Resonance interaction of flow-conveying nanotubes under forced vibration

Exploring the size-dependent nonlinear behavior and its related stability phenomena of nano-fluid-solid interaction under multi-source excitation is of great significance to the rational design of nano-electromechanical systems that are required to maintain in stable states. The size-dependent nonlinear combined resonance of nanotubes conveying pulsatile flow while subjected to external forced excitation with two immovable ends is studied. As the flow-carrying nanotubes are subjected to large deformation under two simultaneous excitations, nonlinear stiffening effects arising from curvature and boundary tensile hardening are investigated in detail. A Zhang-Fu's higher-order beam theory to model the displacement field of the nanotubes is modified to take accurate nonlinear curvature into account. Key parameters which are related to size dependency such as slip-flow, surface effect, nonlocal stress and strain gradient on the nonlinear dynamic behavior are comprehensively studied. A two-step perturbation technique followed by incremental harmonic balance method is employed to attain the bifurcation diagram; its accuracy is confirmed by a convergence analysis and validation using conventional Runge-Kutta method. The bifurcation diagrams which exhibit both weak and strong interactions are shown under different excitation amplitudes. As expected, the nonlinear combined resonance is not a simple superposition of two vibration responses; the interaction of the two excitations yields different bifurcation topologies with different jump and hysteresis paths. Also, it is revealed that size-dependency of both nano-solid and nano-fluid can not only affect the resonance band and resonance amplitude but also lead to the shift between strong and weak interactions.

Automated summary

Studying the size-dependent nonlinear behavior and stability phenomena of nano-fluid-solid interaction under multi-source excitation is crucial for designing stable nano-electromechanical systems. This study focuses on the combined resonance of nanotubes conveying pulsatile flow under external forced excitation. The effects of curvature and boundary tensile hardening on nonlinear stiffening are investigated, and a modified beam theory is used to model the displacement field accurately. Key parameters related to size-dependency, such as slip-flow, surface effect, and nonlocal stress and strain gradient, are comprehensively studied. The results show that size-dependency not only affects the resonance band and amplitude but also leads to the shift between strong and weak interactions.