Abstract

Modeling of viscoelastic behavior can be useful to accurate study of micro-shell vibration. In this study, influence of viscoelastic coefficient and material length scale parameter on frequency of a cylindrical micro-shell with/without conveying fluid are investigated. Considering trapezoidal shape factor via Kirchhoff-Love’s hypotheses and modified couple stress theory (MCST), governing equations of motion are derived using Hamilton’s principle. Viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The novelty of the current study is the consideration of viscoelastic effect, trapezoidal shape factor and size effect based on shell theory as well as influence of conveying viscous fluid on the frequency of micro-shells in thermal environment using MCST. Equations of motion are solved using Fourier series expansion along the axial and circumferential coordinates with Navier procedure as an analytical solution of frequency for a simply-supported micro-shell. As a numerical solution, considering conveying fluid with changing temperature, generalized differential quadrature (GDQ) method along the axial direction for different boundary conditions are utilized. Influences of length-to-mid-radius, thickness-to-mid-radius, length-to-thickness ratio and the number of the mode shapes of the micro-shell on the natural frequencies are examined. Considering fluid flow, effects of length-to-outer-radius, viscoelastic coefficient, fluid viscosity, Knudsen number with the effect of slip/no-slip boundary condition and temperature changes on critical flow velocity versus fundamental frequency of the micro-shell are investigated. Numerical results reveal that structural damping effect of viscoelastic coefficients and damping effect of fluid flow on frequency of the linear vibration are more significant to detect the stability domain of the micro-shell.

摘要

粘弹性行为的建模可用于精确研究微壳振动。在这项研究中，研究了粘弹性系数和材料长度尺度参数对有/无输送流体的圆柱形微壳频率的影响。通过 Kirchhoff-Love 假设和修正耦合应力理论 (MCST) 考虑梯形形状因子，使用 Hamilton 原理推导出运动控制方程。粘弹性特性根据 Kelvin-Voigt 粘弹性建模。目前研究的新颖之处在于基于壳理论考虑粘弹性效应、梯形形状因子和尺寸效应，以及使用MCST在热环境中输送粘性流体对微壳频率的影响。运动方程使用傅里叶级数展开沿轴向和圆周坐标和 Navier 程序作为简支微壳的频率解析解来求解。作为数值解，考虑到输送流体随温度的变化，采用了针对不同边界条件的沿轴向方向的广义微分求积（GDQ）方法。研究了长中半径、厚中半径、长厚比和微壳振型数对固有频率的影响。考虑流体流动、长度到外半径的影响、粘弹性系数、流体粘度、研究了滑动/无滑动边界条件和温度变化对微壳临界流速与基频的影响的克努森数。数值结果表明，粘弹性系数的结构阻尼效应和流体流动对线性振动频率的阻尼效应对于检测微壳的稳定性域更为显着。