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足尺胶合板弹性模量的两对边简支振动检测研究

李焕 管成 张厚江 刘晋浩 周建徽 辛振波

李焕, 管成, 张厚江, 刘晋浩, 周建徽, 辛振波. 足尺胶合板弹性模量的两对边简支振动检测研究[J]. 北京林业大学学报, 2021, 43(2): 138-149. doi: 10.12171/j.1000-1522.20200300
引用本文: 李焕, 管成, 张厚江, 刘晋浩, 周建徽, 辛振波. 足尺胶合板弹性模量的两对边简支振动检测研究[J]. 北京林业大学学报, 2021, 43(2): 138-149. doi: 10.12171/j.1000-1522.20200300
Li Huan, Guan Cheng, Zhang Houjiang, Liu Jinhao, Zhou Jianhui, Xin Zhenbo. Determining modulus of elasticity of full-size plywood panel simply supported on two opposite sides using a vibration method[J]. Journal of Beijing Forestry University, 2021, 43(2): 138-149. doi: 10.12171/j.1000-1522.20200300
Citation: Li Huan, Guan Cheng, Zhang Houjiang, Liu Jinhao, Zhou Jianhui, Xin Zhenbo. Determining modulus of elasticity of full-size plywood panel simply supported on two opposite sides using a vibration method[J]. Journal of Beijing Forestry University, 2021, 43(2): 138-149. doi: 10.12171/j.1000-1522.20200300

足尺胶合板弹性模量的两对边简支振动检测研究

doi: 10.12171/j.1000-1522.20200300
基金项目: 中国博士后科学基金面上资助项目(2018M641225),林业公益性行业科研专项(201304512),中央高校基本科研业务费专项资金资助(BLX201817)
详细信息
    作者简介:

    李焕。主要研究方向:木材无损检测技术。Email:1433049495@qq.com 地址:100083北京市海淀区清华东路35号北京林业大学工学院

    责任作者:

    管成,博士,讲师。主要研究方向:木材无损检测技术。Email:648911029@qq.com 地址:同上

    张厚江,教授,博士生导师。主要研究方向:木材无损检测技术。Email:hjzhang6@bjfu.edu.cn 地址:同上

  • 中图分类号: S781.23

Determining modulus of elasticity of full-size plywood panel simply supported on two opposite sides using a vibration method

  • 摘要:   目的   研究足尺胶合板两个主要方向(即长度和宽度方向)弹性模量的两对边简支振动检测,为足尺胶合板两个主要方向弹性模量的在线无损检测提供一种新方法。   方法   以4种厚度共20块足尺胶合板为研究对象,采用有限元软件COMSOL Multiphysics和PULSE振动测试系统分别对两对边简支的足尺胶合板进行了模态灵敏度分析和试验模态分析;提出了一种两对边简支边界条件下的足尺胶合板弹性模量振动检测试验方法,运用此方法提取出足尺胶合板所需模态的频率,将其带入到编写的弹性模量检测算法中,用以计算足尺胶合板两个主要方向的动态弹性模量值;进行了三点弯曲静态试验检测足尺胶合板两个主要方向的静态弹性模量值,用以验证动态弹性模量检测结果的准确性。   结果   确定了用于计算足尺胶合板两个主要方向弹性模量的频率所对应的模态,分别为其自由振动前9阶模态中的第1阶模态(2, 0)和第7阶模态(2, 2);厚度变化对足尺胶合板的前9阶模态的阶次排序没有影响;足尺胶合板两个主要方向的动态弹性模量均大于静态弹性模量,且同一厚度足尺胶合板的力学性能存在不均匀性;足尺胶合板长度和宽度方向的动态弹性模量与静态弹性模量间均具有显著的线性关系,决定系数分别为0.907和0.655。   结论   基于两对边简支振动和弹性模量振动检测算法检测足尺胶合板两个主要方向的弹性模量具有可行性。

     

  • 图  1  足尺胶合板两对边简支

    Figure  1.  Full-size plywood panel simply supported on two opposite sides

    图  2  两对边简支的足尺胶合板的前9阶计算模态振型图

    Figure  2.  Diagrams of the first nine calculated mode shapes of full-size plywood panels simply supported on two opposite sides

    图  3  两对边简支足尺胶合板前9阶模态对弹性模量的灵敏度分析结果

    Figure  3.  Sensitivity analysis results of the first nine modes to MOE of full-size plywood panels simply supported on two opposite sides

    图  4  两对边简支足尺胶合板弹性模量的振动检测算法程序流程图

    Figure  4.  Flowchart of vibration detection algorithm for MOE of the full-size plywood panels simply supported on two opposite sides

