Flexural sensitivity and resonance of cantilever micro-sensors based on nonlocal elasticity theory

Sensors based on microcantilevers, especially ones with uniform structure, have ultrahigh sensitivities. The normalized natural frequencies and the sensitivity of lateral vibration of an elastic microcantilever sensor in contact with a surface are derived analytically based on the Euler–Bernoulli beam theory by taking into account the small scale effect. The interaction of the sensor with the surface is modeled by linear springs, which restricts the results to experiments involving low-amplitude excitations. The results show that the normalized natural frequencies of nonlocal microcantilever are smaller than those for its local counterpart, especially for higher values of small scale parameters. Also, each mode has a different sensitivity to variations in surface stiffness. Moreover, the most sensitivity is observed at the first mode of vibration. When the nonlocal effect is not taken into account, the natural frequencies and the sensitivity of the microcantilever in contact with the surface are compared with those obtained in previous study without considering the nonlocal effect.     

Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory

A nonlocal Euler–Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid.     

Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach

The magnetic properties of carbon nanotubes and their mechanical behaviour in a magnetic field have attracted considerable attention among the scientific and engineering communities. This paper reports an analytical approach to study the effect of a longitudinal magnetic field on the transverse vibration of a magnetically sensitive double-walled carbon nanotube (DWCNT). The study is based on nonlocal elasticity theory. Equivalent analytical nonlocal double-beam theory is utilised. Governing equations for nonlocal transverse vibration of the DWCNT under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell's relation. Numerical results from the model show that the longitudinal magnetic field increases the natural frequencies of the DWCNT. Both synchronous and asynchronous vibration phases of the tubes are studied in detail. Synchronous vibration phases of DWCNT are more affected by nonlocal effects than asynchronous vibration phases. The effects of a longitudinal magnetic field on higher natural frequencies are also presented. Vibration response of DWCNT with outer-wall stationary and single-walled carbon nanotube under the effect of longitudinal magnetic field are also discussed in the paper.     

Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory

A nonlocal Euler–Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid.     

并苯纳米环[6]CA及其衍生物的电子结构和光物理性质的密度泛函理论研究

采用密度泛函理论PBE0方法在6-31G(d, p) 基组水平上对比研究并六苯纳米环[6]CA及BN取代纳米环[6]CA-BN的几何结构及电子性质. 同时探讨锂离子掺杂对不同体系的芳香性、前线分子轨道、电子吸收光谱及传输性质的影响. 通过电离势、亲合势及重组能的计算, 预测纳米环体系得失电子的能力及传输性能. 结果表明:[6]CA的能隙很小, BN取代后, 能隙明显增大; 锂离子掺杂到两种纳米环中, 在不明显改变前线分子轨道分布的前提下, 几乎同步降低了最高占据轨道、 最低未占据轨道能级, 锂离子掺杂使载流子传输性能得到很大改善; 电子吸收光谱拟合发现, BN取代使吸收光谱很大程度蓝移, 吸收强度明显减小; 而锂离子掺杂对光谱的强度及吸收范围没有明显影响. 关键词： 碳纳米环 硼氮纳米环 锂离子掺杂 密度泛函理论     

The role of dipolar interactions for the magnetic properties of ferromagnetic nanoring

We investigate numerically the effects of the dipolar interactions on magnetic properties in small ferromagnetic nanorings using a Monte Carlo technique. Our simulated results show that the strength of dipolar interaction in the magnetic nanoring has an important influence on the magnetization reversal processes and further the coercivity and the remanence. As the dipolar interaction increases, the transition of magnetization reversal processes from the onion-rotation state to the vortex state can occur, which results in an increase in coercivity and a decrease in remanence. On the other hand, it is found that the coercivity and the remanence depend more strongly on the strength of dipolar coupling for the relatively small size nanoring than for the large size nanoring in width. This can be attributed to the stable vortex state without core in smaller width nanoring in contrast to the metastable vortex state with core in larger width nanoring, induced by strong dipolar interactions. Additionally, the temperature dependence of coercivity and remanence in magnetic nanoring is also studied at a fixed dipolar interaction.     

Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads

This paper is concerned with the investigation of thermal loads and small scale effects on free dynamics vibration of slender simply-supported nanobeams perforated with periodic square holes network and subjected to temperature-induced loads. The Euler–Bernoulli beam model (EBM) and shear beam model (SBM) developed for the determination of resonance frequency are derived by modifying the standard Timoshenko beam equations. The small scale effect is included by using the Eringen's nonlocal elasticity theory while the thermal loads effect is included by considering the additional axial thermal force in the standard differential equations. Numerical results are shown that the resonance frequency change, the thermal loads and the small scale effects are depended on size and number of holes. Thus, numerical results are discussed in detail for a properly investigation of the dynamic behavior of perforated nanobeams which are of interest in the development of resonant devices integrated in micro/nanoelectromichanical systems (M(N)EMS).     

Nonlocal plate model for free vibrations of single-layered graphene sheets

Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.     

Thermal stability and morphological variation of carbon nanorings of different radii during the temperature elevating process: a molecular dynamics simulation study

We study the thermal stability and morphological variations of nanorings with different radii during the temperature elevation using the molecular dynamics (MD) simulation method. Five metastable nanorings were generated using the different initial C–C bond length of armchair carbon nanotubes. The stable structures of the two smallest nanorings have several kinked regions around the nanorings, with the deformations of the inner and outer walls occurring at the same temperature. For the largest three cases, the morphologies of nanorings from the top view display circular shapes at 0 K. For the nanoring with a radius of 146 Å(350 units), the thermal deformation process is very similar to the smallest two cases, but the temperature at which the thermal deformation begins is higher. For the nanoring with nanoring radii of 165 Å (400 units) and 185 Å (450 units), thermal deformation will take place at the inner wall of the nanoring, and then will induce deformation of the outer wall at a higher temperature. Variations of local structures at the kinked regions at different temperatures are also drawn.     

The effect of calibrated nonlocal constant on the modal parameters and stability of axially compressed CNTs

Nowadays investigating the vibration behavior of carbon nanotubes (CNTs) has drawn considerable attention due to the superior mechanical properties of the CNTs. One of the powerful theoretical methods to study the vibration behavior of CNTs is implementing the nonlocal theory. Most of studies on the vibration behavior of CNTs have assumed a fixed value for small scale parameter for all vibration modes, however, this value is mode-dependent. Therefore, in this paper, the small scale parameter is calibrated for a single-walled carbon nanotube (SWCNT) with respect to each vibration mode. For this propose, the governing equation of motion based on the nonlocal beam theory is extracted by applying the Hamilton's principle. Then, by using the power series method, an eigenvalue problem is defined to derive the calibrated value of small scale constant and nonlocal mode shapes of the CNT. By using the expansion theory, the equation of motion is discretized, and the effect of nonlocality on the modal parameters and stability of the CNT under compressive force is investigated. Finally, the possibility of estimating nonlocal parameter based on simulated frequency domain response of the system by using modal analysis methods is studied. The results show that the calibration of small scale constant is important and the critical axial force is highly sensitive to this value.     

Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium

In the present paper, the sinusoidal shear deformation plate theory (SDPT) is reformulated using the nonlocal differential constitutive relations of Eringen to analyze the bending and vibration of the nanoplates, such as single-layered graphene sheets, resting on two-parameter elastic foundations. The present SDPT is compared with other plate theories. The nanoplates are assumed to be subjected to mechanical and thermal loads. The equations of motion of the nonlocal model are derived including the plate foundation interaction and thermal effects. The governing equations are solved analytically for various boundary conditions. Nonlocal theory is employed to bring out the effect of the nonlocal parameter on the bending and natural frequencies of the nanoplates. The influences of nonlocal parameter, side-to-thickness ratio and elastic foundation moduli on the displacements and vibration frequencies are investigated.     

金纳米环双体尺寸和耦合效应对表面等离子体共振特性的影响

采用离散偶极子近似方法系统地研究了金纳米环双体的消光光谱及其电场分布. 计算结果表明, 金纳米环双体在耦合作用下的共振消光峰对应着不同振动模式, 改变金纳米环双体的排列方式、 间距和尺寸大小, 其表面等离子体共振消光峰发生红移或蓝移. 因此可以通过对金纳米环双体结构参数和排列方式的设定, 调节其表面等离子体共振消光峰的位置. 电场分布表明, 水平排列的金纳米环双体较单个金纳米环产生更强的局部表面增强电场. 适当的小间距, 较大的内外半径的金纳米环水平阵列更适合做表面增强拉曼散射的衬底, 在生物分子检测等领域具有潜在的应用.     

