Fractional Euler-Bernoulli beams：理论、数值研究和实验验证
Fractional Euler-Bernoulli beams: theory, numerical study and experimental validation
摘要：
本文利用分数阶微积分对经典Euler-Bernoulli梁（CEBB）理论进行了修正。这种推广被称为分数欧拉-伯努利梁（FEBB），并导致非局部空间描述。该模型的参数识别的基础上的AFM实验有关的弯曲刚度的聚合物SU-8制成的微梁。在实验中，力以及挠度数据记录揭示显着的尺寸效应相对于外部尺寸的标本。特别注意的是，也集中在适当的数值解所获得的分数阶微分方程。
英文摘要：
In this paper the classical Euler-Bernoulli beam (CEBB) theory is reformulated utilising fractional calculus. Such generalisation is called fractional Euler-Bernoulli beams (FEBB) and results in non-local spatial description. The parameters of the model are identified based on AFM experiments concerning bending rigidities of micro-beams made of the polymer SU-8. In experiments both force as well as deflection data were recorded revealing significant size effect with respect to outer dimensions of the specimens. Special attention is also focused on the proper numerical solution of obtained fractional differential equation.
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