Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate

In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.

Complex coordinate rotation method based on gradient optimization

In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.

Control of Virtual Synchronous Generator for Frequency Regulation Using a Coordinated Self-adaptive Method

Power inverter adopting virtual synchronous generator(VSG)control can provide inertia support for distributed generation systems.However,it cannot take into account the dynamic regulation characteristics of frequency.Thus,when the system encounters a sudden change in load or disturbance,the dynamic process of frequency regulation will be greatly influenced.In view of this issue,an improved VSG control strategy based on a coordinated self-adaptive(CSA)method is proposed.The time domain analysis method is used to study the influences of virtual inertia and damping parameter perturbation on the system steady and dynamic performances.Furthermore,in order to make the control strategy suitable for large load changes and suppress frequency variations beyond the limit,the secondary frequency modulation is introduced into the control loop.Through the coordinated adaptive control of virtual inertia,virtual damping and frequency modulation,the dynamic performance of vSG frequency regulation can be obviously improved.Simulation and experiment results have verified the effectiveness of the proposed CSA control strategy.

Nano/Micro HKUST-1 Fabricated by Coordination Modulation Method at Room Temperature

A simple and fast route for the synthesis of metal-organic framework（MOF） particles was presented.Cu 3（BTC） 2（HKUST-1,BTC=1,3,5-benzenetricarboxylate）,one of the most well-known MOFs,was synthesized at room temperature via coordination modulation method.By adding different modulators（monocarboxylic acids） into the reaction system,the morphologies of HKUST-1 crystals were tuned from nano spheres to micro octahedrons at room temperature without any complex equipment.X-Ray diffractions and gas sorption measurements revealed highly crystalline particles with large Brunauer-Emmett-Teller（BET） surface areas（1116―1273 m^ 2 /g） and total pore volumes（0.62―0.73 cm^ 3 /g）.The significantly small particle sizes and high capacity of gas sorption are considered advantageous for envisaged application in practical industrial process.

Coordinate scheduling approach for EDS observation tasks and data transmission jobs

Electromagnetic detection satellite（EDS） is a type of Earth observation satellite（EOS）. Satellites observation and data down-link scheduling plays a significant role in improving the efficiency of satellite observation systems. However, the current works mainly focus on the scheduling of imaging satellites, little work focuses on the scheduling of EDSes for its specific requirements.And current works mainly schedule satellite resources and data down-link resources separately, not considering them in a globally optimal perspective. The EDSes and data down-link resources are scheduled in an integrated process and the scheduling result is searched globally. Considering the specific constraints of EDS, a coordinate scheduling model for EDS observation tasks and data transmission jobs is established and an algorithm based on the genetic algorithm is proposed. Furthermore, the convergence of our algorithm is proved. To deal with some specific constraints, a solution repairing algorithm of polynomial computing time is designed. Finally, some experiments are conducted to validate the correctness and practicability of our scheduling algorithms.

Study of elastic wave propagation in two phase anisotropic media by numerical modeling of pseudospectral method

When there exists anisotropy in underground media elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed.

Wave reflection, transmission and harmonics due to different submerged structures

Comparisons of wave reflection, transmission and harmonics due to different types of sub merged structures are investigated by a numerical method, the boundary-fitted coordinate (BFC) method. The types of submerged structures include a submerged horizontal plate, submerged breakwa ters (rectangular and trapezoidal) and a step-type structure (topography). First, the BFC method is ver ified by comparing the computed results with the experimental data, including wave surface elevations, reflected and transmitted wave heights, and amplitudes of higher harmonics, showing that the method is a reasonable one to predict wave deformations due to the submerged structures. Secondly, the wave sur face elevations and the higher harmonics over different submerged structures are compared. Thirdly, re flected and transmitted waves due to different submerged structures are investigated.

Wavemotionsarounddifferentsubmergedstructures

Wave motions around different types of submerged structures are investigated by a numerical method, theboundary fitted coordinate method. The types of submerged structures include a submerged horizontal plate, submerged breakwaters (rectangular and trapezoidal) and a step-type structure (topography) . Water level fluctuations, wave height distributions, velocity fields and wave energies around submerged structures are studied comprehensively.

Large Displacement Analysis of Tapered Beam Structures

A Bernoulli-Euler beam mechanism for static analysis of large displacement,large rotation but small strain planar tapered beam structures is proposed using the Updated Lagrangian formulation and the moving coordinate method.The object beam is the tapered one whose profile is assumed to be varying linearly.From the governing differential equation of lateral deflection including second-order effects by beam-column theory,the geometric nonlinear tangent elemental stiffness matrix is derived.The nonlinear effect of the bending distortions on the axial action is considered to manifest itself as an axial change in length.The aforementioned stiffness matrix is amended,by developing the auxiliary stiffness of bowing effect.The moving coordinate method is employed for obtaining the large displacement total equilibrium equations,and the hinged-hinged moving coordinate system is constructed at the last updated configuration.The multiple load steps Newton-Raphson iteration is adopted for the solution of the nonlinear equations.The validity and efficiency of the proposed method are shown by solving various typical numerical examples.