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.     

Thermo-electro-mechanical vibration of coupled piezoelectric-nanoplate systems under non-uniform voltage distribution embedded in Pasternak elastic medium

In the present paper, the thermo-electro-mechanical vibration characteristics of a piezoelectric-nanoplate system (PNPS) embedded in a polymer matrix are investigated. The system is subjected to a non-uniform voltage distribution. The voltage distribution and in-plane preloads are very important in the resonance mode of smart composite nanostructures using PNPS. Small scale effects are taken into consideration using the nonlocal continuum mechanics. Hamilton's principle is employed to derive the nonlocal equations of motion. The governing equations are solved for various boundary conditions by using differential quadrature method (DQM). To verify the accuracy of the present results, a closed-form solution is also derived for the natural frequencies of simply supported PNPSs. The results of DQM are compared with those of exact solution and an excellent agreement is found. Finally, the effects of initial preload, temperature change, boundary conditions, aspect ratio, length-to-thickness ratio, nonlocal and non-uniform parameters on the vibration characteristics of PNPSs are studied. It is shown that the natural frequencies are quite sensitive to the non-uniform and nonlocal parameters.     

Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium

The effect of longitudinal magnetic field on vibration response of a sing-walled carbon nanotube (SWCNT) embedded in viscoelastic medium is investigated. Based on nonlocal Euler-Bernoulli beam theory, Maxwell’s relations, and Kelvin viscoelastic foundation model, the governing equations of motion for vibration analysis are established. The complex natural frequencies and corresponding mode shapes in closed form for the embedded SWCNT with arbitrary boundary conditions are obtained using transfer function method (TFM). The new analytical expressions for the complex natural frequencies are also derived for certain typical boundary conditions and Kelvin-Voigt model. Numerical results from the model are presented to show the effects of nonlocal parameter, viscoelastic parameter, boundary conditions, aspect ratio, and strength of the magnetic field on vibration characteristics for the embedded SWCNT in longitudinal magnetic field. The results demonstrate the efficiency of the proposed methods for vibration analysis of embedded SWCNTs under magnetic field.     

Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle

In this study, an analytical method of the small scale parameter on the vibration of single-walled Boron Nitride nanotube (SWBNNT) under a moving nanoparticle is presented. SWBNNT is embedded in bundle of carbon nanotubes (CNTs) which is simulated as Pasternak foundation. Using Euler–Bernoulli beam (EBB) model, Hamilton's principle and nonlocal piezoelasticity theory, the higher order governing equation is derived. The effects of electric field, elastic medium, slenderness ratio and small scale parameter are investigated on the vibration behavior of SWBNNT under a moving nanoparticle. Results indicate the importance of using surrounding elastic medium in decrease of normalized dynamic deflection. Indeed, the normalized dynamic deflection decreases with the increase of the elastic medium stiffness values. The electric field has significant role on the nondimensional fundamental frequencies, as a smart controller. The results of this work is hoped to be of use in design and manufacturing of smart nano-electro-mechanical devices in advanced medical applications such as drug delivery systems with great applications in biomechanics.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.     

Transverse Vibration of Tapered Single-Walled Carbon Nanotubes Embedded in Viscoelastic Medium

Based on the nonlocal theory, Euler-Bernoulli beam theory and Kelvin viscoelastic foundation model, free transverse vibration is studied for a tapered viscoelastic single-walled carbon nanotube (visco-SWCNT) embedded in a viscoelastic medium. Firstly, the governing equations for vibration analysis are established. And then, we derive the natural frequencies in closed form for SWCNTs with arbitrary boundary conditions by applying transfer function method and perturbation method. Numerical results are also presented to discuss the effects of nonlocal parameter, relaxation time and taper parameter of SWCNTs, and material property parameters of the medium. This study demonstrates that the proposed model is available for vibration analysis of the tapered SWCNTs-viscoelastic medium coupling system.     

Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory

In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.