Free vibration and instability analysis of a viscoelastic micro-shell conveying viscous fluid based on modified couple stress theory in thermal environment

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.