值模拟

Abstract: In order to study the dynamic response of two kinds of viscoelastic axially moving plates, the governing equations of the axially moving plates are derived by using the variable-fractional model. Firstly, the variable-fractional differential equations are solved by using the shifted Bernstein polynomial as the basis function, and the operator matrix of the shifted Bernstein polynomial is derived. Secondly, the feasibility of the algorithm is verified by numerical examples. Thirdly, the displacement of ceramic plate and PET plate under harmonic load is further studied and compared. Finally the influence of axial moving speed on displacement of axial viscoelastic plate is analyzed, and the displacement changes of different material plates under different thickness changes are compared. The research results break through the variable-fractional order model of viscoelastic moving plate and provide a theoretical basis for the study of viscoelastic structure.

Key words: viscoelastic axially moving plate, differential equation of variable fractional order, shifted Bernstein polynomial, numerical simulation

中图分类号:  O221

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