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Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory

机译：基于应变梯度理论的FG微管输液非线性动力学分析

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In this article, an analytical solution is presented for the size dependent nonlinear vibration behavior of micro-pipes conveying fluid made of functionally graded materials (FGMs). On the basis of the Euler-Ber-noulli beam model, the strain gradient theory and von Karman geometric nonlinearity, the mathematical formulations are developed in terms of three length scale parameters. The material properties of the functionally graded (FG) micro-pipes vary continuously across the thickness according to the power law distribution. The Hamilton's principle is employed to obtain the differential equation of motion and the corresponding boundary conditions. Without loss of generality, simply supported pipes are considered. The governing equation is written in the form of duffing equation by using Galerkin method. Subsequently, a powerful analytical technique called the homotopy analysis method (HAM) is employed to determine the explicit expressions for nonlinear fundamental frequency for different fluid velocities and power law gradient indices. Comprehensive comparison studies between linear and nonlinear theories using the strain gradient, the couple stress and classical theories are conducted. The results show that the length scale parameter and the FG power law index have significant effect on the fundamental frequency of the FG micro-pipes and the fluid critical velocity.
机译：在本文中，提出了一种解析解决方案，用于处理由功能梯度材料（FGM）制成的流体的微管的尺寸相关的非线性振动行为。在Euler-Ber-noulli梁模型，应变梯度理论和von Karman几何非线性的基础上，根据三个长度尺度参数建立了数学公式。功能梯度（FG）微管的材料特性根据幂律分布在整个厚度上连续变化。利用汉密尔顿原理获得运动的微分方程和相应的边界条件。在不失一般性的前提下，只考虑了受支持的管道。用Galerkin法将控制方程写为达芬方程。随后，采用一种称为同位分析法（HAM）的强大分析技术来确定不同流体速度和幂律梯度指数的非线性基频的显式。利用应变梯度，耦合应力和经典理论对线性和非线性理论进行了全面的比较研究。结果表明，长度尺度参数和FG幂律指数对FG微管的基本频率和流体临界速度有显着影响。

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