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基于非局部弹性理论的分数阶粘弹性纳米板的振动
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Abstract:
本文基于Kirchhoff板理论，同时考虑了非局部弹性理论和分数阶Kelvin-Voigt粘弹性本构关系，利用Hamilton原理建立了粘弹性纳米板的控制方程。通过给出解的形式，利用拉普拉斯变换及其逆变换对问题就进行求解，在得到数值解后并分析了分数阶导数的阶数、非局部参数以及粘弹性系数对纳米板的振动影响。
Based on Kirchhoff plate theory, this paper takes into account the nonlocal elasticity theory and the fractional Kelvin-Voigt viscoelastic constitutive relation. It establishes the governing equations of the viscoelastic nano-plate using the Hamilton principle. By giving the form of the solution and using the Laplace transform and its inverse to solve the problem, the influence of the order of fractional derivative, nonlocal parameter, and viscoelastic coefficient on the vibration of the nano-plate is analyzed after obtaining the numerical solution.
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