Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Nonlinear Analysis of Organic Polymer Solar Cells Using Differential Quadrature Technique with Distinct and Unique Shape Function

Four numerical schemes are introduced for the analysis of photocurrent transients in organic photovoltaic devices.Themathematicalmodel for organic polymer solar cells contains a nonlinear diffusion-reaction partial differential equation system with electrostatic convection attached to a kinetic ordinary differential equation.To solve the problem,Polynomial-based differential quadrature,Sinc,and Discrete singular convolution are combined with block marching techniques.These schemes are employed to reduce the problem to a nonlinear algebraic system.The iterative quadrature technique is used to solve the reduced problem.The obtained results agreed with the previous exact one and the finite element method.Further,the effects of different times,different mobilities,different densities,different geminate pair distances,different geminate recombination rate constants,different generation efficiencies,and supporting conditions on photocurrent have been analyzed.The novelty of this paper is that these schemes for photocurrent transients in organic polymer solar cells have never been presented before,so the results may be useful for improving the performance of solar cells.

Shaped Offset Quadrature Phase Shift Keying Based Waveform for Fifth Generation Communication

Fifth generation(5G)wireless networks must meet the needs of emerging technologies like the Internet of Things(IoT),Vehicle-to-everything(V2X),Video on Demand(VoD)services,Device to Device communication(D2D)and many other bandwidth-hungry multimedia applications that connect a huge number of devices.5G wireless networks demand better bandwidth efficiency,high data rates,low latency,and reduced spectral leakage.To meet these requirements,a suitable 5G waveform must be designed.In this work,a waveform namely Shaped Offset Quadrature Phase Shift Keying based Orthogonal Frequency Division Multiplexing(SOQPSK-OFDM)is proposed for 5G to provide bandwidth efficiency,reduced spectral leakage,and Bit Error Rate(BER).The proposed work is evaluated using a real-time Software Defined Radio(SDR)testbed-Wireless open Access Research Platform(WARP).Experimental and simulation results show that the proposed 5G waveform exhibits better BER performance and reduced Out of Band(OOB)radia-tion when compared with other waveforms like Offset Quadrature Phase Shift Key-ing(OQPSK)and Quadrature Phase Shift Keying(QPSK)based OFDM and a 5G waveform candidate Generalized Frequency Division Multiplexing(GFDM).BER analysis shows that the proposed SOQPSK-OFDM waveform attains a Signal to Noise Ratio(SNR)gain of 7.2 dB at a BER of 10�3,when compared with GFDM in a real-time indoor environment.An SNR gain of 8 and 6 dB is achieved by the proposed work for a BER of 10�4 when compared with QPSK-OFDM and OQPSK-OFDM signals,respectively.A significant reduction in OOB of nearly 15 dB is achieved by the proposed work SOQPSK-OFDM when compared to 16 Quadrature Amplitude Modulation(QAM)mapped OFDM.

带渐消因子的Quadrature卡尔曼滤波

为了解决无源传感器机动目标跟踪系统非线性较强、传统的跟踪滤波方法不稳定容易发散的缺陷,提出了一种带渐消因子的QKF(FQKF)算法。该算法通过引入时变渐消因子来实时调整状态预测误差协方差阵、量测预测误差协方差阵及状态预测误差和量测预测误差之间的互协方差阵,利用公式推导得出渐消因子实际上是对状态传播积分点和量测传播积分点进行渐消,进而达到实时调整滤波器增益矩阵的目的。并通过算法的机理分析和仿真实验表明FQKF算法具有强跟踪滤波器(STF)的优良性能,能够克服QKF算法的缺陷,对于无源传感器机动目标跟踪中系统的突变状态具有较强的跟踪能力,较QKF算法稳定性有所提高,并且计算量适中。

变截面梁大挠度振动的 Quadrature 解

使用Ｑｕａｄｒａｔｕｒｅ法求解了全简支和全固支两种边界条件下的各两种变截面梁的大挠度自由振动频率，当退化为等截面梁时其结果与现有文献的精确解高度一致，而以Ｑｕａｄｒａｔｕｒｅ法求解等截面梁同一问题的文献则是求解变截面梁的特殊情形．

NONLINEAR DYNAMICS OF AXIALLY ACCELERATING VISCOELASTIC BEAMS BASED ON DIFFERENTIAL QUADRATURE

This paper investigates nonlinear dynamical behaviors in transverse motion of an axially accelerating viscoelastic beam via the differential quadrature method. The governing equation, a nonlinear partial-differential equation, is derived from the viscoelastic constitution relation using the material derivative. The differential quadrature scheme is developed to solve numerically the governing equation. Based on the numerical solutions, the nonlinear dynamical behaviors are identified by use of the Poincare map and the phase portrait. The bifurcation diagrams are presented in the case that the mean axial speed and the amplitude of the speed fluctuation are respectively varied while other parameters are fixed. The Lyapunov exponent and the initial value sensitivity of the different points of the beam, calculated from the time series based on the numerical solutions, are used to indicate periodic motions or chaotic motions occurring in the transverse motion of the axially accelerating viscoelastic beam.

