Molecular dynamics simulation study on mechanical responses of nanoindented monolayer-graphene-nanoribbon

We investigated the mechanical responses of the nanoindented graphene-nanoribbon (GNR)-resonator using classical molecular dynamics simulations. The nanoindented force in this work was applied to the GNR's local point and then, GNR-resonator's frequency could be tuned by a nanoindented depth. We found the hardening or the softening of the GNR during its nanoindented-deflections, and such properties were recognized by the shift of the resonance frequency. The linear elastic regime in low applied force is explicitly separated with the non-linear elastic regime in high applied force. In particular, at the threshold point, a very small change of the nanoindented depth can cause great change in the resonance frequency, and this property can enable the GNR to be applied to electromechanical relay switching devices and the quantum-computer in quantum-mechanical coupling as well as mass detectors, pressure sensors, accelerometers, and alarms.     

Nonlinear ponderomotive force effects on plasma resonance cones

The nonlinear equation is derived governing the field on two-dimensional resonance cones in a plasma for all frequencies for which the resonance cones exist. This equation reduces to the modified Korteweg-de Vries equation only if the electric field is real.     

Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field

Free transverse vibration and instability of current-carrying nanowires immersed in a longitudinal magnetic field are of concern. On the basis of the surface elasticity theory, a model is developed to investigate the problem. The analytical expressions of dynamic transverse displacements as well as natural frequencies of the magnetically affected nanowire for carrying electric current are obtained. The influences of the surface effect, initial tensile force within the nanowire, strength of the longitudinal magnetic field, and electric current on the natural frequencies as well as dynamic displacements are examined. The obtained results reveal that the transverse stiffness of the nanostructure is enhanced by the surface effect and the initial tensile force, while electric current or longitudinal magnetic field reduces the nanowire's stiffness. The condition which leads to the dynamic instability of the nanostructure is obtained. Further, the roles of the influential parameters on its stability are inclusively discussed.     

Resonance frequencies and stability of two flexible permanent magnetic beams facing each other

This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler–Bernoulli beam model along with Hamilton's principle. Assuming that the beams' tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies. Using the obtained model, the stability regions of the beams for both cases of opposite poles and same poles facing each other are obtained. Also the effect of magnet's strength and flexibility of the beams on the stability boundaries are illustrated.     

Stability in parametric resonance of axially accelerating beams constituted by Boltzmann's superposition principle

Stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated. The governing equation is derived from Newton's second law, Boltzmann's superposition principle, and the geometrical relation. When the axial speed is a constant mean speed with small harmonic variations, the governing equation can be treated as a continuous gyroscopic system with small periodically parametric excitations and a damping term. The method of multiple scales is applied directly to the governing equation without discretization. The stability conditions are obtained for combination and principal parametric resonance. Numerical examples demonstrate that the increase of the viscosity coefficient causes the lager instability threshold of speed fluctuation amplitude for given detuning parameter and smaller instability range of the detuning parameter for given speed fluctuation amplitude. The instability region is much bigger in lower order principal resonance than that in the higher order.     

Electronic properties of Z-shaped graphene nanoribbon under uniaxial strain

Based on tight-binding approximation and a generalized Green's function method, the effect of uniaxial strain on the electron transport properties of Z-shaped graphene nanoribbon (GNR) composed of an armchair GNR sandwiched between two semi-infinite metallic armchair GNR electrodes is numerically investigated. Our results show that the increase of uniaxial strain enhances the band gap and leads to a metal-to-semiconductor transition for Z-shaped GNR. Furthermore, in the Landauer–Büttiker formalism, the current–voltage characteristics, the noise power resulting from the current fluctuations and Fano factor of strained Z-shaped GNR are explored. It is found the threshold voltage for the current and the noise power increased so that with reinforcement of the uniaxial strain parameter strength, the noise power goes from the Poisson limit to sub-Poisson region at higher bias voltages.     

Nonlinear Resonance Cone Surfaces

The nonlinear modification of the equation describing the surface (the resonance cone) on which the maximum electric field occurs in a magnetized plasma excited by an arbitrary, axially symmetric, localized RF source is derived. The nonlinearity is assumed to be due to the ponderomotive force. The nonlinear modification of the slope of the resonance cone is most pronounced near the plasma and upper hybrid frequencies, and is inversely proportional to the distance from the exciter. For frequencies of the lower branch the slope is decreased, whereas for upper branch frequencies the slope is increased.     

Nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer subject to a vertical oscillating force and a horizontal electric field

Weakly nonlinear stability of interfacial waves propagating between two electrified inviscid fluids influenced by a vertical periodic forcing and a constant horizontal electric field is studied. Based on the method of multiple-scale expansion for a small-amplitude periodic force, two parametric nonlinear Schrödinger equations with complex coefficients are derived in the resonance cases. A standard nonlinear Schrödinger equation with complex coefficients is derived in the nonresonance case. A temporal solution is carried out for the parametric nonlinear Schrödinger equation. The stability analysis is discussed both analytically and numerically.     

Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions

This paper investigates the thermo-electro-mechanical vibration of the rectangular piezoelectric nanoplate under various boundary conditions based on the nonlocal theory and the Mindlin plate theory. It is assumed that the piezoelectric nanoplate is subjected to a biaxial force, an external electric voltage and a uniform temperature rise. The Hamilton's principle is employed to derive the governing equations and boundary conditions, which are then discretized by using the differential quadrature (DQ) method to determine the natural frequencies and mode shapes. The detailed parametric study is conducted to examine the effect of the nonlocal parameter, thermo-electro-mechanical loadings, boundary conditions, aspect ratio and side-to-thickness ratio on the vibration behaviors.     

Dynamic stability of a slender beam under horizontal–vertical excitations

The dynamic stability of a vertically standing cantilevered beam simultaneously excited in both horizontal and vertical directions at its base is studied theoretically. The beam is assumed to be an inextensible Euler–Bernoulli beam. The governing equation of motion is derived using Hamilton's principle and has a nonlinear elastic term and a nonlinear inertia term. A forced horizontal external term is added to the parametrically excited system. Applying Galerkin's method for the first bending mode, the forced Mathieu–Duffing equation is derived. The frequency response is obtained by the harmonic balance method, and its stability is investigated using the phase plane method. Excitation frequencies in the horizontal and vertical directions are taken as 1:2, from which we can investigate the influence of the forced response under horizontal excitation on the parametric instability region under vertical excitation. Three criteria for the instability boundary are proposed. The influences of nonlinearities and damping of the beam on the frequency response and parametric instability region are also investigated. The present analytical results for instability boundaries are compared with those of experiments carried out by one of the authors.     

Molecular dynamics simulation study on graphene-nanoribbon-resonators tuned by adjusting axial strain

A tunable graphene-nanoribbon (GNR)-resonator was investigated via classical molecular dynamics simulations. Resonance frequencies increased with increasing externally applied gate-force and axial-strain, and could be tuned above several hundred GHz. Tunable resonance frequencies achieved from the gate force were higher than those achieved from the axial-strain. The operating frequencies of GNR-resonators without axial-strain or with small axial-strains were most widely tuned by the gate, and almost linearly increased with increasing mean deflection. As the axial strain increased, the tunable ranges of the GNR-resonators were exponentially decreased, although the operating frequencies increased. GNR-resonators without axial-strain could be applied to wide-range-tuners, whereas GNR-resonators with high axial-strain could be applied to high-frequency-fine-tuners.     

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.     

Self-assembly of graphene nanoribbon ring on metallic nanowires

Molecular dynamics simulations demonstrate that metallic nanowires (NWs) can activate and guide the self-assembly of graphene nanoribbon rings (GNR), allowing them to adopt a bilayered helical configuration on NWs. This unique technology attributes to the combined effects of the van der Waals force and the π–π stacking interaction. The size and chirality effects of GNR on the self-assembly of GNR–NW system are calculated. Diverse NWs, acting as an external force, can initiate the conformational change of the GNRs to form bilayered helical structures. The stability of the formed nanosystems is further analyzed for numerous possible applications.     

A moiré method of visualizing electromagnetic force lines

We propose a simple moiré method of visualizing electromagnetic force lines. The indicial equation is first derived for the tangent (or normal) curve to the electric field (or magnetic induction) around two parallel-line charges (or currents). The derived equation is then shown to have a one-to-one correspondence with that of the moiré fringe formed by two overlapped radial gratings. Since the tangent (or normal) curve to the electric field (or the magnetic induction) corresponds to the direction of the electric (or magnetic) force on a test charge (or current), the radial grating moirés can be used for the visualization of electric (or magnetic) force lines.     

Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition

Journal of Statistical Physics - The Vlasov–Poisson–Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We...     

Nonlinear EHD stability of cylindrical walters B' fluids: effect of an axial time periodic electric field

The current article is concerned with a nonlinear stability analysis of cylindrical Walters B' fluids. The system is pervaded by an axial time periodic electric field. A cylindrical interface is supposed to be disconnected from two dielectric fluids. The fluids are fully saturated in porous media. The motivation to scrutinize this area is attributed to the great attention it receives in many practical situations in physics and engineering applications. The implementation of the appropriate nonlinear boundary conditions of the linearized equations of motion yields a nonlinear characteristic dispersion equation. This equation manages the surface deflection of the surface waves. The use of the non-dimensional analysis resulted in various well-known non-dimensional numbers. A new approach to the characteristic equation is inspected by employing the Homotopy perturbation method (HPM). This new methodology resulted in a Klein-Gordon equation. Utilizing a travelling-wave solution to the linear part of the characteristic equation, a new restriction of the stability analysis appears. The investigation reveals the non-resonance as well as the resonance cases, and the stability criteria are established in both arguments. A set of diagrams is plotted to display the influence of various non-dimensional physical numbers on the stability profile and shows interesting features.     

Stability analysis of a parametrically excited functionally graded piezoelectric, MEM system

In this paper the mechanical behavior of a parametrically actuated functionally graded piezoelectric (FGP) clamped-clamped micro-beam is investigated. The micro-beam is supposed to be a composite material with silicon and piezoelectric base. The mechanical properties of the structure, including elasticity modulus, density, and piezoelectricity coefficient are supposed to vary along the height of the micro-beam with an exponential functionality. It is supposed that the FGP clamped-clamped micro-beam is actuated with a combination of direct and alternative electric potential difference. Application of DC and AC actuation voltage leads in a constant and a time-varying axial force. The governing differential equation of the motion is derived using Hamiltonian principle and discretized using expansion theorem with the corresponding shape functions of a clamped-clamped beam. The discretized system is governed by Mathieu equation which’s stability is investigated using Floquet theory for single degree of freedom systems and verified using multiple time scales of perturbation technique.     

微平行管道内Eyring流体的电渗滑移流动

研究了微平行管道内非牛顿流体––Eyring 流体在外加电场力和压力作用下的电渗流动. 在考虑微尺度效应, 电场作用, 非牛顿特性, 滑移边界等情况下, 建立Eyring流体在微平行管道内电渗流动的力学模型. 通过解线性Possion-Boltzmann方程和Cauchy动量方程, 给出Eyring 流体速度分布的精确解和近似解析解, 并探讨了上述因素对电渗流动的影响. 将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析, 得到有意义的结果.     

Nonlinear Oscillations Analysis of the Elevator Cable in a Drum Drive Elevator System

This paper aims to investigate nonlinear oscillations of an elevator cable in a drum drive. The governing equation of motion of the objective system is developed by virtue of Lagrangian's method. A complicated term is broached in the governing equation of the motion of the system owing to existence of multiplication of a quadratic function of velocity with a sinusoidal function of displacement in the kinetic energy of the system. The obtained equation is an example of a well-known category of nonlinear oscillators, namely, non-natural systems. Due to the complex terms in the governing equation, perturbation methods cannot directly extract any closed form expressions for the natural frequency. Unavoidably, different non-perturbative approaches are employed to solve the problem and to elicit a closed-form expression for the natural frequency. Energy balance method, modified energy balance method and variational approach are utilized for frequency analyzing of the system. Frequency-amplitude relationships are analytically obtained for nonlinear vibration of the elevator's drum. In order to examine accuracy of the obtained results, exact solutions are numerically obtained and then compared with those obtained from approximate closed-form solutions for several cases. In a parametric study for different nonlinear parameters, variation of the natural frequencies against the initial amplitude is investigated. Accuracy of the three different approaches is then discussed for both small and large amplitudes of the oscillations.     

Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.