Nonlinear dynamic characteristics of bi-graphene sheets/piezoelectric laminated films considering high order van der Walls force and scale effect

This paper presents an analytical method to investigate the nonlinear vibration characteristics of bi-graphene sheets/piezoelectric (BGP) laminated films subjected to electric loading based on a nonlocal continuum model, in which the two adjacent layers are coupled by van der Walls force. Utilizing von Kármán nonlinear geometric relation and nonlocal physical relation, the nonlinear dynamic equation of BGP laminated films under electric loading exerted on the piezoelectric layer is found, then the relation between the nonlinear resonant frequency and the nonlinear vibration amplitude for each layer of the BGP laminated films is obtained by using Galerkin method and harmonic-balance method. Results show that the nonlinear vibration amplitude for each layer of laminated films can be controlled by adjusting the electric potential exerted on piezoelectric layer, and the coupled effect of van der Walls force between graphene sheet and piezoelectric layer on the vibration amplitude of each layer depends on the order number of nonlinear resonant frequency and the mode shape.     

Hertzian contact problem: Numerical reduction and volumetric modification

A technique for the analytical formulation and numerical implementation of an elastic contact model for rigid bodies in the framework of the Hertzian contact problem is described. The normal elastic force and the semiaxes of the contact area are computed so that the problem is sequentially reduced to a scalar transcendental equation depending on complete elliptic integrals of the first and second kinds. Based on the classical solution to the Hertzian contact problem, an invariant volumetric force function is proposed that depends on the geometric characteristics of interpenetration of two undeformed bodies. The normal forces computed using the force function agree with results obtained previously for non-Hertzian contact of elastic bodies. As an example, a ball bearing is used to compare the contact dynamics of elastic bodies simulated in the classical Hertzian model and its volumetric modification.     

Long-time behaviour of solutions of an electrophoretic model with a single reaction

A electrochemical model consisting of three charged speciesis considered. The ions diffuse owing to concentration gradientsand migrate because of electric force. Reversible reaction isallowed to take place between these species. It is shown that,provided the total of initial charges in the electrolyte iszero, any initial distribution of species concentrations willconverge to a unique steady state as time becomes large.     

On computer implementation of the Hertz elastic contact model and its simplifications

The paper is concerned with an elastic contact model of rigid bodies which is developed in the framework of the Hertz model. For this new model, we suggest more effective algorithms with reduced computational time. We also present an algorithm for representation of the geometry of the contacting surfaces in the local contact coordinate system. This coordinate system tracks permanently the surfaces of the bodies, which are able to contact. An approach to computation of the normal elastic force is presented. It is based on the reduction to a single transcendental scalar equation that includes the complete elliptic integrals of the first and second kinds. The computational time in the Hertz-model simulation was considerably reduced due to the use of the differential technique for computation of the complete elliptic integrals and due to the replacement of the implicit transcendental equation by a differential one. Using the classic solution of the Hertz contact problem, we then present an invariant form for the force function, which depends on the geometric properties of the intersection of the undeformed volumes occupied with the rigid bodies (so-called volumetric model). The reduced expression for the force function obtained is shown to be different from that accepted in the classic contact theory hypotheses. Our expression has been tested in several examples dealing with bodies that contact elastically including Hertz’s classical model. In the context of the Hertz contact problem, an approximate model for computation the resulting wrench of the dry friction tangent forces is set up. The wrench consists of the total friction force and the drilling friction torque. The approach under consideration naturally extends the contact model constructed earlier. The dry friction forces and torque are integrated over the contact elliptic spot. Generally an analytic computation of the integrals mentioned is bulk and cumbersome leading to decades of terms that include rational functions depending on complete elliptic integrals. To be able to implement a fast computer model of elastically contacting bodies, one should first set up an approximate model in the way initially proposed by Contensou. To verify the model developed, we have used results obtained by several authors. First we test our method on the Tippe-Top dynamic model. Simulations show that the top’s evolution can be verified with a high quality compared with the use of the theory of set-valued functions. In addition, the ball bearing dynamic model has been also used for a detailed verification of different approaches to the computation of tangent forces. Then the friction model of the regularized Coulomb type and the approximate Contensou one, each embedded into the whole bearing dynamic model, were thoroughly tested and compared. It turned out that the simplified Contensou approach provides a computer model that runs even faster compared with the case of the point contact. In addition, the volumetric model demonstrated a reliable behavior and an acceptable accuracy.     

