This work investigates, for the first time, nonlinear wave dynamics and chaos in nanocomposite micropipes conveying a viscous fluid, reinforced with graphene origami (GOr), and subjected to thermal loading. It extends the previous study by considering the influence of a transverse load and fluid viscosity, both of which were ignored previously. The Painlevé integrability of the governing equation is tested using the Ablowitz–Ramani–Segur (ARS) algorithm. Our findings prove the non-integrability of the governing equation, motivating a qualitative dynamical approach. Bifurcation theory is applied to multiple possible forms of the transverse load. In the absence of a transverse load, neither periodic nor solitary axial wave displacements exist. This is guaranteed by applying Bendixson’s criterion and confirmed through phase portraits. However, with a specific form of the transverse load, bifurcation analysis analytically provides the existence conditions for periodic, super-periodic, and solitary axial displacement waves. Furthermore, it is shown that kink and anti-kink solutions are absent. Explicit exact solutions are constructed in terms of elliptic functions, and their consistency and validity are verified through orbital degeneracy. The key material parameters’ impacts—GOr weight fraction, temperature change, hydrogen coverage, and shear layer stiffness—on the wave profiles are inspected numerically and eludicated physically. When an additional periodic transverse load is inserted, the system manifests quasi-periodic behavior at frequencies with small loads, transitioning to chaotic motion as the frequency grows. Both Lyapunov exponents and a Poincaré section are utilized to confirm this chaotic behavior. Our findings show the impact of fluid viscosity and the transverse load structure are significant in GOr-reinforced microtubes and highlight their relevance for advanced fluid-conveying systems.
Elmandouh et al. (Thu,) studied this question.