DIFFERENTIAL QUADRATURE METHOD TO STABILITY ANALYSIS OF PIPES CONVEYING FLUID WITH SPRING SUPPORT

It is a new attempt to extend the differential quadrature method(DQM) to stability analysis of the straight and curved centerlinepipes conveying fluid. Emphasis is placed on the study of theinfluences of several parameters on the critical flow velocity.Compared to other methods, this method can more easily deal with thepipe with spring support at its boundaries and asks for much lesscomputing effort while giving ac- ceptable precision in the numericalresults.

Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method

The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the governing equations for the beam are presented. Second, an extended differential quadrature method(DQM)in the spatial domain and a differential method in the temporal domain are combined to transform the integro-partial-differential governing equations into the ordinary differential equations. Third, the accuracy of the present discrete method is verified by elastic/viscoelastic examples, and the effects of thermal load parameters, material and geometrical parameters on the quasi-static and dynamic responses of the beam are discussed. Numerical results show that the thermal function parameter has a great effect on quasi-static and dynamic responses of the beam. Compared with the thermal relaxation time, the initial vibrational responses of the beam are more sensitive to the mechanical relaxation time of the thermoviscoelastic material.

Buckling analysis of functionally graded plates partially resting on elastic foundation using the differential quadrature element method

We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.

ERROR ANALYSIS IN DIFFERENTIAL QUADRATURE METHOD

Error estimation for the differential quadrature (DQ)with various sets of grid spacing is presented. A general formula is given to compute the weighting coefficients directly. It is found that the maximum error of the Do method with roots of Chebyshev polynomials including two end POints (-1 and + 1 ) is the smallest among the several sets of grid spacing investigated herein.

Quadrature Kalman particle fitler

In order to resolve the state estimation problem of nonlinear/non-Gaussian systems, a new kind of quadrature Kalman particle filter （QKPF） is proposed. In this new algorithm, quadrature Kalman filter （QKF） is used for generating the impor- tance density function. It linearizes the nonlinear functions using statistical linear regression method through a set of Gaussian- Hermite quadrature points. It need not compute the Jacobian matrix and is easy to be implemented. Moreover, the importantce density function integrates the latest measurements into system state transition density, so the approximation to the system poste- rior density is improved. The theoretical analysis and experimen- tal results show that, compared with the unscented partcle filter （UPF）, the estimation accuracy of the new particle filter is improved almost by 18%, and its calculation cost is decreased a little. So, QKPF is an effective nonlinear filtering algorithm.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

Differential Quadrature Method for Bending Problem of Plates with Transverse Shear Effects

A differential quadrature (DQ) method for orthotropic plates was proposed based on Reddy' s theory of plates with the effects of the higher-order transverse shear deformations. Wang-Bert's DQ approach was also further extended to handle the boundary conditions of plates. The computational convergence was studied, and the numerical results were obtained for different grid spacings and compared with the existing results. The results show that the DQ method is fairly reliable and effective.

ON QUADRATURE FORMULAE FOR SINGULAR INTEGRALS OF ARBITRARY ORDER

Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.

Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming(RAB)algorithms require the covariance matrix reconstruction(CMR)by high-complexity integral computation.A Gauss-Legendre quadrature(GLQ)method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity.The interference angular sector in RAB is regarded as the GLQ integral range,and the zeros of the threeorder Legendre orthogonal polynomial is selected as the GLQ nodes.Consequently,the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral.The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques,and it is able to provide the similar performance close to the optimal.These advantages are verified by numerical simulations.

Generalized cubature quadrature Kalman filters:derivations and extensions

A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the QR decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.

Research and test of the adaptive quadrature demodulation technology for silicon micro-machined gyroscope

A program of adaptive quadrature demodulation is proposed to supply the gaps in the traditional analog detection technology of a silicon micro-machined gyroscope (SMG). This program is suitable for digital phase locked loop (DPLL) drive technology that proposed in other papers. In addition the program adopts an adaptive filtering algorithm, which selects the in-phase and quadrature components that are outputs of the DPLL of the SMG's drive mode as reference signals to update the amplitude of the in-phase and quadrature components of the input signal by iteratively. An objective of the program is to minimize the mean square error of the accurate amplitudes and the estimated amplitudes of SMG's detection mode. The simulation and test results prove the feasibility of the program that lays the foundation for the further improvement of the SMG's system performance and the implementation of the SMG system's self-calibration and self-demarcation in future.

Machine Learning Enhanced Boundary Element Method:Prediction of Gaussian Quadrature Points

This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods.A model based on the neural network multi-classification algorithmis constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy.The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected.The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model,and the accuracy of the model is about 90%.Finally,by incorporating the predicted Gaussian quadrature points into the boundary element analysis,we find that the numerical solution and the analytical solution are in good agreement,which verifies the robustness of the proposed method.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.