基于多项式拟合的细长梁结构振动位移重构方法

马烨璇,徐万海,徐增伟

振动与冲击 ›› 2020, Vol. 39 ›› Issue (11) : 152-157.

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (11) : 152-157.
论文

基于多项式拟合的细长梁结构振动位移重构方法

  • 马烨璇,徐万海,徐增伟
作者信息 +

Displacement reconstruction of slender beam based on polynomial fitting method

  • MA Yexuan, XU Wanhai, XU Zengwei
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文章历史 +

摘要

细长梁结构易受内外因素的干扰而振动,由此引发的疲劳损伤问题不利于结构安全。实时重构结构的振动位移是健康监测和振动智能控制中的关键环节。目前,模态分析法广泛用于细长梁结构的振动位移重构,但对于边界条件复杂的细长梁结构或结构受较强非线性因素干扰时,采用模态分析法重构结构位移将存在诸多不便。针对此问题,提出了基于多项式拟合的细长梁结构振动位移重构方法,并采用延展结构边界的方式有效规避了多项式拟合经常出现的龙格现象。通过有限元模拟和实验数据的对比,验证了基于多项式的位移重构方法的精确性和可行性。结果表明:基于多项式拟合的位移重构方法适用于细长梁结构线性振动和非线性振动的位移重构;延展结构边界可有效规避多项式拟合出现的龙格现象;延展长度为0.875L-1.125L (L为细长梁结构的长度),虚拟测点应变的量级小于等于真实测点应变最大值的量级时,重构得到的结构位移精度较高。

Abstract

Vibrations of slender flexible beam are induced easily by the inner and outer interference factors, which may cause severe fatigue damage and threaten the safety of the structure. Real-time reconstruction of structural vibration displacement is the key technology for structural health monitoring (SHM) and intelligent oscillation control. Nowadays, modal analysis approach is widely used in the displacement reconstruction of slender flexible beam. When the slender flexible beam has complex boundary conditions and strong nonlinear factors, modal analysis approach is not convenient to reconstruct the displacement. Hence, displacement reconstruction method for slender flexible beam based on polynomial fitting is put forward. The approach of extending structure boundary is employed to avoid the Runge phenomenon which usually occurs in polynomial fitting. The accuracy and feasibility of displacement reconstruction method based on polynomial fitting are validated by finite element simulation and reconstruction of experimental data. Some conclusions are drawn from the results. The displacement reconstruction method based on polynomial fitting is effective for the displacement reconstruction of linear and nonlinear vibrations of slender flexible beams. Extending structure boundary is useful to reduce the Runge phenomenon caused by polynomial fitting. When the extended length is 0.875L-1.125L (L is the length of slender flexible beam) and the magnitude of strains at the virtual measuring points is less than or equal to the magnitude of the maximum strain at the real measuring points, the reconstructed displacements have high accuracy.

关键词

位移重构 / 多项式拟合 / 细长梁 / 龙格现象 / 结构延展

Key words

displacement reconstruction / polynomial fitting / slender flexible beam / Runge phenomenon / structural extension;

引用本文

导出引用
马烨璇,徐万海,徐增伟. 基于多项式拟合的细长梁结构振动位移重构方法[J]. 振动与冲击, 2020, 39(11): 152-157
MA Yexuan, XU Wanhai, XU Zengwei. Displacement reconstruction of slender beam based on polynomial fitting method[J]. Journal of Vibration and Shock, 2020, 39(11): 152-157

