Static Study of Cantilever Beam stiction under Electrostatic Force Influence

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beamsolutions of the loads with different distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation offers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length offers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The effects of dielectric layer thickness and electrostatic voltage on the cantilever beamstiction are studied.The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

Static Shape Control Employing Displacement-Stress Dual Criteria

An approach employing displacement-stress dual criteria for static shape control is presented. This approach is based on normal displacement control, and stress modification is considered in the whole optimization process to control high stress in the local domain. Analysis results show that not only is the stress reduced but al so that the controlled surface becomes smoother than before.

Static shape control of repetitive structures integrated with piezoelectric actuators

In this paper, several simplification methods are presented for shape control of repetitive structures such as symmetrical, rotational periodic, linear periodic, chain and axisymmetrical structures. Some special features in the differential equations governing these repetitive structures are examined by considering the whole structures. Based on the special properties of the governing equations, several methods are presented for simplifying their solution process. Finally, the static shape control of a cantilever symmetrical plate with piezoelectric actuator patches is demonstrated using the present simplification method. The result shows that present methods can effectively be used to find the optimal control voltage for shape control.

Molecular/Cluster Statistical Thermodynamics Methods To Simulate Quasi-Static Deformations At Finite Temperature

The rapid evolution of nanotechnology appeals for the understanding of global response of nanoscale systems based on atomic interactions, hence necessitates novel, sophisticated, and physically based approaches to bridge the gaps between various length and time scales. In this paper, we propose a group of statistical thermodynamics methods for the simulations of nanoscale systems under quasi-static loading at finite temperature, that is, molecular statistical thermodynamics (MST) method, cluster statistical thermodynamics (CST) method, and the hybrid molecular/cluster statistical thermodynamics (HMCST) method. These methods, by treating atoms as oscillators and particles simultaneously, as well as clusters, comprise different spatial and temporal scales in a unified framework. One appealing feature of these methods is their "seamlessness" or consistency in the same underlying atomistic model in all regions consisting of atoms and clusters, and hence can avoid the ghost force in the simulation. On the other hand, compared with conventional MD simulations, their high computational efficiency appears very attractive, as manifested by the simulations of uniaxial compression and nanoindenation. (C) 2008 Elsevier Ltd. All rights reserved.

Comparison Of The Quasi-Static Method And The Dynamic Method For Simulating Fracture Processes In Concrete

Concrete is heterogeneous and usually described as a three-phase material, where matrix, aggregate and interface are distinguished. To take this heterogeneity into consideration, the Generalized Beam (GB) lattice model is adopted. The GB lattice model is much more computationally efficient than the beam lattice model. Numerical procedures of both quasi-static method and dynamic method are developed to simulate fracture processes in uniaxial tensile tests conducted on a concrete panel. Cases of different loading rates are compared with the quasi-static case. It is found that the inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, an unrealistic result will be obtained if a fracture process including unstable cracking is simulated by the quasi-static procedure.

Static and fatigue failure behavior of carbon-fiber reinforced epoxy composite-materials with edge notch

A study of carbon fiber reinforced epoxy composite material with 0° ply or ±45°ply(unnotched or with edge notch) was carried out under static tensile and tension-tensioncyclic loading testing. Static and fatigue behaviour and damage failure modes in unnotched/notched specimens plied in different manners were analysed and compared with each other.A variety of techniques (acoustic emission, two types of strain extensometer, high speed pho-tography, optical microscopy, scanning electron microscope, etc.) were used to examine thedamage of the laminates. Experimental results show that when these carbon/epoxy laminateswith edge notch normal to the direction of the load are axially loaded in static or fatiguetension, the crack does not propagate along the length of notch but is in the interface (fiberdirection). The notch has no substantial effect on the stresses at the unnotched portion. Thedamage failure mechanism is discussed.

