PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.

Perturbation Analysis for t-Product-Based Tensor Inverse,Moore-Penrose Inverse and Tensor System

This paper establishes some perturbation analysis for the tensor inverse,the tensor Moore-Penrose inverse,and the tensor system based on the t-product.In the settings of structured perturbations,we generalize the Sherman-Morrison-Woodbury(SMW)formula to the t-product tensor scenarios.The SMW formula can be used to perform the sensitivity analy-sis for a multilinear system of equations.

On Iterative Algorithm and Perturbation Analysis for the Nonlinear Matrix Equation

In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix equation.Comparative analysis for the derived condition numbers and the proposed algorithm are presented.The proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line searches.Componentwise condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.

PERTURBATION ANALYSIS FOR THE POSTBUCKLING OF RECTANGULAR ORTHOTROPIC PLATES

In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under in-plane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

Parachute dynamics and perturbation analysis of precision airdrop system

To analyze the parachute dynamics and stability characteristics of precision airdrop system, the fluid-structure interaction （FSI） dynamics coupling with the flight trajectory of a para- chute payload system is comprehensively predicted by numerical methods. The inflation behavior of a disk-gap-band parachute is specifically investigated using the arbitrary Lagrangian Euler （ALE） penalty coupling method. With the available aerodynamic data obtained from the FSI sim- ulation, a nine-degree-of-freedom （9DOF） dynamic model of a parachute-payload system is built and solved to simulate the descent trajectory of the multi-body dynamic system. Finally, a linear five-degree-of-freedom （5DOF） dynamic model is developed, the perturbation characteristics and the motion laws of the parachute and payload under a wind gust are analyzed by the linearization method and verified by a comparison with flight test data. The results of airdrop test demonstrate that our method can be further applied to the guidance and control of precision airdrop systems.

Image registration based on matrix perturbation analysis using spectral graph

We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.

Modelling、Simulation and Perturbation Analysis for Manufacturing Scheduling and Planning( MSP) System

Scheduling of finite capacity discrete manufacturing processes is attracting increasing attention. The major difficulty in this area is concerned with the combinatorial explosion which occurs once one begins to consider the scheduling of workpieces through more than a few machines. What kind of laws must be satisfied in modelling、simulation and perturbation analysis? In this paper, we show how to deal with the structure of complex assembly production systems hierarchically to achieve simplicity for these purposes. We will also describe two ′conservation laws of workpieces′ applicable to manufacturing scheduling problems and then develop a complete state space representation. Some experiments and results will also be included. This approach can be used for both stochastic and deterministic dynamical systems in this area and can also be extended to other areas which require decision support.

Perturbation analysis of stochastic hybrid systems and applications to resource contention games

We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner.We also propose a general scheme for systematically deriving an abstraction of a discrete event system(DES)in the form of an SHS.Then,as an application of the general IPA framework,we study a class of stochastic non-cooperative games termed“resource contention games”modeled through stochastic flow models(SFMs),where two or more players(users)compete for the use of a sharable resource.Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.

A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES

In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.

High-frequency structure design and RF stability analysis of a 4-vane radio frequency quadrupole with pi-mode stabilizer loops

Compact accelerator-based neutron source facilities are garnering attention and play an important and expanding role in material and engineering sciences,as well as in neutron science education and training.Neutrons are produced by bombarding a low-energy proton beam onto a beryllium or lithium target.In such an acceleratorbased neutron source,a radio frequency quadrupole(RFQ)is usually utilized to accelerate a high-intensity proton beam to a few MeV.This study mainly covers the highfrequency structure design optimizations of a 4-vane RFQ with pi-mode stabilizer loops(PISLs)and its RF stability analysis.A 176 MHz RFQ accelerator is designed to operate at a 10%duty factor and could accelerate an80 mA proton beam from 65 keV to 2.5 MeV within a length of 5.3 m.The adoption of PISLs ensures high RF stability,eases the operation of the accelerator,and implies less stringent alignment and machining tolerances.

On the Downshift of Wave Frequency for Bragg Resonance

For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples,strong wave reflection occurs under the Bragg resonance condition.The critical wave frequency,at which the peak reflection coefficient is obtained,has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction.It has long been speculated that the downshift may be attributed to higher-order rippled bottom and free-surface boundary effects,but the intrinsic mechanism remains unclear.By a regular perturbation analysis,we derive the theoretical solution of frequency downshift due to third-order nonlinear effects of both bottom and free-surface boundaries.It is found that the bottom nonlinearity plays the dominant role in frequency downshift while the free-surface nonlinearity actually causes frequency upshift.The frequency downshift/upshift has a quadratic dependence in the bottom/free-surface steepness.Polychromatic bottom leads to a larger frequency downshift relative to the monochromatic bottom.In addition,direct numerical simulations based on the high-order spectral method are conducted to validate the present theory.The theoretical solution of frequency downshift compares well with the numerical simulations and available experimental data.

