جستجوی مقالات مرتبط با کلیدواژه « Nonlocal theory » در نشریات گروه « فنی و مهندسی »

This paper represented a numerical technique for discovering the vibrational behavior of a two-directional FGM (2-FGM) nanobeam exposed to thermal load for the first time. Mechanical attributes of two-directional FGM (2-FGM) nanobeam are changed along the thickness and length directions of nanobeam. The nonlocal Eringen parameter is taken into the nonlocal elasticity theory (NET). Uniform temperature rise (UTR), linear temperature rise (LTR), non-linear temperature rise (NLTR) and sinusoidal temperature rise (STR) during the thickness and length directions of nanobeam is analyzed. Third-order shear deformation theory (TSDT) is used to derive the governing equations of motion and associated boundary conditions of the two-directional FGM (2-FGM) nanobeam via Hamilton’s principle. The differential quadrature method (DQM) is employed to achieve the natural frequency of two-directional FGM (2-FGM) nanobeam. A parametric study is led to assess the efficacy of coefficients of two-directional FGM (2-FGM), Nonlocal parameter, FG power index, temperature changes, thermal rises loading and temperature rises on the non-dimensional natural frequencies of two-directional FGM (2-FGM) nanobeam.

This paper investigates the nonlinear-coupled radial-axial vibration of single-walled carbon nanotubes (SWCNTs) based on numerical methods. Two coupled partial differential equations that govern the nonlinearcoupled radial-axial vibration for such nanotube are derived using nonlocal doublet mechanics (DM) theory. To obtain the nonlinear natural frequencies in coupled radial-axial vibration mode, these equations are solved using Homotopic perturbation method (HPM). It is found that the coupled radial-axial vibrational frequencies are complicated due to coupling between two vibration modes. The influences of some commonly used boundary conditions, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear-coupled radial-axial vibration characteristics of SWCNTs are discussed. It was shown that boundary conditions and maximum vibration velocity play significant roles in the nonlinear-coupled radial-axial vibration response of SWCNTs. It was shown that unlike the linear one, the nonlinear natural frequencies are dependent to maximum vibration velocity. Increasing the maximum vibration velocity increases the natural frequency of vibration compared to the prediction of the linear model. However, with increase in tube length, the effect of the maximum vibration velocity on the natural frequencies decreases. It was also shown that the amount and variation of nonlinear natural frequencies are more apparent in higher vibration modes and two clamped boundary conditions. To show the accuracy and capability of this method, the results obtained herein are compared with the fourth order Runge-Kuta numerical results and also with the other available results and good agreement is observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.

This paper investigates the bending vibration of rotating single-walled carbon nanotubes (SWCNTs) based on nonlocal theory. To this end, the rotating SWCNTs system modeled as a beam with a circular cross section and the Euler-Bernoulli beam theory (EBT) is applied with added effects such as rotary inertia, gyroscopic effect and rotor mass unbalance. Using nonlocal theory, two coupled sixth order partial differential equations that govern the vibration of rotating SWCNTs are derived. To obtain the natural frequency and dynamic response of the nanorotor system, the equation of motion for the rotating SWCNTs are solved. It is found that there are two frequencies in the frequency spectrum. The positive rootintroduced as forward whirling mode, while the negative root represents backward whirling mode. The detailed mathematical derivations are presented while the emphasis is placed on investigating the effect of the several parameters such as, tube radius, angular velocity and small scale parameter on the vibration behavior of rotating nanotubes. It is explicitly shown that the vibration of a spinning nanotube is significantly influenced by these effects. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed. To the knowledge of authors, the vibration of rotating SWCNTs considering gyroscopic effect has not investigated analytically yet and then the results generated herein can be served as a benchmark for future works.