Nonlinear harmonic vibration analysis of fluid-conveying piezoelectric-layered nanotubes

Nonlinear harmonic vibration of a piezoelectric-layered nanotube conveying fluid flow is investigated. The mathematical modeling of the structure is developed by means of the nonlocal theory and energy approach. The piezoelectric layer is assumed to be slender and the fluid flows through the nanotube at a uniform velocity. The forced vibration of the system is resulted from an external loading and hence, the parametric excitation is analyzed. Three different scenarios for its resonance conditions, known as the primary, parametric, and the simultaneous primary-parametric resonances, employing a strong perturbation technique known as the multiple time-scales method, are investigated. The effects of the variation of different parameters, such as the applied voltage, piezoelectric layer, nonlocal parameter and the fluid flow velocity, on both the frequency-amplitude relationship and the frequency response of the system are studied. Finally, a detailed discussion on the numerical results obtained were fully presented.