Nonlinear Vibration Analysis of Curved Piezoelectric-Layered Nanotube Resonator

Piezoelectric-based nano resonators are smart structures that can be used for mechanical sensors and actuators in miniature systems. In this study, the nonlinear vibration behavior of a curved piezoelectric-layered nanotube resonator was investigated. The curved structure comprises a core nanotube and a slender layer of piezoelectric material covering the inner nanotube where a harmonic voltage is applied to the piezoelectric layer. Applying the energy method and Hamiltonian principle in association with non-local theories, the governing equations of motion of the targeted system are obtained. Then, the problem is solved using the Galerkin and multiple scales methods, and the system responses under external excitation and parametric load are found. Various resonance conditions are investigated including primary and parametric resonances, and the frequency responses are obtained considering steady state motions. The effects of different parameters such as applied voltage, piezoelectric thickness, and structural curvature on the system responses are investigated. It is shown that the applied harmonic voltage to the piezoelectric layer can cause a parametric resonance in the structural vibration, and the applied harmonic point load to the structure can cause a primary resonance in the vibration response. Considering two structural curvatures including quadratic and cubic curves, it is also found that the waviness and curve shape parameters can tune the nonlinear hardening and softening behaviors of the system and at specific curve shapes, the vibration response of the targeted structure acts similar to that of a linear system. This study can be targeted toward the design of curved piezoelectric nano-resonators in small-scale sensing and actuation systems.