Abstract

A dynamic analysis of the fractional viscoelastic nanobeam conveying fluid, resting on a viscoelastic foundation, with simply-supported boundary conditions and uniformly loaded, is performed. The existence of a significant internal damping of the nanotube led to the choice of a nonlinear and fractional Zener model for the nanotube material. Solving of the integral-differential governing equation is done using Galerkin’s method and an iterative method that uses the Laplace transformation techniques, Bessel functions theory and the binominal series. The effects of the nonlocal parameter and of the fractional order on the transverse displacements of the nanotube conveying fluid are studied. In order to validate the approached iterative method, the results of the dynamic analysis were compared with those of the quasi-static calculation of the structure. The proposed algorithm for solving the governing equation and the accompanying graphical data are useful in the engineering design of the nanotubes conveying fluid.

摘要

对基于粘弹性基础的分数粘弹性纳米束输送流体进行动态分析，具有简支边界条件和均匀加载。纳米管的显着内部阻尼的存在导致为纳米管材料选择非线性和分数齐纳模型。积分-微分控制方程的求解是使用 Galerkin 方法和使用拉普拉斯变换技术、贝塞尔函数理论和二项式级数的迭代方法完成的。研究了非局部参数和分数阶对纳米管输送流体横向位移的影响。为了验证逼近的迭代方法，将动力分析的结果与结构的准静态计算结果进行了比较。所提出的求解控制方程的算法和随附的图形数据在纳米管输送流体的工程设计中很有用。