MODIFIED CLOSED-FORM NUMERICAL ALGORITHM FOR PERIODIC VIBRATION RESPONSE OF MECHANICAL TRANSMISSIONS

A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coefficients. The principle of the algorithm is todiscretize the motion period into many short time intervals, so the coefficient matrices of theequation set are regarded as constant in a time interval. Defects are found in the originalalgorithm in treating the modal coordinates at the two end-nodes and important modifications to thedefects is made for the algorithm. The modified algorithm is finally used to solve the dynamicproblem of a three-ring planetary gear transmission.

L^p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_(0,0) ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.

A Formal Method for Developing Algebraic and Numerical Algorithms

The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.

An improved algorithm for numerical calculation of seismic response spectra

The information of seismic response spectra is key to many problems concerned with aseismic structure and is also helpful for earthquake disaster relief if it is generated in time when earthquake happens. While current numerical calculation methods suffer from poor precision, especially in frequency band near Nyquist frequency, we present a set of improved parameters for precision improvement. It is shown that precision of displacement and velocity response spectra are both further improved compared to current numerical algorithms. A uniform fitting formula is given for computing these parameters for damping ratio range of 0.01-0.9, quite convenient for practical application.

Research on Steward Dynamic Platform Simulation Numerical Algorithm

In order to achieve attitude control of the six degrees of freedom steward dynamic platform, as well as the real time simulation cockpit attitude, Washout Filtering method was adopted in this paper as the simulation algorithm to derive Washout Fiher high-pass, low-pass filter transfer functions into a differential equation algorithm and longitudinal acceleration tilt strategy, pitching strategies etc. Experimental examples are used to verify correctness of the algorithm.

Application of PCA Numalgorithm in Remote Sensing Image Processing

A numerical algorithm of principal component analysis (PCA) is proposed and its application in remote sensing image processing is introduced: (1) Multispectral image compression;(2) Multi-spectral image noise cancellation;(3) Information fusion of multi-spectral images and spot panchromatic images. The software experiments verify and evaluate the effectiveness and accuracy of the proposed algorithm.

Adaptive backtracking search optimization algorithm with pattern search for numerical optimization

The backtracking search optimization algorithm（BSA） is one of the most recently proposed population-based evolutionary algorithms for global optimization. Due to its memory ability and simple structure, BSA has powerful capability to find global optimal solutions. However, the algorithm is still insufficient in balancing the exploration and the exploitation. Therefore, an improved adaptive backtracking search optimization algorithm combined with modified Hooke-Jeeves pattern search is proposed for numerical global optimization. It has two main parts： the BSA is used for the exploration phase and the modified pattern search method completes the exploitation phase. In particular, a simple but effective strategy of adapting one of BSA＇s important control parameters is introduced. The proposed algorithm is compared with standard BSA, three state-of-the-art evolutionary algorithms and three superior algorithms in IEEE Congress on Evolutionary Computation 2014（IEEE CEC2014） over six widely-used benchmarks and 22 real-parameter single objective numerical optimization benchmarks in IEEE CEC2014. The results of experiment and statistical analysis demonstrate the effectiveness and efficiency of the proposed algorithm.

MATRIX ALGEBRA ALGORITHM OF STRUCTURE RANDOM RESPONSE NUMERICAL CHARACTERISTICS

A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.

The Numerical Scheme Development of a Simplified Frozen Soil Model

In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.

A time integral formulation and algorithm for structural dynamics with nonlinear stiffness

A newly-developed numerical algorithm, which is called the new Generalized-α （G-α） method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zero- stable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.

Large deformation and wrinkling analyses of bimodular structures and membranes based on a peridynamic computational framework

In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant and tangential stiffness matrices of the implicit peridynamic formulations for the nonlinear problems are derived,respectively.The former is con structed from the linearization of the bond strain on the basis of the geometric approximation while the latter is established according to the linearization of the pairwise force by using first-order Taylor’s expansion.Then,a bimodular material model in peridynamics is developed,in which the tensile or compressive behavior of the material at each point is conveniently described by the tensile or compressive states of the bonds in its neighborhood.Moreover,the bimodular material model is extended to deal with the wrinkling and fracture problems of membranes by setting the compressive micro-modulus to be zero.In addition,the incremental-iterative algorithm is adopted to obtain the convergent solutions of the nonlinear problems.Finally,several representative numerical examples are presented and the results demonstrate the accuracy and efficiency of the proposed method for the large deformation,wrinkling and fracture analyses of bimodular structures and membranes.

Near time optimal control with perturbation estimation for flexible spacecraft slewing maneuvers

A feedforward approach for generating near time optimal controller for flexible spacecraft rest-to-rest maneuvers is presented with the objective insensitivity to modeling errors, parameter uncertainty and minimizing the residual energy of the flexible modes. The perturbation estimation of flexible appendages to the rigid-hub is accomplished simply via compare the output of real plant with the reference model, and the approach is based on combine this estimation with the bang-bang control for the rigid-hub modes through analysis the basic constraint and the additional constraint, i.e. zero coupling torque and zero coupling torque derivative for general two orders system and three orders system with considerate attitude acceleration mode near time optimal controls. These time optimal controls with control constraints and state constraints leads to forming a boundary-value problem, and resolved the problem using an iterative numerical algorithm. The near time optimal control with perturbation estimation shows a good robust to parameter uncertainty and can suppress the vibration and minimizing the residual energy. The capability of this approach is demonstrated through a numerical example in detail.