    图  5  两对边简支足尺胶合板的模态参数振动检测装置图

    Figure  5.  Diagram of vibration detection equipment for modal parameters of the full-size plywood panel simply supported on two opposite sides

    图  6  激振点的频率响应函数幅值图

    Figure  6.  Amplitude diagram of frequency response function of excitation point

    图  7  两对边简支的足尺胶合板的前9阶模态振型图

    Figure  7.  The first nine mode shapes of full-size plywood panels simply supported on two opposite sides

    图  8  运用振动法测得的足尺胶合板两个方向弹性模量与ρ/h2间的关系

    Ex dEy d分别为足尺胶合板的长度和宽度方向的动态弹性模量,h为板材厚度, ρ为板材密度。Ex d and Ey d represent the dynamic MOE in length and width directions of full-size plywood panel, respectively. h is thickness, and ρ is density of the panel.

    Figure  8.  Relationship between MOE values in both directions of full-size plywood panels obtained from vibration method and ρ/h2

    图  9  运用振动法测得的足尺胶合板两个方向弹性模量与其对应振动模态的f 2ρ/h2间的关系

    Figure  9.  Relationship between MOE values in both directions of full-size plywood panels obtained from vibration method and f 2ρ/h2 of the corresponding modes

    图  10  两种方法测得的足尺胶合板弹性模量间的关系

    Figure  10.  Relationship between MOE results of full-size plywood panels measured by two methods

    表  1  固有频率表达式中的系数值

    Table  1.   Coefficient values of the natural frequency expression

    宽度方向 Width direction长度方向 Length direction
    系数
    Coefficient
    取值 Value系数
    Coefficient
    取值 Value
    m = 2n = 0n = 2
    Pm1Pn01.506
    Im1In01.247
    Jm1Jn05.013
    Km0Kn1.8835.328
    Lm0Ln00.182
    Mm0Mn03.584
    P(m+2)3P(n+2)1.5063.500
    I(m+2)9I(n+2)1.24710.022
    J(m+2)9J(n+2)5.01318.935
    K(m+2)0K(n+2)5.3286.092
    L(m+2)0L(n+2)0.1820.999
    M(m+2)0M(n+2)3.5847.914
    注:P、IJKLM均为与足尺胶合板的模态振型相关的系数,其取值引自参考文献[8]。Notes:P, I, J, K, L and M are the coefficients related to mode shapes of full-size plywood panel, and the values of these coefficients are cited from reference [8].
    下载: 导出CSV

    表  2  两对边简支的足尺胶合板计算模态分析的初始参数

    Table  2.   Initial parameters for calculated modeanalysis of full-size plywood panels simply supported on two opposite sides

    板材种类
    Panel type
    弹性模量
    Modulus of elasticity (MOE)/MPa
    剪切模量
    Shear modulus/MPa
    泊松比
    Poisson’s ratio (υxy)
    密度
    Density/(kg·m−3)
    尺寸
    Dimension
    ExEyGxyGyzGxz
    胶合板 Plywood5 2006 9509501702200.0395742 440 mm × 1 221 mm × 18 mm
    注:表中数据引自参考文献[10]、[13]和[14]。ExEy分别为足尺胶合板长度和宽度方向的弹性模量,GxyGyzGxz分别为足尺胶合板x-yy-zx-z平面内的剪切模量。下同。Notes:data in the table are cited from reference [10], [13] and [14]. Ex and Ey represent the MOE in length and width directions of full-size plywood panel, respectively. Gxy, Gyz and Gxz represent the shear modulus in the x-y, y-z and x-z planes of full-size plywood panels, respectively. Same as below.
    下载: 导出CSV

    表  3  被测足尺胶合板的基本参数

    Table  3.   Basic parameters of the measured full-size plywood panels

    板材
    Panel
    板材尺寸
    Panel dimension
    平均密度
    Average density/(kg·m−3)
    PW122 441 mm × 1 221 mm × 12 mm541
    PW152 440 mm × 1 221 mm × 15 mm534
    PW182 441 mm × 1 222 mm × 18 mm532
    PW202 440 mm × 1 221 mm × 20 mm524
    注:PW12、PW15、PW18和PW20分别代表标称厚度为12、15、18和20 mm的胶合板。Notes: PW12, PW15, PW18 and PW20 represent the full-size plywood panels with nominal thickness of 12, 15, 18 and 20 mm, respectively.
    下载: 导出CSV

    表  4  两对边简支足尺胶合板的前9阶模态参数

    Table  4.   The first nine mode parameters of full-size plywood panels simply supported on two opposite sides Hz

    阶次 OrderPW12PW15PW18PW20振型 Vibration mode
    13.13.64.34.5(2, 0)
    26.47.59.19.4(2, 1)
    311.313.816.717.2(3, 0)
    415.317.322.224.6(3, 1)
    524.830.234.035.0(4, 0)
    629.834.642.243.0(4, 1)
    731.038.246.749.0(2, 2)
    835.243.254.356.5(3, 2)
    948.557.070.071.0(4, 2)
    下载: 导出CSV

