Nonlinear Oscillations of CNT Nano-resonator Based on Nonlocal Elasticity: The Energy Balance Method

This paper deals with investigating the nonlinear oscillation of carbon nanotube manufactured nano-resonator. The governing equation of the nano-resonator is extracted in the context of the nonlocal elasticity. The impact of the Casimir force is also incorporated in the developed model. A closed-form solution based on the energy balance method is presented for investigating the oscillations of the nano-resonator. The proposed closed-form solution is compared with the numerical solution. The impact of influential parameters including applied voltage, Casimir force, geometrical and nonlocal parameters on the nano resonator’s vibration and frequency are investigated. The obtained results demonstrated that the Casimir force reduces the nano-resonator frequency. However, the nonlocal parameter has a hardening effect and enhances the system’s frequency.

Wrinkling Analysis of Double Nanofilms Embedded in Compliant Substrates Based on Nonlocal Elasticity Theory

In this paper, an analytical approach for wrinkling analysis of double nanofilms embedded in compliant substrates is presented. The governing differential equations for wrinkling of double nanofilms are derived based on Eringen’s nonlocal elasticity theory and the classical plate theory (CLPT). Substrates are regarded as elastic bodies of finite thickness and the normal pressure of substrates on the films is assumed to be linear with the lateral deformation of the films. Solutions for critical wrinkling load and wave number are computed in terms of the nonlocal parameter, the elastic properties and thickness of double nanofilms, the elastic properties and thickness of the substrates, and wrinkle modes. The parametric study shows that the dimensionless critical wave number and the dimensionless critical load decrease gradually with the increase of the nonlocal parameter. Four typical wrinkling states are studied: in-phase wrinkling, out-of-phase wrinkling, single-film wrinkling and asymmetric wrinkling. In-phase wrinkling has the highest chance to occur among four wrinkle modes. In addition, the results show that the dimensionless critical load and wave number are much smaller when the films become much stiffer and thinner than the substrates.