Optimal portfolios for DC pension plans under a CEV model

This paper studies the portfolio optimization problem for an investor who seeks to maximize the expected utility of the terminal wealth in a DC pension plan. We focus on a constant elasticity of variance (CEV) model to describe the stock price dynamics, which is an extension of geometric Brownian motion. By applying stochastic optimal control, power transform and variable change technique, we derive the explicit solutions for the CRRA and CARA utility functions, respectively. Each solution consists of a moving Merton strategy and a correction factor. The moving Merton strategy is similar to the result of Devolder et al. [Devolder, P., Bosch, P.M., Dominguez F.I., 2003. Stochastic optimal control of annunity contracts. Insurance: Math. Econom. 33, 227-238], whereas it has an updated instantaneous volatility at the current time. The correction factor denotes a supplement term to hedge the volatility risk. In order to have a better understanding of the impact of the correction factor on the optimal strategy, we analyze the property of the correction factor. Finally, we present a numerical simulation to illustrate the properties and sensitivities of the correction factor and the optimal strategy.     

结构参数对静电驱动微机械陀螺动态性能的影响

为研究结构参数对静电驱动微机械陀螺动态性能的影响,考虑支承刚度的三次非线性和静电力的分式非线性,基于两自由度动力学模型,利用谐波平衡法结合留数定理求解了系统的周期响应,得到了驱动电极的梳齿厚度、梳齿间隙以及检测电极的极板面积、极板间隙变化时电容变化量随驱动力频率和载体角速度的变化曲线,以及电容灵敏度和非线性度随这些参数的变化曲线。结果表明,检测电容变化量随驱动力频率的变化曲线会呈现明显的非线性特征,即第二个峰向右倾斜,从而引起跳跃现象。驱动电极的梳齿厚度、梳齿间隙和检测电极的极板间隙对检测电容变化量随载体角速度的变化影响较大,而检测电极的极板面积的影响很小。驱动电极梳齿厚度、梳齿间隙以及检测电极的极板面积对电容灵敏度和非线性度的影响基本上是线性的,但检测电极的极板间隙对电容灵敏度和非线性度的影响是非线性的。     

Locomotion of Articulated Bodies in a Perfect Fluid

This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the coupling between their shape changes and the fluid dynamics in their environment. The equations of motion are obtained by making use of a two-stage reduction process which leads to significant mathematical and computational simplifications. The first reduction exploits particle relabeling symmetry: that is, the symmetry associated with the conservation of circulation for ideal, incompressible fluids. As a result, the equations of motion for the submerged solid bodies can be formulated without explicitly incorporating the fluid variables. This reduction by the fluid variables is a key difference with earlier methods, and it is appropriate since one is mainly interested in the location of the bodies, not the fluid particles. The second reduction is associated with the invariance of the dynamics under superimposed rigid motions. This invariance corresponds to the conservation of total momentum of the solid-fluid system. Due to this symmetry, the net locomotion of the solid system is realized as the sum of geometric and dynamic phases over the shape space consisting of allowable relative motions, or deformations, of the solids. In particular, reconstruction equations that govern the net locomotion at zero momentum, that is, the geometric phases, are obtained. As an illustrative example, a planar three-link mechanism is shown to propel and steer itself at zero momentum by periodically changing its shape. Two solutions are presented: one corresponds to a hydrodynamically decoupled mechanism and one is based on accurately computing the added inertias using a boundary element method. The hydrodynamically decoupled model produces smaller net motion than the more accurate model, indicating that it is important to consider the hydrodynamic interaction of the links.     

