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AN ANALYTICAL MODEL FOR A CLAMPED ISOTROPIC BEAM UNDER THERMAL EFFECTS

机译:受热效应的束缚各向同性梁的解析模型

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摘要

Structures and industrial equipment often operate in environments where temperature variations take place. Although thermal effects may be negligible in some cases, they have caused the unexpected failure of mechanical systems many times. Whether or not temperature has significant effects on the dynamical behavior of such machines and structures depends upon several aspects, amongst which are geometry, material properties and boundary conditions. In this paper we investigate the dynamical behavior of a clamped beam under the influence of a uniform, quasi-statically varying temperature field. An analytical model was used, based on Euler-Bernoulli's beam theory with the introduction of the proper boundary conditions. Temperature effects are included in terms of an axial force that shows up when the beam tends to thermally expand, but this expansion is restrained by the clamping. Preliminary results do not agree with experimental data, since perfect clamping is difficult to achieve in practice. Finally the model is updated with the inclusion of axial and torsional springs connecting the beam to the support. The spring constants were calculated through optimization procedure to minimize the differences between the natural frequencies obtained from the analytical model and the corresponding experimental ones. Agreement with experimental results is reasonable up to the 4th mode of the beam. In the future, this analytical model is to be used for design and simulation of an active controller that accounts for temperature changes in the structure.
机译:结构和工业设备通常在温度变化的环境中运行。尽管在某些情况下热效应可以忽略不计,但它们已多次导致机械系统的意外故障。温度是否对此类机器和结构的动力学行为产生重大影响,取决于几个方面,其中包括几何形状,材料特性和边界条件。在本文中,我们研究了在均匀,准静态变化的温度场的影响下,夹紧梁的动力学行为。基于欧拉-伯努利梁理论,在引入适当边界条件的基础上,使用了解析模型。温度影响包括在梁趋于热膨胀时出现的轴向力方面,但这种膨胀受到夹紧的限制。初步结果与实验数据不一致,因为在实践中很难实现完美的夹紧。最后,使用将梁连接到支架的轴向和扭转弹簧对模型进行更新。通过优化程序计算弹簧常数,以最小化从分析模型获得的固有频率与相应的实验频率之间的差异。直到光束的第四个模态,与实验结果的吻合是合理的。将来,这种分析模型将用于设计和仿真有源控制器,以考虑结构中的温度变化。

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