Abstract
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.
Highlights
Nano resonators are emerging materials and structures to be used for sensing and actuation in microelectromechanical (MEMS) and nanoelectromechanical systems (NEMS)
One of the main aspects of nanotube behaviors for mechanical sensing and actuation is their vibrational response, and the research of nanotubes vibrations has been observed in various studies using different methods, such as experimental methods, molecular dynamics, and continuum mechanic theories [3,4,5,6]
The piezoelectric thickness effect is analyzed when the maximum point position is close to the end or to the middle. For both hard and soft behaviors caused by the peak point position, the thickness growth lowers the amplitude, and the amplitude is smaller for the softening behavior in comparison with the harder one
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. These structures were fabricated by coating the piezoelectric material on the nanotube and linear assumptions were developed for modeling the corresponding vibration [18] In this respect, the vibration of piezoelectriclayered nano beams, non-local instability behavior of piezoelectric-layer nanotubes, and the vibration of piezoelectric-based nano plates have been studied recently [19,20,21]. The following hold forlinear the strains, moments, and shear forces of each layer: and the dielectric constant, respectively [30] It of piezoelectric, piezoelectric constant, should be noted that due to the symmetry and slenderness of the beam -type model of ε xx, ilayer,. To obtain the governing equation, the Lagrangian function of the system is written as: Such that T, U and W denote the total kinetic energy, potential energy, and the external force work, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