Exact and approximate expressions for resistance coefficients of a colloidal sphere approaching a solid surface at intermediate Reynolds numbers

A mathematical model has been developed to describe the force of liquid flow acting on a colloidal spherical particle as it approaches a solid surface at intermediate-Reynolds-number-flow regime. The model has incorporated bispherical coordinates to determine a stream function for the flow disturbed by the sphere. The stream function was then used to derive the flow force on the particle as a function of the inter-surface separation distance. The force equation was related to the modified Stokes equation to obtain an exact analytical expression for the correction factor to the Stokes law. Finally, a rational approximation is presented, which is in good agreement with the exact numerical result, and can be readily applied to more general particle–surface interactions involving short-range hydrodynamics associated with colloidal particles in the near vicinity of a large solid collector surface at intermediate Reynolds number of the supporting flow.     

Influence of model reduction techniques on the impact force calculation of two flexible bodies

One important issue for the simulation of flexible multibody systems is the reduction of the flexible body's degrees of freedom. For the reduction process finite element data and user inputs are necessary. The model reduction program for elastic multibody systems MOREMBS, which is developed at the ITM, has an easy-to-use interface and the data can be gained from the programs ABAQUS or ANSYS. In this work, the simulation of a fuel injection process is investigated with MOREMBS. We focus on the interaction between valve and armature. These two bodies impact in every injection circle. The impacting bodies are modeled as flexible and the contact force is calculated by a penalty approach. One essential part of this work is the investigation of the influence of different model reduction techniques on the impact force calculation of the flexible multibody system. The main reduction techniques modal reduction, Krylov-subspace based and Gramian matrix based techniques are compared. The results achieved with modal reduction, the state of the art reduction method, are not acceptable here. Krylov-subspace based techniques are especially well-suited for large sparse systems but are not error controlled. However, by choosing appropriate moment-matching properties the impact force calculation is nearly as good as with a full finite element model. The Gramian matrix based reduction techniques can be fully automated and are error controlled but require high computational effort. Hence, appropriate approximation schemes have to be used for them. With Gramian matrix based methods we can even further reduce the size of the subsystems compared to Krylov-subspace based methods and still have an impact force calculation nearly as good as with finite element results, but we gain a simulation speedup by the factor 4000. In addition, a parameter study of the parameters involved in the model reduction process is presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bending of sinusoidal functionally graded piezoelectric plate under an in-plane magnetic field

This work investigates the bending of a simply supported functionally graded piezoelectric plate under an in-plane magnetic field. The extended sinusoidal plate theory for piezoelectric plate is adopted. The governing equations are derived by the principle of the virtual work considering the Lorentz magnetic force obtained from the Maxwell's relation. The effect of magnetic field, electric loading and gradient index on the displacement, electric potential, stress and electric displacement are numerically presented and discussed in detail. These conclusions will be of particular interest to the future analysis of piezoelectric plate in magnetic field.     

Electrohydrodynamic flow in a retarding electric field with allowance for charged particle inertia : PMM vol. 43, no. 6, 1979, pp. 1029–1039

The one-dimensional electrohydrodynamic flow is considered in a retarding electric field when, owing to the inertia of charged particles, it is necessary to use the complete equation of momenta for the charged component. It is shown that in spite of the negligibly small relative volume occupies by particles in the initial cross section of the stream, there is a section in which particles move at low but finite velocity with a finite relative volume of the charged component, when the particles are retarded by an external homogeneous electric field (without taking into account the induced field). Interaction of the charged and neutral components, which may be absent in the initial cross section, is always substantial. The pressure drop required for such flow is determined. The flow is investigated with allowance for induced electric fields that diminish the effect of concentration increase of charged particles.     

微通道周期流动电位势及电粘性效应

求解了双电层的Poisson-Boltzmann方程和流体运动的Navier-Stokes方程,得到在周期压差作用下,二维微通道的周期流动电位势,流动诱导电场和液体流动速度的解析解．量纲分析表明,流体电粘性力与以下3个参数有关:1) 电粘性数,它表示定常流动时,通道最大电粘性力与压力梯度的比;2) 形状函数,它表示电粘性力在通道横截面的分布形态; 3) 耦合系数,它表示电粘性力的振幅衰减特征和相位差．分析结果表明,微通道周期流动诱导电场、流动速度与频率Reynolds数有关．在频率Reynolds数小于1时,流动诱导电场随频率Reynolds数变化很慢．在频率Reynolds数大于1时,流动诱导电场随频率Reynolds数的增加快速衰减．在通道宽度与双电层厚度比值较小情况下,电粘性效应对周期流动速度和流动诱导电场有重要影响．     