Novel Analytical Thermal Performance Rate Analysis in ZnO-SAE50 Nanolubricant: Nonlinear Mathematical Model

The investigation of local thermal transport rate in the nanolubricants is significant.These lubricants are broadly used in environmental pollution,mechanical engineering and in the paint industry due to high thermal performance rate.Therefore,thermal transport in ZnO-SAE50 nanolubricant under the impacts of heat generation/absorption is conducted.The colloidal suspension is flowing between parallel stretching disks in which the lower disk is positioned at z=0 and upper disk apart from distance d.The problem is transformed in dimensionless version via described similarity transforms.In the next stage,an analytical technique(VPM)is implemented for the solution purpose.The graphical results against multiple flow parameters were furnished over the region of interest and explained comprehensively.It is imperative to mention that the results are plotted for ZnO-SAE50 and conventional liquid as well.Further,rapid motion of the fluid is perceived against high Reynolds andγparameters.The wall shear stresses at the upper end rises for multiple Reynolds andγwhile;decrement is detected at the lower end.The significant contribution of an internal heat source is noted for thermal performance rate at the upper end.Foremost,the local heat transport rate declines at the lower disk.By altering Reynolds number,prompt heat transfer rate is gained at the upper disk and increasing behavior of the local heat transport rate is slow at the lower disk.From the study,it is concluded that the nanolubricants have high thermal characteristics.Therefore,such fluids are reliable to use in above stated areas.

A NOVEL METHOD FOR NONLINEAR IMPULSIVE DIFFERENTIAL EQUATIONS IN BROKEN REPRODUCING KERNEL SPACE

In this article,a new algorithm is presented to solve the nonlinear impulsive differential equations.In the first time,this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations.Then,the uniform convergence of the numerical solution is proved,and the time consuming Schmidt orthogonalization process is avoided.The algorithm is employed successfully on some numerical examples.

Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale （SSOTS） analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro- characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.

Stable and accurate schemes for smoothed dissipative particle dynamics

Smoothed dissipative particle dynamics （SDPD） is a mesoscopic particle method that allows to select the level of resolution at which a fluid is simulated. The numerical integration of its equations of motion still suffers from the lack of numerical schemes satisfying all the desired properties such as energy conservation and stability. Similarities between SDPD and dissipative particle dynamics with energy （DPDE） con- servation, which is another coarse-grained model, enable adaptation of recent numerical schemes developed for DPDE to the SDPD setting. In this article, a Metropolis step in the integration of the fluctuation/dissipation part of SDPD is introduced to improve its stability.

;ast forward kinematics algorithm for real-time and ligh-precision control of the 3-RPS parallel mechanism

A new forward kinematics algorithm for the mechanism of 3-RPS （R： Revolute; P： Prismatic; S： Spherical） parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10 6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.

Serrated flow in NaI:Tl scintillator crystals

The serrated-flow behavior is an important phenomenon that unveils material-deformation mechanisms,as reported for various kinds of materials.NaI doped with Tl(NaI:Tl)is unique among scintillation ma-terials in that the structure contains glide planes that are linked to serration behavior.In the present work,single crystals of NaI:Tl were subjected to room-temperature compression experiments at different strain rates.The serrated flow was observed,and complexity and multifractal analyses were performed to analyze the serration behavior.The findings revealed that the strain rate had a pronounced effect on the complexity and multifractality of the serrated flow,similar to what has been found in other alloy systems.The results also indicate that there may be a strong link between the complexity of the serrated flow behavior and the heterogeneity of the underlying dynamics.It is expected that the present work could be a step toward a better understanding of the deformation behavior and forgeability of NaI:Tl single crystals.

A Novel Fractional Plastic Damage Model for Quasi-brittle Materials

In this work,a novel constitutive model is developed within the framework of fractional plasticity to delineate the coupling between inelastic deformation and damage of quasi-brittle materials.Faced with the common challenge of determining plastic flow direction,we resort herein to the Riemann–Liouville definition of fractional derivatives,instead of introducing an additional plastic potential.The pre-peak hardening behavior is described using an exponential function,while the post-peak softening response is viewed as the consequence of material damage.For describing damage evolution,a damage criterion is constructed in terms of plastic volume dilation related to micro-crack growth.This is conducive to supply a new insight for describing the complex influence of the non-orthogonality of plastic flow on damage evolution.For numerical applications,a semi-implicit return mapping algorithm is proposed.The predictive performance of the model is evaluated by comparing numerical simulations with experimental data under various loading paths.