具有sliding-clamped端强阻尼屈曲梁方程整体解的存在性

对固体力学中提出的具有强阻尼效应的非线性粘弹性梁方程进行了研究。在给定具有sliding-clamped端和简支端的边界条件下,利用Galerkin方法,证明了该非线性梁方程的整体弱解和强解的存在性。

基于Clamped B样条的空间非合作目标抓捕策略研究

空间机械臂技术是未来实施在轨服务与维护任务的关键技术之一.利用机械臂对空间非合作目标,特别是翻滚目标的抓捕仍然存在巨大的挑战.本文提出一种基于Clamped B样条的空间非合作目标抓捕策略方案.在对非合作目标与空间机械臂运动学与动力学分析的基础上,结合非合作目标被空间机械臂抓捕后的动静态对偶性分析,构建抓捕后的力可操作度椭球作为抓捕策略设计的优化指标.其次,考虑目标的运动预测和空间机械臂的抓捕能力图谱构建,确定空间机械臂应对目标的最优抓捕时机与抓捕终端状态.基于Clamped B样条对空间机械臂各关节轨迹进行时间归一化参数描述,并对抓捕过程中的机械臂关节角、速度、避撞、抓捕走廊等约束进行数学变换,最终将抓捕策略转换为多约束、多目标的非线性优化问题,利用自适应惯性权重的粒子群优化算法进行求解.将所设计的抓捕策略应用于空间七自由度运动学冗余机械臂,实现了对空间中翻滚目标的成功捕获,验证了所提抓捕策略的可行性与有效性.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.

Elasticity solution of clamped-simply supported beams with variable thickness

This paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differefitial equations and the boundary conditions attwo ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated.

Analytical solutions for a uniformly loaded circular plate with clamped edges

A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier (1970). The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.(2004), and the solutions for both types were compared with the FEM results and the calculations of thin plate theory.

Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation

The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of tile problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green＇s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.

Evaluation Method of Output Waveform Quality for Neutral⁃Point⁃ Clamped Three⁃Level Converter

An analytical evaluation method for output waveform quality of space vector pulse width modulation(PWM)strategies applied in neutral⁃point⁃clamped three⁃level converter(3L⁃NPC)is proposed in this paper.Low frequency error caused by neutral point voltage ripple and high frequency error introduced by space vector synthesis were both taken into account,and the unified error model of output current ripple was established.By taking continuous and discontinuous modulation strategies as examples,the unified error model was validated through Fourier analysis of the experimental results.The proposed evaluation method will be helpful for the switching sequence optimization and the modulation strategy selection.

THE APPLICATION OF WEINSTEIN-CHIEN′S METHOD——THE UPPER AND LOWER LIMITS OF FUNDAMENTAL FREQUENCY OF RECTANGULAR PLATES WITH EDGES ARE THE MIXTURE OF SIMPLY SUPPORTED PORTIONS AND CLAMPED PORTIONS

In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.

Some Aspects of the Behavior for Orthotropic Thin Plates with Clamped Edges

In most structural applications, composite structures can be idealized as beams, plates or shells. The analysis is reduced from three-dimensional elasticity problem to a one-dimensional, or two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin. In this article is presented the mathematical model properly thin orthotropic plates, based on simplifying assumptions Love- Kirchhoff and small deformations. Proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis, in the case of plates with clamped edges. The purposed solutions were analysed considering a FEM solution for comparison and the experimental test results.

THE BENDING OF A THICK RECTANGULAR PLATE WITH THREE CLAMPED EDGES AND ONE FREE EDGE

The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary[1] in Reissner's theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered.

Bergan-Wang Solution of Clamped Moderately Thick Rectangular Plates

Bergan-Wang approach has one governing equation in one variable only, namely the transverse deflection of a moderately thick plate. This approach faces no numerical difficulties as the thickness becomes very small. The solution of a fully clamped rectangular plate is presented using two different series solutions. The results of a square plate are compared with the results of the classical plate theory, Reissner- Mindlin theory and the three dimensional theory of elasticity for different aspect ratios. Two types of clamped boundary conditions are investigated. The obtained results show that Bergan-Wang approach gives good agreement for both very thin and moderately thick plates.

Parameter Plane Synthesis and Performance Investigation of a Three-Phase Neutral-Point Clamped Bidirectional Rectifier

In this paper, parameter plane synthesis of a three-phase neutral-point clamped bidirectional rectifier has been performed. The converter involves one outer-loop PI voltage controller and two inner-loop PI current controllers for the closed-loop control. D-partition technique has been employed for the precise design of the voltage controller. The performance of the converter has been evaluated using MATLAB/Simulink software. An experimental prototype of converter has been developed and the experimental investigation of converter in closed-loop has been carried out. DSP DS 1104 of dSPACE has been used for real-time implementation of the designed controller. The performance of the converter has been found satisfactory using the designed controller parameters.

Improved Clamped Diode Based Z-Source Network for Three Phase Induction Motor

The 3Φinduction motor is a broadly used electric machine in industrial applications,which plays a vital role in industries because of having plenty of beneficial impacts like low cost and easiness but the problems like decrease in motor speed due to load,high consumption of current and high ripple occurrence of ripples have reduced its preferences.The ultimate objective of this study is to control change in motor speed due to load variations.An improved Trans Z Source Inverter(ΓZSI)with a clamping diode is employed to maintain constant input voltage,reduce ripples and voltage overshoot.To operate induction motor at rated speed,different controllers are used.The conventional Proportional-Inte-gral(PI)controller suffers from high settling time and maximum peak overshoot.To overcome these limitations,Fractional Order Proportional Integral Derivative(FOPID)controller optimized by Gray Wolf Optimization(GWO)technique is employed to provide better performance by eliminating maximum peak overshoot pro-blems.The proposed speed controller provides good dynamic response and controls the induction motor more effectively.The complete setup is implemented in MATLAB Simulation to verify the simulation results.The proposed approach provides optimal performance with high torque and speed along with less steady state error.

