This study investigates the primary resonance response of a composite micropipe reinforced with graphene nanoplatelets conveying fluid, with applications in remote selfpowered micro-sensors, precise drug delivery, the safety of chemical reactions, ecological assessments, and the transport of cells. A sequential pseudo-nonlinear normal mode scheme, combined with the modified Rauscher technique and harmonic balance method, is employed to derive the frequency response. The gyroscopically coupled equations are systematically reduced, at each stage, to a single degree-of-freedom equation through nonlinear normal mode framework, treating the system as a two-dimensional invariant manifold. The harmonic balance method generates nonlinear algebraic equations, which are solved using an arclength continuation method with an adaptive arc length. Critical to this analysis, Hill’s method is implemented to determine the stability of periodic solutions along the frequency response branches, enabling classification of solution branches as stable or unstable. This stability classification reveals that the bandwidth of multi-valued response coincides with the region of unstable periodic solutions, with stability transitions occurring at the saddle-node bifurcation points (turning points) of the frequency response curves. Parametric studies demonstrate that an increase in the slenderness ratio, radius ratio, flow velocity, and flow mass density and considering laminar flow instead of turbulent flow widen the multi-valued response bandwidth, while micro-scale contribution narrows it. A comprehensive sensitivity analysis reveals that the multi-valued response bandwidth and maximum frequency response amplitude are least sensitive to nanocomposite weight fraction, flow mass density, and micro-scale parameter, while exhibiting the highest sensitivity to slenderness ratio and radius ratio. The primary resonance characteristics show moderate sensitivity to the flow speed. These findings can be implemented for the design of remote self-powered micro-sensors, system identification, and structural health monitoring applications.
Zhang et al. (Thu,) studied this question.