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.

Joint Optimization for on-Demand Deployment of UAVs and Spectrum Allocation in UAVs-Assisted Communication

To improve the efficiency and fairness of the spectrum allocation for ground communication assisted by unmanned aerial vehicles(UAVs),a joint optimization method for on-demand deployment and spectrum allocation of UAVs is proposed,which is modeled as a mixed-integer non-convex optimization problem(MINCOP).An algorithm to estimate the minimum number of required UAVs is firstly proposed based on the pre-estimation and simulated annealing.The MINCOP is then decomposed into three sub-problems based on the block coordinate descent method,including the spectrum allocation of UAVs,the association between UAVs and ground users,and the deployment of UAVs.Specifically,the optimal spectrum allocation is derived based on the interference mitigation and channel reuse.The association between UAVs and ground users is optimized based on local iterated optimization.A particle-based optimization algorithm is proposed to resolve the subproblem of the UAVs deployment.Simulation results show that the proposed method could effectively improve the minimum transmission rate of UAVs as well as user fairness of spectrum allocation.

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.

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.

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.

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.

Generalized time-dependent generator coordinate method for induced fission dynamics

The generalized time-dependent generator coordinate method(TD-GCM)is extended to include pairing correlations.The correlated GCM nuclear wave function is expressed in terms of time-dependent generator states and weight functions.The particle–hole channel of the effective interaction is determined by a Hamiltonian derived from an energy density functional,while pairing is treated dynamically in the standard BCS approximation with time-dependent pairing tensor and single-particle occupation probabilities.With the inclusion of pairing correlations,various time-dependent phenomena in open-shell nuclei can be described more realistically.The model is applied to the description of saddle-to-scission dynamics of induced fission.The generalized TD-GCM charge yields and total kinetic energy distribution for the fission of 240Pu,are compared to those obtained using the standard time-dependent density functional theory(TD-DFT)approach,and with available data.

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.

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.

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.

Non-hypergeometric Type of Polynomials and Solutions of Schrodinger Equation with Position-Dependent Mass

Using the coordinate transformation method, we study the polynomial solutions of the Schr6dinger equation with position-dependent mass （PDM）. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The issues related to normalization of the wavefunetions and Hermiticity of the Hamiltonian are also analyzed.

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 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.

Finite Element Method Formulation in Polar Coordinates for Transient Heat Conduction Problems

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method(FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

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.

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.

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.

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.