Eigenvalues for the Clamped Plate Problem of L_(ν)^(2) Operator on Complete Riemannian Manifolds

L_(ν) operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L_(ν)^(2)operator on a bounded domain of the complete Riemannian manifolds.A general formula of eigenvalues of L_(ν)^(2) operator is established.Applying this general formula,we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds.As several fascinating applications,we discuss this eigenvalue problem on the complete translating solitons,minimal submanifolds on the Euclidean space,submanifolds on the unit sphere and projective spaces.In particular,we get a universal inequality with respect to the L_(II) operator on the translating solitons.Usually,it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds.Therefore,this work can be viewed as a new contribution to universal estimate.

Low-complexity model predictive control of a four-level active neutral point clamped inverter without weighting factors

The four-level active neutral point clamped(ANPC)inverter has become increasingly widely used in the renewable energy indus-try since it offers one more voltage level without increasing the total number of active switches compared to the three-level ANPC inverter.The model predictive current control(MPCC)is a promising control method for multi-level inverters.However,the conven-tional MPCC suffers from high computational complexity and tedious weighting factor tuning in multi-level inverter applications.A low-complexity MPCC without weighting factors for a four-level ANPC inverter is proposed in this paper.The computational burden and voltage vector candidate set are reduced according to the relationship between voltage vector and neutral point voltage balance.The proposed MPCC shows excellent steady-state and dynamics performances while ensuring the neutral point voltage balancing.The efficacy of the proposed MPCC is verified by simulation and experimental results.

GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF CLAMPED THIN PLATES

The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.

NONLINEAR DYNAMICS OF A FGM PLATE WITH TWO CLAMPED OPPOSITE EDGES AND TWO FREE EDGES

This paper deals with the nonlinear forced vibration of FGM rectangular plate with a boundary of two edges clamped opposite and the other two free. The plate is subjected to transversal and in-plane excitations. The present research treats the material properties of the FGM plates as temperature-dependent and graded continuously throughout the thickness direction, following the volume fraction of the constituent materials according to the power law. The temperature is assumed to be constant in the plane and varied only in the thickness direction of the plate. In the framework of geometrical nonlinearity the plate is modeled and the equations of motion are obtained on Hamilton＇s principle. With the help of Galerkin discretization, the nonlinear ordinary differential equations describing transverse vibration of the plate are proposed. By the numerical method, the nonlinear dynamical responses of the FGM plate with two clamped opposite and two free edges are analyzed.

Adaptive Neuro Fuzzy Inference System Based Decoupled Control for Neutral Point Clamped Multi Level Inverter Fed Induction Motor Dri

The presence of an integrator in a reference model of a rotor flux-based model reference adaptive system(RF-MRAS)and non-linearity of the inverter in the output voltage degrade the speed response of the sensorless operation of the electric drive system in terms of DC drift,initial value issues,and inaccurate voltage acquisition.To improve the speed response,a compensating voltage component is supplemented by an amending integrator.The compensating voltage is a coalition of drift and offset voltages,and reduces DC drift and initial value issues.During low-speed operation,inaccurate voltage acquisition distorts the stator voltage critically,and it becomes considerable when the stator voltage of the machine is low.Implementing a three-level neutral point clamped inverter in speed-sensorless decoupled control of an induction motor improves the performance of the drive with superior quality of inverter output voltage.Further,the performance of the induction motor drive is improved by replacing the proportional-integral(PI)controller in the adaption mechanism of RF-MRAS with an adaptive neuro-fuzzy inference system(ANFIS)controller.A prototype model of the three-level neutral point clamped inverter(3L-NPC)-fed induction motor drive is fabricated in a laboratory,and its performance for a RF-MRAS,modified RFMRAS,and modified RFMRAS using ANFIS are compared using different benchmark tests.

Eigenvalue inequalities for the clamped plate problem of L_(ν)^(2) operator

The ■ operator is introduced by Xin(2015), which is an important extrinsic elliptic differential operator of divergence type and has profound geometric meaning. In this paper, we extend the ■ operator to a more general elliptic differential operator ■, and investigate the clamped plate problem of the bi-■ operator,which is denoted by ■ on the complete Riemannian manifolds. A general formula of eigenvalues for the ■ operator is established. Applying this formula, we estimate the eigenvalues on the Riemannian manifolds. As some further applications, we establish some eigenvalue inequalities for this operator on the translating solitons with respect to the mean curvature flows, submanifolds of the Euclidean spaces, unit spheres and projective spaces. In particular, for the case of translating solitons, all of the eigenvalue inequalities are universal.

EXISTENCE OF MINIMIZING SOLUTIONSAROUND“EXTENDED STATES”FOR A NONLINEARLY ELASTICCLAMPED PLANE MEMBRANE

The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo[10] has justified the twodimensional nonlinear "membrane" equations for a plate made of a Saint Venant-Kirchhoff material.This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of R3, is equivalent to finding the critical points of a functional whose nonlinear part depends on the first fundamental form of the unknown deformed surface.The author establishes here, by the inverse function theorem, the existence of an injective solution to the clamped membrane problem around particular forces corresponding physically to an "extension" of the membrane. Furthermore, it is proved that the solution found in this fashion is also the unique minimizer to the nonlinear membrane functional, which is not sequentially weakly lower semi-continuous.