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林业科学 ›› 2022, Vol. 58 ›› Issue (8): 173-181.doi: 10.11707/j.1001-7488.20220818

• 研究论文 • 上一篇    下一篇

Timoshenko自由梁迭代法计算木材弹性模量和剪切模量的适用性

王正,周宇昊,沈肇雨,何宇航   

  1. 南京林业大学材料科学与工程学院 南京 210037
  • 收稿日期:2021-09-17 出版日期:2022-08-25 发布日期:2022-12-19
  • 基金资助:
    2021年江苏省现代农业产业单项技术研发项目(CX(21) 3049)

Applicability of Timoshenko Beam Iterative Method to Calculate Wood Elastic Modulus and Shear Modulus

Zheng Wang,Yuhao Zhou,Zhaoyu Shen,Yuhang He   

  1. College of Materials Science and Engineering, Nanjing Forestry University Nanjing 210037
  • Received:2021-09-17 Online:2022-08-25 Published:2022-12-19

摘要:

目的: 基于试验探究Timoshenko自由梁迭代法计算木材弹性模量和剪切模量的适用性,重点考虑木材弹性模量和剪切模量的测试精度,寻求梁试件合适的长厚比。方法: 通过山毛榉、云杉-松-冷杉(SPF)和单板层积材(LVL)试件截短试验,动态测试不同长厚比试件的频谱,从频谱图上读出自由梁的第一阶和第二阶弯曲频率;应用迭代程序计算木材和木质复合材料的弹性模量和剪切模量;采用自由杆件扭转振动法和自由板扭转振型法验证自由梁迭代法计算剪切模量的有效性。结果: 存在一个与树种有关的试件长厚比下限值,当试件长厚比小于该下限值时, 自由梁迭代法不能计算出正常的弹性模量和剪切模量或根本计算不出弹性模型和剪切模量;自由梁迭代法计算出的弹性模量高于Euler自由梁法计算出的弹性模量,其程度与试件长厚比有关,仅当试件长厚比大于24时其偏高值才在4%以内;自由梁迭代法计算出的剪切模量与矩形截面因子k取值有关,当k取0.833和0.913时,分别高于自由杆件扭转振动法(自由板扭转振型法)剪切模量测试值12.2%和2.3%(19.9%和9.3%)。结论: 为保证自由梁迭代法测试精度,推荐采用长厚比20~24的梁试件动态测试其第一阶和第二阶弯曲频率,并用矩形截面因子取0.913进行迭代计算木材的弹性模量和剪切模量。

关键词: 固有频率, Timoshenko自由梁迭代法, 弹性模量, 剪切模量, 适用性, 测试精度

Abstract:

Objective: When Timoshenko free beam iteration method is used to dynamically test the elastic modulus and shear modulus of wood, its test accuracy is greatly affected by the different length thickness ratios of the specimen. Therefore, this paper was implemented to explore the applicability of calculating wood elastic modulus and shear modulus according to the iterative method of Timoshenko beam, and further focus on the test accuracy. Method: Through the truncated test of beech, SPF(spruce, pine and fir) and LVL(laminated venner lumber) specimens, the spectrums under different length thickness ratios were dynamically measured, and the first and second-order bending frequencies of free beam were read out from the spectrum. At the same time, the elastic modulus and shear modulus of wood and wood composites were calculated by iterative program. The effectiveness of the iterative method to calculate the shear modulus was verified by the free member torsional vibration method and the free plate torsional vibration mode method. Result: There was a lower limit value of length thickness ratio related to tree species. When the length thickness ratio of the specimen was less than the lower limit value, the elastic modulus and shear modulus could not be iterated by the iterative method. The elastic modulus determined by iterative method was higher than the elastic modulus test value of Euler beam. The iterative method also could give a too high calculated value of shear modulus. The elastic modulus calculated by iterative method might be higher than the elastic modulus test value based on Euler beam, and its degree is related to the length thickness ratio of the specimen. Only when the length thickness ratio of the specimen is greater than 24, the high value is less than 4%. The calculated value of shear modulus given by iterative method is related to the value of rectangular section factor k. When the rectangular section factor k is equal to 0.833 and 0.913, the calculated value of the shear modulus obtained by the iterative method is 12.2% and 2.3% (19.9% and 9.3%) higher than the measured value of the free member torsional vibration method (free plate torsional vibration mode method), respectively. Conclusion: In order to ensure the test accuracy, it is recommended to use beam specimens with length thickness ratio of 20-24 to dynamically test the first and second-order bending frequencies, and iteratively calculate the elastic modulus and shear modulus of wood with rectangular section factor of 0.913.

Key words: natural frequency, Timoshenko free beam iterative method, modulus of elasticity, shear modulus, applicability, test accuracy

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