Static equilibrium of horizontal ring prominence

In 1980 the Beijing Observatory had successively observed sevesal rare completely closed ring prominences whose ring plane was approximately parallel to the solar surface with a characteristic life about 1—2 days. In this paper we discuss the static equilibrium of this kind of horizontal ring plasma under the simultaneous actions of magnetic force, gravity and pressure gradients. Assuming ring plasma with axisymmetry and rectangular plasma cross-section and adopting closed magnetic field boundary condition from the basic equations we obtain the exact zero order general solutions for magnetic field (force-free field) and density (pressure). We further obtain an eigen-solution for the zero order magnetic field and density as well as the first order magnetic field, thus giving a kind of the possible distribution of magnetic field and density for the horizontal closed ring prominence. The closed magnetic structure of ring prominence as presented in this paper, has no link with the force lines of the outside corona magnetic field. This is helpful to explain the great temperature difference between prominenee and corona.

Comparisons of static, quasi-static and dynamic 3D porous media scale network models for two-phase immiscible flow in porous media

A dynamic 3D pore-scale network model is formulated for investigating the effect of interfacial tension and oil-water viscosity during chemical flooding. The model takes into account both viscous and capillary forces in analyzing the impact of chemical properties on flow behavior or displacement configuration, while the static model with conventional invasion percolation algorithm incorporates the capillary pressure only. From comparisons of simulation results from these models. it indicates that the static pore scale network model can be used successfully when the capillary number is low. With the capillary increases due to the enhancement of water viscosity or decrease of interfacial tension, only the quasi-static and dynamic model can give insight into the displacement mechanisms.

Enhancing Kerr nonlinearity in an asymmetric double quantum well via Fano interference

We investigate the enhancement of Kerr nonlinearity in an asymmetric GaAs double quantum well via Fano interference, which is caused by tunneling from the excited subband to the continuum. In our structure, owing to Fano interference, the Kerr nonlinearity can be enhanced by appropriately choosing the values of the detunings and the intensity of the pump field, while cancel the linear and nonlinear absorptions.

Enhancing Kerr nonlinearity via spontaneously generated coherence

A theoretical investigation is carried out into the effect of spontaneously generated coherence on the Kerr nonlinearity of general three-level systems of Lambda, ladder, and V-shape types. It is found, with spontaneously generated coherence present, that the Kerr nonlinearity can be clearly enhanced. In the Lambda- and ladder-type systems, the maximal Kerr nonlinearity increases and at the same time enters the electromagnetically induced transparency window as the spontaneously generated coherence intensifies. As for the V-type system, the absorption property is significantly modified and therefore enhanced Kerr nonlinearity without absorption occurs for certain probe detunings. We attribute the enhancement of Kerr nonlinearity mainly to the presence of an extra atomic coherence induced by the spontaneously generated coherence.

Giant Kerr nonlinearity induced by interacting dark resonances

A scheme for giant enhancement of the Kerr nonlinearity in a four-level system with double dark resonances is proposed. Compared with that generated in a single-dark-resonance system, the Kerr nonlinearity can be enhanced by several orders of magnitude with vanishing linear absorption. We attribute this dramatic enhancement to the interaction of dark resonances. (c) 2005 Optical Society of America.

Controllable Kerr nonlinearity with perfect transparency in the existence of spontaneously generated coherence

We investigate the Kerr nonlinearity of a V-type three-level atomic system where the upper two states decay outside to another state and hence spontaneous generated coherence may exist. It is shown that dark state and hence perfect transparency present under certain conditions. Meanwhile, the Kerr nonlinearity can be controlled by manipulation of the decay rates and the splitting of the two excited states. Therefore, enhanced Kerr nonlinearity without absorption can be obtained under proper parameters.

Phase control of the Kerr nonlinearity in electromagnetically induced transparency media

We investigate an enhancement of the Kerr nonlinearity in phase-dependent double electromagnetically induced transparency (EIT) media. We find, by changing the relative phase of the driven fields, that the properties of EIT and the Kerr nonlinearity can be modified significantly. Choosing the relative phase appropriately, a giant Kerr nonlinearity can be achieved with vanishing absorptions.

Trichromatic manipulation of Kerr nonlinearity in a three-level lambda atomic system

Trichromatic manipulation of Kerr nonlinearity in a three-level A atomic configuration is investigated theoretically. It is shown that for a weak monochromatic probe field, the enhanced Kerr nonlinearity can be achieved in multiple separate transparent windows due to interference effect of multiple two-photon Raman channels. Furthermore, the property of Kerr nonlinearity can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field compared to the central component.