Nonlinear free vibrations of a nanocomposite micropipes conveying laminar flow subjected to thermal ambient: Employing invariant manifold approach

This research presents, for the first time, essential insights into the free vibrations of a composite micropipe enriched by means of graphene sheets (a GRC micropipe) conveying laminar flow subjected to a thermal ambient, preparing precious discernment for designers and engineers. The study develops the governing equations in the framework of the Euler–Bernoulli beam theory, the modified couple stress theory (MCST), von-Karman nonlinear relations for strains, and revised Halpin–Tsai relationships. Taking the advantage of invariant manifold procedure the two-degrees-of-freedom (DOFs) discretized governing equations, coupled gyroscopically, are reduced efficiently to one nonlinear governing equation with inertial nonlinearity that coping with it is considerably simpler. Leveraging the method of multiple scales (MMS) the nonlinear natural frequency, along with the accompanying nonlinearity constant is disclosed. It is underscored that the contribution of layer stacking on the vibrational behavior of GRC micropipes carrying laminar flow is substantially highlighted when the GRC micropipe is subjected to a thermal medium. It is observed that although it is expected to have a larger fundamental linear natural frequency for an FGV GRC micropie, at low temperatures UD GRC micropipe has the largest one for thin micropipes. It is shown that the hardening behavior of the first mode of the GRC micropipe is alleviated regarding the small scale factor while it is intensified regarding the flow profile effect. In sum imposing both factors relieves the first mode hardening behavior.