Coordinate difference homogenization matching method for motion correction in 3D range-intensity correlation laser imaging

This Letter proposes a coordinate difference homogenization matching method to solve motion influence in three-dimensional（3D） range-intensity correlation laser imaging. Firstly, features and feature pairs of gate images are obtained by speeded-up robust figures and bi-directional feature matching methods. The original mean value of the feature-pair coordinate differences is calculated. Comparing the coordinate differences with the original mean value, the wrong feature pairs are removed, and then an optimized mean value is updated. The final feature-pair coordinates are re-registered based on the updated mean value. Thus, an accurate transformation is established to rectify motion gate images for 3D reconstruction. In the experiment, a 3D image of a tower at 780 m is successfully captured by our laser gated imaging system on a pan-tilt device.

An iteration method for correcting the located coordinates of an underwater target

An iteration method for correcting the target coordinates determined by a locating system with a Cartesian array is reported. Under the complex hydrological condition, the method can give the target position not only accurately but also quickly. The preliminary experimental results show that the correction is effective. An application of the method has been completed.

APPLICATION OF BOUNDARY FITTED COORDINATE TECHNIQUE ON 2-D STEADY FLOW OF TAIL RACE RIVER

In this paper,a modified boundary fitted coordinate method is presented.The transformation equations are solved by finite analytic method.The control equations after trans- formation are solved by splitting operator method.The results of calculation consist well with experiments.

Multi-boiler System Optimization in Integrated Steelworks Based on Decomposition and Coordination Method

As for the existing problems of boilers in integrated steelworks, the multi-boiler system could be quantitatively optimized with the decomposition and coordination method. Then, case studies were carried out based on the data of an integrated steelworks. Two groups of actual production records were contrastively analyzed, and the calculation results from the optimized program of these two groups indicated that for groups 1 and 2, the costs fall by 5.06% and 3.79%and the fuel consumptions decrease by 2.72% and 1.45%, respectively, compared with the actual data. To analyze the cost and fuel consumption change under the same condition of total load demand, assigned fuel consumption and water temperature, five sets of data were selected for further analysis. It was shown that the total cost and fuel consumption of the optimized program could fall by 3.5% and 1.6% respectively, compared with the actual production records. The optimal allocation significantly contributed to energy conservation and cost reduction. The effects of the system energy conservation cannot be realized by single equipment energy conservation. They were complementary to each other, and should be put on the same stage.

A Parallel Line Search Subspace Correction Method for Composite Convex Optimization

In this paper,we investigate a parallel subspace correction framework for composite convex optimization.The variables are first divided into a few blocks based on certain rules.At each iteration,the algorithms solve a suitable subproblem on each block simultaneously,construct a search direction by combining their solutions on all blocks,then identify a new point along this direction using a step size satisfying the Armijo line search condition.They are called PSCLN and PSCLO,respectively,depending on whether there are overlapping regions between two imme-diately adjacent blocks of variables.Their convergence is established under mild assumptions.We compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilai-Borwein step size and the greedy coordinate block descent method for solving the l1-regularized minimization problems.Our numerical results showthatPSCLN andPSCLOcan run fast and return solutions notworse than those from the state-of-theart algorithms on most test problems.It is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures.

On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization

Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.

A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology

We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains.The technique is based on a smooth coordinate transformation,which maps an unbounded domain into a unit square.Arbitrary geometries are defined by suitable level-set functions.The equations are discretized by classical nine-point stencil on interior points,while boundary conditions and high order reconstructions are used to define the field variables at ghost-points,which are grid nodes external to the domain with a neighbor inside the domain.The linear system arising from such discretization is solved by a multigrid strategy.The approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure sources.The method is suitable to treat problems in which the geometry of the source often changes(explore the effects of different scenarios,or solve inverse problems in which the geometry itself is part of the unknown),since it does not require complex re-meshing when the geometry is modified.Several numerical tests are successfully performed,which asses the effectiveness of the present approach.

A review of dynamic analysis on space solar power station

The concept of a space solar power station(SSPS)was proposed in 1968 as a potential approach for solving the energy crisis.In the past 50 years,several structural concepts have been proposed,but none have been sent into orbit.One of the main challenges of the SSPS is dynamic behavior prediction,which can supply the necessary information for control strategy design.The ultra-large size of the SSPS causes difficulties in its dynamic analysis,such as the ultra-low vibration frequency and large fexibility.In this paper,four approaches for the numerical analysis of the dynamic problems associated with the SSPS are reviewed:the finite element,absolute nodal coordinate,foating frame formulation,and structure-preserving methods.Both the merits and shortcomings of the above four approaches are introduced when they are employed in dynamic problems associated with the SSPS.Synthesizing the merits of the aforementioned four approaches,we believe that embedding the structure-preserving method into finite element software may be an effective way to perform a numerical analysis of the dynamic problems associated with the SSPS.

WAVE TRANSMISSION AND REFIECTION DUE TO A THIN VERTICAL BARRIER

WT5”BZ]A numerical method, the boundary fitted coordinate method (BFC), was used to investigate the transmission and reflection of water waves due to a rigid thin vertical barrier descending from the water surface to a depth, i.e., a curtain-wall type breakwater. A comparison between the present computed results and previous experimental and analytical results was carried out which verifies the prediction of the BFC method. Wave transmission and reflection due to the barrier were computed, and the transmission and refiection coefficients were given in a figure. [WT5”HZ]

Stress Intensity Factor for the Interaction between a Straight Crack and a Curved Crack in Plane Elasticity

Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.