    表  5  两种方法测得的足尺胶合板弹性模量结果

    Table  5.   Results for MOE values of full-size plywood panels measured by two methods

    板材 PanelMOE振动法 Vibration method静态法 Static method
    Ex dEy dEx sEy s
    PW12 平均值 Mean value/MPa 7 057 6 841 5 864 5 964
    标准偏差 Standard deviation/MPa 481 210 410 178
    变异系数 Coefficient of variation/% 6.8 3.1 7.0 3.0
    相对偏差 Relative deviation/% 20.4 14.7
    PW15 平均值 Mean value/MPa 5 151 6 954 4 625 6 262
    标准偏差 Standard deviation/MPa 470 267 360 211
    变异系数 Coefficient of variation/% 9.1 3.8 7.8 3.4
    相对偏差 Relative deviation/% 11.4 11.0
    PW18 平均值 Mean value/MPa 4 846 6 886 4 383 6 619
    标准偏差 Standard deviation/MPa 460 144 362 126
    变异系数 Coefficient of variation/% 9.5 2.1 8.3 1.9
    相对偏差 Relative deviation/% 10.6 4.0
    PW20 平均值 Mean value/MPa 5 358 5 755 5 041 5 644
    标准偏差 Standard deviation/MPa 863 260 733 270
    变异系数 Coefficient of variation/% 16.1 4.5 14.5 4.8
    相对偏差 Relative deviation/% 6.3 2.0
    注:变异系数 = 标准偏差/平均值;相对偏差 = (动态弹性模量 − 静态弹性模量)/静态弹性模量。Notes: coefficient of variation is the ratio of standard deviation to mean value; relative deviation is the ratio of difference between dynamic MOE and static MOE to the static MOE.
    下载: 导出CSV

    表  6  两种方法测得的足尺胶合板弹性模量的一元线性回归及相关参数

    Table  6.   One-dimensional linear regression and related parameters of MOE of full-size plywood panels measured by two methods

    MOE板材
    Panel
    数量
    Number
    y = kx + r相关系数
    Correlation coefficient
    F
    F value
    显著性
    Significance
    kr
    Ex PW1250.812134.2250.95229.3290.012
    PW1550.704996.4820.92116.7330.026
    PW1850.754727.5150.95732.9570.010
    PW2050.841534.5700.991157.7100.001
    PW200.6911 107.2890.965246.1230.000
    Ey PW1250.771690.2560.91114.6350.031
    PW1550.6931 440.0950.87810.0620.050
    PW1850.839842.4780.96136.1340.009
    PW2051.028−272.7610.993206.3270.001
    PW200.6162 052.2290.80934.1850.000
    注:y = kx + r,式中xy分别代表足尺胶合板的动态和静态弹性模量,k为回归系数,r为常数。Notes: in the formula y = kx + r, x and y represent the dynamic and static MOE of full-size plywood panel, respectively, k is the regression coefficient and r is a constant.
    下载: 导出CSV
  • [1] 张厚江, 管成, 文剑. 木质材料无损检测的应用与研究进展[J]. 林业工程学报, 2016, 1(6):1−9.

    Zhang H J, Guan C, Wen J. Applications and research development of nondestructive testing of wood based materials[J]. Journal of Forestry Engineering, 2016, 1(6): 1−9.
    [2] 管成, 刘晋浩, 张厚江, 等. 足尺人造板力学性能无损检测研究进展[J]. 北京林业大学学报, 2019, 41(9):164−172.

    Guan C, Liu J H, Zhang H J, et al. Literature review of mechanical properties of full-size wood composite panels using nondestructive testing technique[J]. Journal of Beijing Forestry University, 2019, 41(9): 164−172.
    [3] Sobue N, Katoh A. Simultaneous determination of orthotropic elastic-constants of standard full-size plywoods by vibration method[J]. Mokuzai Gakkaishi, 1992, 38(10): 895−902.
    [4] Bos F, Casagrande S B. On-line non-destructive evaluation and control of wood-based panels by vibration analysis[J]. Journal of Sound and Vibration, 2003, 268(2): 403−412. doi: 10.1016/S0022-460X(03)00342-0.
    [5] 管成, 张厚江, 苗虎, 等. 无损检测足尺人造板弹性模量和面内剪切模量[J]. 南京林业大学学报(自然科学版), 2017, 41(4):153−159.

