Resonance interaction of flow-conveying nanotubes under forced vibration. (English) Zbl 1521.74090
Summary: 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.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
Keywords:
Zhang-Fu higher-order beam model; large deformation; surface effect; nonlocal stress; strain gradient; two-step perturbation method; Runge-Kutta schemeReferences:
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