参考文献

[1] Chaplin J R, Bearman P W, Huera-Huarte F J, et al. Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current [J]. Journal of Fluids and Structures, 2005, 21(1): 3-24.
[2] Le TH, Caracoglia L. Modeling vortex-shedding effects for the stochastic response of tall buildings in non-synoptic winds [J]. Journal of Fluids and Structures, 2016, 61: 461-491.
[3] Jing H, Xia Y, Li H, et al. Excitation mechanism of rain–wind induced cable vibration in a wind tunnel [J]. Journal of Fluids and Structures, 2017, 68(Supplement C): 32-47.
[4] Omidi E, Mahmoodi S N, Shepard W S. Vibration reduction in aerospace structures via an optimized modified positive velocity feedback control [J]. Aerospace Science and Technology, 2015, 45(Supplement C): 408-415.
[5] Lochan K, Roy B K, Subudhi B. A review on two-link flexible manipulators [J]. Annual Reviews in Control, 2016, 42(Supplement C): 346-367.
[6] Tessler A, Spangler J L. A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells [J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(2): 327-339.
[7] Gherlone M, Cerracchio P, Mattone M, et al. Shape sensing of 3D frame structures using an inverse Finite Element Method [J]. International Journal of Solids & Structures, 2012, 49(22):3100-3112.
[8] 蔡鹏越. 用于结构位移场重构的逆有限元法研究[D]. 南京:南京航空航天大学, 2016.
CAI Peng-yue. Investigation on the inverse FEM for structural displacement reconstruction [D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016.
[9] 刘坤. 基于力法的梁-柱单元位移场构造方法研究[D].哈尔滨:哈尔滨工业大学, 2008.
LIU Kun. Study on construction methods of displacement field for force-based beam-column element [D]. Harbin: Harbin Institute of Technology, 2008.
[10] Ko W L, Richards W L, Tran V T. Displacement theories for in-flight deformed shape predictions of aerospace structures [R]. NASA/TP-2007-214612, H-2652, Edwards (CA): NASA Dryden Flight Research Center (US), 2007.
[11] Foss G C, Haugse E D. 1995. Using modal test results to develop strain to displacement transformations [J]. The International Society for Optical Engineering, 1995, 2460:112.
[12] Li C J, Ulsoy A G. High-precision measurement of tool-tip displacement using strain gauges in precision flexible line boring [J]. Mechanical Systems and Signal Processing, 1999, 13(4): 531-546.
[13] Lie H, Kaasen K E. Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow [J]. Journal of Fluids and Structures, 2006, 22(4): 557-575.
[14] Trim A D, Braaten H, Lie H, et al. Experimental investigation of vortex-induced vibration of long marine risers [J]. Journal of Fluids and Structures, 2005, 21(3): 335-361.
[15] 高云, 付世晓, 宋磊建. 柔性立管涡激振动抑制装置试验研究[J]. 振动与冲击, 2014, 33(14): 77-83.
GAO Yun, Fu Shi-xiao, SONG Lei-jian. Experimental investigation on the suppression device of VIV of a flexible riser [J]. Journal of vibration and shock, 2014, 33(14): 77-83.
[16] 高云, 任铁, 付世晓,等. 柔性立管涡激振动响应特性试验研究[J]. 振动与冲击, 2015, 34(17):6-11.
GAO Yun, REN Tie, FU Shi-xiao, et al. Tests for response characteristics of VIV of a flexible riser [J]. Journal of vibration and shock, 2015, 34(17):6-11.
[17] 徐万海, 马烨璇, 杜杰, 等. 45°大倾角倾斜柔性圆柱涡激振动不相关原则实验验证[J]. 振动与冲击, 2017, 36(7):177-183.
XU Wan-hai, MA Ye-xuan, DU Jie, et al. Test verification for independence principle applied in vortex-induced vibrations of a flexible cylinder inclined at 45° [J]. Journal of vibration and shock, 2017, 36(7): 177-183.
[18] Xu W, Ma Y, Ji C, et al. Laboratory measurements of vortex-induced vibrations of a yawed flexible cylinder at different yaw angles [J]. Ocean Engineering, 2018, 154: 27-42.
[19] 张雨浓, 李名鸣, 陈锦浩,等. 龙格现象难题破解之系数与阶次双确定方法[J]. 计算机工程与应用, 2013, 49(3): 44-49.
ZHANG Yu-nong, LI Ming-ming, CHEN Jinhao, et al. Solving the problem of Runge phenomenon by coefficients-and-order-determination method. Computer Engineering and Applications, 2013, 49(3): 44-49.
[20] 赵峰, 欧阳永忠, 晏新村,等. 精密星历插值中龙格现象处理策略[J]. 海洋测绘, 2013, 33(4): 62-65.
ZHAO Feng, OUYANG Yong-zhong, YAN Xin-cun, et al. Disposal strategy of Runge’s phenomenon in interpolating precise ephemeris. Hydrographic Surveying and Charting, 2013, 33(4): 62-65.

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