Shallow Water Model On Cubed-Sphere By Multi-Moment Finite Volume Method

A global numerical model for shallow water flows on the cubed-sphere grid is proposed in this paper. The model is constructed by using the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM). Two kinds of moments, i.e. the point value (PV) and the volume-integrated average (VIA) are defined and independently updated in the present model by different numerical formulations. The Lax-Friedrichs upwind splitting is used to update the PV moment in terms of a derivative Riemann problem, and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the VIA moment. The cubed-sphere grid is applied to get around the polar singularity and to obtain uniform grid spacing for a spherical geometry. Highly localized reconstruction in CIP/MM FVM is well suited for the cubed-sphere grid, especially in dealing with the discontinuity in the coordinates between different patches. The mass conservation is completely achieved over the whole globe. The numerical model has been verified by Williamson's standard test set for shallow water equation model on sphere. The results reveal that the present model is competitive to most existing ones. (C) 2008 Elsevier Inc. All rights reserved.

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Pull-in Instability Study of Carbon Nanotube Tweezers Under the Influence of Van der Waals Forces

The pull-in instability of two nanotubes under van der Waals force is studied. The cantilever beam with large deformation model is used. The influence of nanotube parameters such as the interior radius, the gap distance between the two nanotubes, etc, on the pull-in instability is studied. The critical nanotube length is determined for each specific set of nanotube parameters. The Galerkin method is applied to discretize the governing equations, and it shows good convergence.

Numerical and Analytical Study on the Pull-in Instability of Micro-Structure under Electrostatic Loading

The one-mode analysis method on the pull-in instability of micro-structure under electrostatic loading is presented. Taylor series are used to expand the electrostatic loading term in the one-mode analysis method, which makes analytical solution available. The one-mode analysis is the combination of Galerkin method and Cardan solution of cubic equation. The one-mode analysis offers a direct computation method on the pull-in voltage and displacement. In low axial loading range, it shows little difference with the established multi-mode analysis on predicting the pull-in voltages for three different structures (cantilever, clamped-clamped beams and the plate with four edges simply-supported) studied here. For numerical multi-mode analysis, we also show that using the structural symmetry to select the symmetric mode can greatly reduce both the computation effort and the numerical fluctuation.

Vibration of an Adhered Microbeam Under a Periodically Shaking Electrical Force

The vibration analysis of an adhered S-shaped microbeam under alternating sinusoidal voltage is presented. The shaking force is the electrical force due to the sinusoidal voltage. During vibration, both the microbeam deflection and the adhesion length keep changing. The microbeam deflection and adhesion length are numerically determined by the iteration method. As the adhesion length keeps changing, the domain of the equation of motion for the microbeam (unadhered part) changes correspondingly, which results in changes of the structure natural frequencies. For this reason, the system can never reach a steady state. The transient behaviors of the microbeam under different shaking frequencies are compared. We deliberately choose the initial conditions to compare our dynamic results with the existing static theory. The paper also analyzes the changing behavior of adhesion length during vibration and an asymmetric pattern of adhesion length change is revealed, which may be used to guide the dynamic de-adhering process. The abnormal behavior of the adhered microbeam vibrating at almost the same frequency under two quite different shaking frequencies is also shown. The Galerkin method is used to discretize the equation of motion and its convergence study is also presented. The model is only applicable in the case that the peel number is equal to 1. Some other model limitations are also discussed.

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.

Hopf bifurcation in wakes behind a rotating and translating circular cylinder

A low-dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two-dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time-periodic solution is investigated. A curve indicating the transitional boundary is given in the two-dimensional parameter plane of Reynolds number Re and rotating parameter alpha. Our results show that rotation may delay the onset of vortex street and decrease the vortex-shedding frequency. (C) 1996 American Institute of Physics.

人工源频率域大地电磁法正反演研究

The CSAMT method is playing an important role in the exploration of geothermal and the pre-exploration in tunnel construction project recently. In order to instruct the interpretation technique for the field data, the forward method from ID to 3D and inversion method in ID and 2D are developed in this paper for the artificial source magnetotelluric in frequency domain. In general, the artificial source data are inverted only after the near field is corrected on the basis of the assumption of half-homogeneous space; however, this method is not suitable for the complex structure because the assumption is not valid any more. Recently the new idea about inversion scheme without near field correction is published in order to avoid the near field correction error. We try to discuss different inversion scheme in ID and 2D using the data without near field correction.The numerical integration method is used to do the forward modeling in ID CSAMT method o The infinite line source is used in the 2D finite-element forward modeling, where the near-field effect is occurred as in the CSAMT method because of using artificial source. The pseudo-delta function is used to modeling the source distribution, which reduces the singularity when solving the finite-element equations. The effect on the exploration area is discussed when anomalous body exists under the source or between the source and exploration area; A series of digital test show the 2D finite element method are correct, the results of modeling has important significant for CSAMT data interpretation. For 3D finite-element forward modeling, the finite-element equation is derived by Galerkin method and the divergence condition is add forcedly to the forward equation, the forward modeling result of the half homogeneous space model is correct.The new inversion idea without near field correction is followed to develop new inversion methods in ID and 2D in the paper. All of the inversion schemes use the data without near field correction, which avoid introducing errors caused by near field correction. The modified grid parameter method and the layer-by-layer inversion method are joined in the ID inversion scheme. The RRI method with artificial source are developed and finite-element inversion method are used in 2D inversion scheme. The inversion results using digital data and the field data are accordant to the model and the known geology data separately, which means the inversion without near field correction is accessible. The feasibility to invert the data only in exploration area is discussed when the anomalous body exists between the source and the exploration area.

Analysis of critical excavation depth for a jointed rock slope using a face-to-face discrete element method

The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D-s and the natural slope angle alpha, the joint inclination angle theta as well as the strength parameters of the joints c(r) ,phi(r) is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Novel method to construct a quality map for phase unwrapping based on modulation and the phase gradient

A novel method to construct a quality map, called modulation-phase-gradient variance (MPGV), is proposed, based on modulation and the phase gradient. The MPGV map is successfully applied to two phase-unwrapping algorithms - the improved weighted least square and the quality-guided unwrapping algorithm. Both simulated and experimental data testify to the validity of our proposed quality map. Moreover, the unwrapped-phase results show that the new quality map can have higher reliability than the conventional phase-derivative variance quality map in helping to unwrap noisy, low-modulation, and/or discontinuous phase maps. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

A novel three-dimensional imaging array recording and computational method by means of coded cameras reconstruction

In this paper, we propose a novel three-dimensional imaging method by which the object is captured by a coded cameras array (CCA) and computationally reconstructed as a series of longitudinal layered surface images of the object. The distribution of cameras in array, named code pattern, is crucial for reconstructed images fidelity when the correlation decoding is used. We use DIRECT global optimization algorithm to design the code patterns that possess proper imaging property. We have conducted primary experiments to verify and test the performance of the proposed method with a simple discontinuous object and a small-scale CCA including nine cameras. After certain procedures such as capturing, photograph integrating, computational reconstructing and filtering, etc., we obtain reconstructed longitudinal layered surface images of the object with higher signal-to-noise ratio. The results of experiments show that the proposed method is feasible. It is a promising method to be used in fields such as remote sensing, machine vision, etc. (c) 2006 Elsevier GmbH. All rights reserved.

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.