Boundary-layer eigen solutions for multi-field coupled equations in the contact interface

The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact in- terface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This pa- per describes the field affected by the gravity constraints. Applying the multi-scale anal- ysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analy- sis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic per- turbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.

Adjoint Matching Condition for Parameterized Discontinuities—A Derivation Using Lagrangian-form Costfunction

The generalized adjoint property and adjoint matching condition for systems that contain discontinuous on/off switches are derived by a perturbation analysis of the Lagranging-form costfunction.

Oblique Wave Scattering by An Undulating Porous Bottom in A Two-Layer Ice-Covered Fluid

The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated and permeable. By using regular perturbation analysis and Fourier transform technique, the problem is solved and the first order reflection and transmission coefficients are determined. It is found that these coefficients depend on the shape as well as the permeability of the undulating bottom. Therefore, from the practical viewpoint, an undulating bottom topography is considered to determine all the aforesaid coefficients. The role of various system parameters, such as porosity, angle of incidence and ice parameters, are discussed to analyze the transformation of incident water wave energy from one layer to another layer. The outcomes are demonstrated in graphical forms.

Electrokinetic flow and energy conversion in a curved microtube

Curved channels are ubiquitous in microfluidic systems.The pressure-driven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number.The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer(EDL)potential.The EDL potential at the outer side of the bend is larger than that at the inner side of the bend.The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow.Since the spanwise pressure gradient is dominant over the inertial force,the resulting axial velocity profile is skewed into the inner region of the curved channel.Furthermore,the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section.The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows.Remarkably,the curved geometry could be beneficial to improving the electrokinetic energy conversion(EKEC)efficiency.

Laminar and Turbulent Characteristics of the Acoustic/Fluid Dynamics Interactions in a Slender Simulated Solid Rocket Motor Chamber

In this paper,analytical,computational,and experimental studies are integrated to examine unsteady acoustic/vorticity transport phenomena in a solid rocket motor chamber with end-wall disturbance and side-wall injection.Acoustic-fluid dynamic interactions across the chamber may generate intense unsteady vorticity with associated shear stresses.These stresses may cause scouring and,in turn,enhance the heat rate and erosional burning of solid propellant in a real rocket chamber.In this modelling,the unsteady propellant gasification is mimicked by steady-state flow disturbed by end-wall oscillations.The analytical approach is formulated using an asymptotic technique to reduce the full governing equations.The equations that arise from the analysis possess wave properties are solved in an initial-boundary value sense.The numerical study is performed by solving the parabolized Navier–Stokes equations for the DNS simulation and unsteady Reynolds-averaged Navier–Stokes equations along with the energy equation using the control volume approach based on a staggered grid system with the turbulence modelling.The v2-f turbulence model has been implemented.The results show that an unexpectedly large amplitude of unsteady vorticity is generated at the injection side-wall of the chamber and is then penetrated downstream by the bulk motion of the internal flow.These stresses may cause a scouring effect and large transient heat transfer on the combustion surface.A comparison between the analytical,computational,and experimental results is performed.

Performance sensitivities for parameterized Markov systems

It is known that the performance potentials (or equivalentiy, perturbation realization factors) can be used as building blocks for performance sensitivities of Markov systems. In parameterized systems, the changes in parameters may only affect some states, and the explicit transition probability matrix may not be known. In this paper, we use an example to show that we can use potentials to construct performance sensitivities in a more flexible way; only the potentials at the affected states need to be estimated, and the transition probability matrix need not be known. Policy iteration algorithms, which are simpler than the standard one, can be established.

THE IMPACT TORSIONAL BUCKLING OF ELASTIC CYLINDRICAL SHELLS WITH ARBITRARY FORM IMPERFECTION

A perturbation analysis for the impact torsional buckling of imperfective elastic cylindrical shells subjected to a step torque is given The imperfection is supposed to be small and has arbitrary form. It is shown that only the imperfection which has the shape of static torsional buckling mode could influence the critical step torque. Finally a formula is presented for the critical step torque.