    Guan C, Zhang H J, Miao H, et al. Non-destructive determination of modulus of elasticity and in-plane shear modulus of full-size wood composite panels[J]. Journal of Nanjing Forestry University (Natural Science Edition), 2017, 41(4): 153−159.
    [6] Hearmon R F S. The fundamental frequency of vibration of rectangular wood and plywood plates[J]. Proceedings of the Physical Society, 1946, 58(1): 78−92. doi: 10.1088/0959-5309/58/1/307.
    [7] Huffington N J, Hoppmann W H. On the transverse vibrations of rectangular orthotropic plates[J]. Journal of Applied Mechanics ASME, 1958, 25(2): 389−395.
    [8] Kim C S, Dickinson S M. Improved approximate expressions for the natural frequencies of isotropic and orthotropic rectangular plates[J]. Journal of Sound and Vibration, 1985, 103(1): 142−149. doi: 10.1016/0022-460X(85)90254-8.
    [9] 张厚江, 申世杰, 崔英颖, 等. 振动方式测定木材弹性模量[J]. 北京林业大学学报, 2005, 27(6):91−94. doi: 10.3321/j.issn:1000-1522.2005.06.017.

    Zhang H J, Shen S J, Cui Y Y, et al. Measuring elastic modulus of wood using vibration method[J]. Journal of Beijing Forestry University, 2005, 27(6): 91−94. doi: 10.3321/j.issn:1000-1522.2005.06.017.
    [10] 管成. 面向力学性能评估的足尺人造板四节点支承振动检测研究[D]. 北京: 北京林业大学, 2018.

    Guan C. Evaluation of mechanical properties of full-size wood composite panels supported on four nodes using vibration methods[D]. Beijing: Beijing Forestry University, 2018.
    [11] 祖汉松. 足尺人造板力学性能无损检测样机总体设计与关键问题研究[D]. 北京: 北京林业大学, 2015.

    Zu H S. Overall design and key issues study of mechanical properties nondestructive testing prototype of the full-size wood composite panels[D]. Beijing: Beijing Forestry University, 2015.
    [12] Guan C, Zhang H J, Wang X P, et al. Experimental and theoretical modal analysis of full-sized wood composite panels supported on four nodes[J]. Materials, 2017, 10(6): 683. doi: 10.3390/ma10060683.
    [13] Yoshihara H. Poisson’s ratio of plywood measured by tension test[J]. Holzforschung, 2009, 63(5): 603−608.
    [14] Yoshihara H. Influence of the specimen depth to length ratio and lamination construction on Young’s modulus and in-plane shear modulus of plywood measured by flexural vibration[J]. Bioresources, 2012, 7(1): 1337−1351.
    [15] Zhou J H, Chui Y H, Gong M, et al. Simultaneous measurement of elastic constants of full-size engineered wood-based panels by modal testing[J]. Holzforschung, 2016, 70(7): 673−682. doi: 10.1515/hf-2015-0117.
    [16] Leissa A W. Vibration of plates[M]. Washington: Scientific and Technical Information Division, National Aeronautics Space Administration, 1969.
    [17] 黄炎. 弹性薄板理论[M]. 长沙: 国防科技大学出版社, 1992.

    Huang Y. Theory of elastic thin plate[M]. Changsha: National University of Defense Technology Press, 1992.
    [18] 全国人造板标准化技术委员会. 普通胶合板: GB/T 9846—2015[S]. 北京: 中国标准出版社, 2015.

    National Technical Committee on Wood-based Panels Standardization of China. Plywood for general use: GB/T 9846–2015[S]. Beijing: Standards Press of China, 2015.
    [19] 全国人造板标准化技术委员会. 人造板及饰面人造板理化性能试验方法: GB/T 17657—2013[S]. 北京: 中国标准出版社, 2014.

    National Technical Committee on Wood-based Panels Standardization of China. Test methods of evaluating the properties of wood-based panels and surfaces decorated wood-based panels: GB/T 17657–2013[S]. Beijing: Standards Press of China, 2014.
    [20] Mclain T E, Bodig J. Determination of elastic parameters of full-size wood composite boards[J]. Forest Products Journal, 1974, 24(4): 48−57.
    [21] 管成, 周卢婧, 张厚江, 等. 用振动方式测定足尺人造板弹性模量[J]. 浙江农林大学学报, 2016, 33(6):1067−1072. doi: 10.11833/j.issn.2095-0756.2016.06.020.

    Guan C, Zhou L J, Zhang H J, et al. Measuring modulus of elasticity of full-size wood composite panels using vibration method[J]. Journal of Zhejiang A&F University, 2016, 33(6): 1067−1072. doi: 10.11833/j.issn.2095-0756.2016.06.020.
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出版历程
  • 收稿日期:  2020-10-06
  • 修回日期:  2020-12-02
  • 网络出版日期:  2020-12-31
  • 刊出日期:  2021-02-24

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