Nonlinear analysis of the micro/nanotube conveying fluid based on second strain gradient theory

Abstract

• The governing equations are derived based on the second strain gradient theory. • The effect of the second gradient of strain on the system stiffness is shown. • The hardening behavior in nonlinear stability analysis is investigated. • The resonance and stability of the response in forced vibration is studied. Nano/Micro tubes are extensively used in fluidic nano/micro circuits, biochemical industries and nano/micro electromechanical systems. In order to investigate the influence of length scale parameters, in the present work for the first time, the second strain gradient is applied along with Euler- Bernoulli beam theory to study the fluid-conveying nanotube. The hamilton principle is used to derive governing equation of the nano/micro tube conveying fluid. The partial governing equation of motion is discretized into ordinary differential equations by the Galerkin method. The possible instabilities are predicted by linear stability analysis. Onsets of the instabilities based on the second strain gradient theory are compared with those based on the classical and strain gradient theories. Afterwards, nonlinear stability analysis is performed by both Perturbation and numerical methods. The results obtained by numerical method are in good agreements with those achieved by perturbation approach. In nonlinear stability analysis, the onsets of instabilities are obtained more precisely considering the hardening effects. The resonance around the first nonlinear natural frequency and the influence of the fluid velocity on the resonance curve are investigated by the perturbation method.