Fractional Visco-Elastic Euler-Bernoulli Beam
Fractional Visco-Elastic Euler-Bernoulli Beam
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DOI：
10.1016/j.ijsolstr.2013.06.010
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发表时间：
2013-10
影响因子：
3.6
通讯作者：
M. Paola;R. Heuer;A. Pirrotta
中科院分区：
文献类型：
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作者：
M. Paola;R. Heuer;A. Pirrotta
研究分数阶粘弹性欧拉-伯努利梁在准静态和动态载荷作用下的响应。从局部分数粘弹性轴向应力和轴向应变之间的关系，它表明，弯矩，曲率，剪切，曲率梯度涉及分数算子。具体的例子问题的解决方案进行了详细研究，提供了正确的位置的力学边界条件。此外，它表明，均匀梁的对应原理也成立的情况下，欧拉-伯努利梁分数本构律。推导了虚功原理，并应用于实例分析。
Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some case studies.