A 2D-Planar Dielectrophoretic Model with Electro-Thermally Induced Fluid Motion and the Stability of Trapping Zones

Dielectrophoresis (DEP) is an electrokinetics-based phenomenon that involves the motion of a particle due to the interaction between an applied nonuniform electric field and an induced dipole moment. This technique is very effective in particle manipulation and separation. Earlier studies on control-amenable models to describe the motion of a neutrally buoyant, neutrally charged particle in a chamber with a parallel electrode array have restricted the motion of the particle to one dimension. Here, incorporating the electro-thermal fluid motion as well, we present a 2D-planar DEP model and study the effect of electro-thermal fluid motion on particle trapping.     

A delayed stochastic volatility correction to the constant elasticity of variance model

The Black-Scholes model does not account non-Markovian property and volatility smile or skew although asset price might depend on the past movement of the asset price and real market data can find a non-flat structure of the implied volatility surface. So, in this paper, we formulate an underlying asset model by adding a delayed structure to the constant elasticity of variance (CEV) model that is one of renowned alternative models resolving the geometric issue. However, it is still one factor volatility model which usually does not capture full dynamics of the volatility showing discrepancy between its predicted price and market price for certain range of options. Based on this observation we combine a stochastic volatility factor with the delayed CEV structure and develop a delayed hybrid model of stochastic and local volatilities. Using both a martingale approach and a singular perturbation method, we demonstrate the delayed CEV correction effects on the European vanilla option price under this hybrid volatility model as a direct extension of our previous work [12].     

Prediction of diameter errors in bar turning: a computationally effective model

Machining accuracy can be considerably affected by the deflections of the machine–workpiece–tool system as well as the thermal expansion of material during machining. An improved model for predicting dimensional errors in turning process is presented. This model uses a geometric analysis in the machine frame, in which the elastic deflections of the machine–workpiece–tool system due to the cutting force are studied. In this paper, our workpiece deflection model [A.-V. Phan, G. Cloutier, J.R.R. Mayer, International Journal of Production Research 37 (1999) 4039–4051; G. Cloutier, J.R.R. Mayer, A.-V. Phan, Computer Modeling and Simulation in Engineering 4 (1999) 133–137] earlier developed is employed. As described in Phan et al. (1999), this deflection model is general, accurate and computationally effective thanks to its closed-form solutions derived from the finite element technique. Also, due to the coupling between the cutting force and actual depth of cut, iterative computations are performed to obtain the coupling value of this force which provides further accuracy to the prediction. Finally, via numerical examples, the predicted diameter error on a workpiece, the ratio between the coupled cutting force and its nominal value along the part axis as well as the influence of the cutting force components on the error prediction are computed using the proposed model. The results provide additional insight into the error formation in the turning process.     

Closed-loop supply chain network equilibrium under legislation

This paper expands previous work dealing with oligopolistic supply chains to the field of closed-loop supply chains. The model presented has been formulated with the intent of examining issues surrounding the recent European Union directive regarding waste of electric and electronic equipment (WEEE). The network modelled consists of manufacturers and consumer markets engaged in a Cournot pricing game with perfect information. Closed-loop supply chain network equilibrium occurs when all players agree on volumes shipped and prices charged. Certain properties of the model are examined analytically. Numeric examples are included and have been solved using an extragradient method with constant step size. The equilibrium solution obtained provide interesting insights that lead into a number of areas for future research.     

Why current flows: A multiparticle one-dimensional model

In all known microscopic models of electric current including the basic Drude model, charged particles are accelerated by an external force and some random environment retards them. We introduce a classical multiparticle deterministic one-dimensional model on an interval with nearest-neighbor interaction, explaining how current can flow if the external force acts only on the ends of the passive part (i.e., outside the generator, battery, etc.) of the conductor. We obtain a family of explicit solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 301–311, May, 2008.     

Periodic solutions for the Lorentz force equation with singular potentials

We provide sufficient conditions for the existence of periodic solutions of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant models with singularities like Coulomb-like electric potentials or the magnetic dipole.