Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

In this work, we applied the spectral element method (SEM) to analyze the dynamic characteristics of fluid conveying single-walled carbon nanotubes (SWCNTs). First, the dynamic equations for fluid conveying SWCNTs were deduced based on the nonlocal Timoshenko beam theory. Then, the spectral element formulation was established for a free/forced vibration analysis of fluid conveying SWCNTs by introducing discrete Fourier transform. Furthermore, the proposed method was validated using several comparison examples. Finally, the natural frequencies and dynamic responses of a simply-supported fluid conveying SWCNTs were calculated by the SEM, considering different internal fluid velocities and small-scale parameters (SSPs). The effects of fluid velocity and SSPs on the dynamic characteristics of SWCNTs conveying fluid were revealed by the numerical results. Compared with other methods, the SEM shows high accuracy and efficiency.

Vibration performance evaluation of smart magneto-electro-elastic nanobeam with consideration of nanomaterial uncertainties

This study is devoted to examining the vibration behaviors of magneto-electro-elastic nanobeams with consideration of nanomaterial uncertainties induced by the atom defect and manufacturing deviation. Based on the nonlocal Timoshenko beam theory, the governing equations of a magneto-electro-elastic nanobeam resting on a Winkler–Pasternak foundation and subjected to electric and magnetic potentials are derived. The material properties of the magneto-electro-elastic nanobeam are treated as uncertain parameters with well-defined bounds to overcome the extensive information required in probabilistic evaluation. The range of natural frequency of the magneto-electro-elastic nanobeam is predicted via a non-probabilistic evaluation methodology, which is validated by comparing with Monte Carlo simulation and probabilistic evaluation methodology. Then, the parametric analyses are performed to reveal the coupling effects of nanomaterial uncertainties, and nonlocal parameter, as well as elastic foundation parameters on the vibration performance of magneto-electro-elastic nanobeams. It is demonstrated that the nanomaterial uncertainties affect the mechanical behaviors of magneto-electro-elastic nanostructures significantly and the present model can be degenerated into the deterministic model as the nanomaterial uncertainty is eliminated.

Buckling Analysis of Nanobeams Based on Nonlocal Timoshenko Beam Model by the Method of Initial Values

Investigated herein is the buckling of nanobeams based on a nonlocal Timoshenko beam model by the method of initial values within the framework of nonlocal elasticity. Since the nonlocal Timoshenko beam theory is of higher order than the nonlocal Euler–Bernoulli beam theory, it is known to be superior in predicting the small-scale effect. The buckling determinants and critical loads for bars with various kinds of supports are presented. The Carry-Over matrix (Transverse Matrix) is presented and the priorities of the method of initial values are depicted. To the best of the researchers’ knowledge, this is the first work that investigates the buckling of nonlocal Timoshenko beam with the method of initial values.

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction. The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction. The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

Surface Effects on Buckling of Double Nanobeam System Based on Nonlocal Timoshenko Model

This paper is concerned with the surface effect on the buckling behavior of double nanobeam system using the nonlocal Timoshenko beam theory. The size effect is taken into consideration by using the Eringen’s nonlocal elasticity theory and the exact solution for buckling loads for simply supported boundary condition is presented. Influences of various parameters such as stiffness constant, nonlocal parameter, shear effect and buckling mode number are investigated. Also for the sake of validation, the present results are compared with those obtained from the Euler–Bernoulli model. It is shown that the proposed nonlocal model is able to produce results with high accuracy and it can be used as a benchmark in future studies on buckling of nano-sandwich structures.

RMVT-Based Nonlocal Timoshenko Beam Theory for Stability Analysis of Embedded Single-Walled Carbon Nanotube with Various Boundary Conditions

On the basis of Reissner’s mixed variational theorem (RMVT), a nonlocal Timoshenko beam theory (TBT) is developed for the stability analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, with various boundary conditions and under axial loads. Eringen’s nonlocal elasticity theory is used to account for the small length scale effect. The strong formulations of the RMVT-based nonlocal TBT and its associated possible boundary conditions are presented. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Pasternak foundation models. The critical load parameters of the embedded SWCNT with different boundary conditions are obtained by using the differential quadrature (DQ) method, in which the locations of [Formula: see text] sampling nodes are selected as the roots of [Formula: see text]-order Chebyshev polynomials. The results of the RMVT-based nonlocal TBT are compared with those obtained using the principle of virtual displacement (PVD)-based nonlocal TBT available in the literature. The influences of some crucial effects on the critical load parameters of the embedded SWCNT are examined, such as different boundary conditions, Winkler stiffness and shear modulus of the foundation, aspect ratios, and the nonlocal parameter.