| 王正直,颜朔庚,王琨,高恩来,税朗泉,何勇,黄凯*.基于不同梁模型的弯曲变形分析与实验教学探讨[J].实验力学,2021,36(5):617~626 |
| 基于不同梁模型的弯曲变形分析与实验教学探讨 |
| Bending deformation analysis and experimental teaching discussion based on different beam models |
| 投稿时间：2021-01-27 修订日期：2021-03-01 |
| DOI：10.7520/1001-4888-21-020 |
| 中文关键词: 基础力学 梁模型 悬臂梁 实验平台 教学实验 |
| 英文关键词:basic mechanics beam model cantilever beam experimental platform teaching experiment |
| 基金项目:国家自然科学基金(11972264， 11602177)；湖北省自然科学基金(2016CFB2418) |
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| 中文摘要: |
| 梁的弯曲变形是基础力学的核心内容之一，以往实验教学中的变形分析通常基于Euler-Bernoulli梁模型进行，而对工程中常见的Timoshenko梁涉及较少，这种变形模式的单一性和局限性教学无疑落后于当前力学学科人才培养的发展趋势。为了使本科生深入理解梁弯曲行为并掌握更为全面的实验技术，本文通过理论分析和模型优化，研发并搭建了一套可同时验证两种梁模型(即Euler-Bernoulli梁和Timoshenko梁)的高精度实验平台。通过位移校准和精确变形测量，验证了两种梁模型的精度和适用条件。实验发现，加载处的跨高比小于5时，实测值与Timoshenko梁的理论解非常吻合；加载处的跨高比大于5时，两种梁模型的差异可以忽略，Euler-Bernoulli梁模型可用于描述弯曲变形。基于该实验平台，编排设计了力学教学实验并进行了初步实践和评估，该课程阐明了剪切变形对梁弯曲变形的影响，使学生对梁模型的类型与相应假定的理解得到了加深；互动式教学和自主设计测量全方位提高了学生解决实际问题的能力。 |
| 英文摘要: |
| The bending deformation of beam is one of the core contents of basic mechanics. The deformation analysis in previous experimental teaching is usually based on Euler-Bernoulli beam model, while the Timoshenko beam that commonly adopted in engineering is rarely involved. The monotony and limitation of the bending deformation teaching undoubtedly lag behind the current development trend of mechanical science training. In order to make undergraduates deeply understand the beam bending theory and master more comprehensive experimental techniques, a set of high-precision cantilever-beam-based experimental system was built based on theoretical analysis and optimization design, which can verify the deformation theories of two types of beams (i.e. Euler-Bernoulli beam and Timoshenko beam). Through displacement calibration and accurate measurement of the bending deformation, the accuracy and applicable conditions of the two beam theories were validated. It was found that when the span to height ratio at the point of concentrated force was smaller than 5, the measured values were in good agreement with the theoretical ones for the Timoshenko beam. While when the span to height ratio was higher than 5, the difference between the two theories gradually decreased and the Euler-Bernoulli beam theory could be adopted. Based on the experimental system, the mechanics teaching experiment was designed and preliminary practices and evaluations were carried out. The results show that the course clarifies the influence of shear deformation on beam bending deformation, and deepens students' understanding of beam model types and corresponding assumptions. The interactive teaching and self-designed measurement greatly improved the students' abilities to solve the practical engineering problems. |
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