摘要
木梁是木结构建筑中关键的承重构件,承受过大载荷时易在中间部位产生裂纹,当裂纹沿梁的厚度方向扩展到一定深度时将发生断裂,因此,对木梁裂纹的监测是木结构建筑构件中的一项重要课题。从弹性动力学的角度出发,建立了有中间部位裂纹木梁的横向振动模型,推导出裂纹深度与梁弯曲振动的固有频率公式,并加以试验验证。首先,基于欧拉-伯努利梁模型提出了含有裂纹的木梁振动力学模型,推导出该木梁各阶固有频率的理论计算公式;其次,选取3种厚度规格的木梁试件,每种规格10个平行试样,测量了各规格试件在不同裂纹深度情况下的一至五阶固有频率,并与理论值进行对比分析。从理论与试验分析发现,梁中间裂纹会使木梁振动的固有频率下降,且随着裂纹深度的增加,木梁固有频率的下降愈发显著,并且固有频率阶数越高,裂纹深度对固有频率影响越大。随着阶数升高,各阶固有频率模型的计算值与实测值之间的误差迅速减小,从平均误差50%降至3%左右,可见本研究提出的理论模型与试验结果吻合度较高。研究结果表明,可以通过监测木梁固有频率的变化来监测木梁断裂裂纹的深度扩展变化,提出的理论模型可为木梁裂纹监测与断裂评估提供新思路。
In timber structures,wooden beams serve as essential load-bearing components.When subjected to excessive loads,these beams can develop cracks,particularly in their middle-sections.As these cracks deepen,they can compromise the structural integrity of the beams,potentially leading to failures.Therefore,monitoring and assessing cracks in wooden beams is crucial for ensuring the safety and durability of timber structures.This study addressed this issue by establishing a transverse vibration model for wooden beams with mid-section cracks from an elastic dynamics'perspective.It derived formulas for the natural frequencies of bending vibrations as functions of crack depth and validated these through experimental data.Initially,based on the Euler-Bernoulli beam model,this study proposed a dynamic model for the vibration of wooden beams containing cracks.It derived theoretical formulas for calculating the natural frequencies of various vibrational modes of the beam.These formulas accounted for the impact of crack depth on the beam's structural integrity and its vibrational properties.Understanding how cracks influence natural frequencies is key to predict and monitor the structural health of wooden beams in construction.In the experimental phase,three different thickness specifications of wooden beam specimens were tested,with 10 parallel samples for each specification.The natural frequencies from the first to the fifth mode of each specification were measured under different crack depths.These experimental results were compared with the theoretical values derived from the model.The analysis of both theoretical and experimental data revealed several important findings.Cracks in the middle of the beam caused a reduction in the natural frequency of the beam's vibrations.As the crack depth increased,the decrease in natural frequency became more significant.This relationship was crucial for evaluating the severity of cracks and predicting potential structural failures.Additionally,it was found that the impact of crack depth on natural frequency was more pronounced in higher vibrational modes.This suggested that the higher-order modes were more sensitive to changes in structural integrity.As the mode number increased,the discrepancy between calculated and measured natural frequencies decreased significantly,from an average error of 50%to about 3%.This high level of agreement indicated that the theoretical model was effective in predicting natural frequencies,particularly for higher-order modes that were critical for crack detection and assessment.Overall,the findings suggested that monitoring changes in the natural frequencies of wooden beams can effectively track crack progression,enabling accurate estimation of the safety and durability of buildings.The proposed theoretical model provided a valuable approach for crack monitoring and assessing in wooden beams,potentially enhancing the safety and longevity of timber structures.
作者
庄怡玲
王佳怡
王宇轩
徐兆军
华洁
ZHUANG Yiling;WANG Jiayi;WANG Yuxuan;XU Zhaojun;HUA Jie(College of Mechanical and Electronic Engineering,Nanjing Forestry University,Nanjing 210037,China)
出处
《林业工程学报》
北大核心
2025年第4期144-152,共9页
Journal of Forestry Engineering
基金
南京林业大学2023年大学生创新创业训练计划项目(2023NFUSPITP0067)
教育部产学合作协同育人项目(231102817220731)。
关键词
木梁
欧拉-伯努利梁模型
固有频率
断裂裂纹
wooden beams
Euler-Bernoulli beam model
natural frequency
fracture crack
