Strain gradient shell model for nonlinear vibration analysis of visco-elastically coupled Boron Nitride nano-tube reinforced composite micro-tubes conveying viscous fluid

•Nonlinear vibration of embedded coupled composite micro-tubes is investigated.•Properties of composite micro-tubes are obtained based on PFRC theory.•Strain gradient shell theory is developed to enhance the accuracy of results.•Volume fraction of BNNT has a significant effect on stability of coupled system.

In the present research, nonlinear vibration in a coupled system of Boron-Nitride nano-tube reinforced composite (BNNTRC) micro-tubes conveying viscous fluid is studied. Single-walled Boron-Nitride nano-tubes (SWBNNTs) are arranged in a longitudinal direction inside Poly-vinylidene fluoride (PVDF) matrix. Damping and shearing effects of surrounded medium are taken into account by visco-Pasternak model. Based on piezoelectric fiber reinforced composite (PFRC) theory, properties of smart coupled BNNTRC micro-tubes are obtained. To enhance the accuracy of results, strain gradient theory is developed in cylindrical shell model, and the motion equations as well as the boundary conditions are derived using Hamilton’s principle. Considering slip flow regime, the effects of various parameters such as Knudsen number, volume fraction and orientation angle of fibers, temperature change, viscosity and density of fluid on stability of coupled BNNTRC micro-tubes are investigated. Results indicate that stability of smart composite system is strongly dependent on orientation angle and volume percent of BNNTs. Results of this investigation can be applied for optimum design of shell and tube heat exchangers in micro scale.

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