THE REMAINDER－EFFECT ANALYSIS OF FINITE DIFFERENCE SCHEMES AND THE APPLICATIONS

ＴＨＥＲＥＭＡＩＮＤＥＲ－ＥＦＦＥＣＴＡＮＡＬＹＳＩＳＯＦＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＡＮＤＴＨＥＡＰＰＬＩＣＡＴＩＯＮＳＬｉｕＲｕ－ｘｕｎ（刘儒勋）ＺｈｏｕＺｈａｏ－ｈｕｉ（周朝晖）（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｕｎｉｖｅｒｓｉｔｙｏ...     

THE DIFFERENTIAL SOLUTION TO THE FLYING LOCUS EQUATION OF THE SHOT AND ITS APPLICATION

ＴＨＥＤＩＦＦＥＲＥＮＴＩＡＬＳＯＬＵＴＩＯＮＴＯＴＨＥＦＬＹＩＮＣＬＯＣＵＳＥＱＵＡＴＩＯＮＯＦＴＨＥＳＨＯＴＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＬｉｕＸｉａｏ－ｘｉａｎｇ（刘小湘）　　（ＸｉａｎｇｔａｎｉｎｓｔｉｔｕｉｅｏｆＭａｃｈｉｎｅｒｙａｎｄ...     

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＭＵＬＴＩ－ＳＣＡＬＥＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＴＯＴＨＥＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＰＬＡＮＥＣＯＵＥＴＴＥＦＬＯＷＺｈｏｕＺｈｅ－ｗｅｉ（周哲玮）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ;Ｓｈａｇ...     

THE THEORETICAL COST OF SEQUENTIAL AND PARALLEL ALGORITHMS FOR SOLVING LINEAR SYSTEMS OF EQUATIONS

ＴＨＥ　ＴＨＥＯＲＥＴＩＣＡＬ　ＣＯＳＴ　ＯＦ　ＳＥＱＵＥＮＴＩＡＬ　ＡＮＤ　ＰＡＲＡＬＬＥＬ　ＡＬＧＯＲＩＴＨＭＳ　ＦＯＲ　ＳＯＬＶＩＮＧ　ＬＩＮＥＡＲ　ＳＹＳＴＥＭＳ　ＯＦ　ＥＱＵＡＴＩＯＮＳＳａｌｍａｎＨ．Ａｂｂａｓ（ＲｅｃｅｉｖｅｄＭａｙ２４...     

THE GENERAL METHOD FOR SOLVING DYNAMIC PROBLEMS

ＴＨＥＧＥＮＥＲＡＬＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＤＹＮＡＭＩＣＰＲＯＢＬＥＭＳ￥(孙右烈)ＳｕｎＹｏｕｌｉｅ（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２０００７２，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｔｈｅａｕ...     

THE BOUNDED EXTERMINATION AND STABILITY OF MUTUAL INTERFERENCE SYSTEM OF FOUR－DIMENSIONAL SPECIES

ＴＨＥＢＯＵＮＤＥＤＥＸＴＥＲＭＩＮＡＴＩＯＮＡＮＤＳＴＡＢＩＬＩＴＹＯＦＭＵＴＵＡＬＩＮＴＥＲＦＥＲＥＮＣＥＳＹＳＴＥＭＯＦＦＯＵＲ－ＤＩＭＥＮＳＩＯＮＡＬＳＰＥＣＩＥＳＨｏｕＧａｎ－ｓｈｅｎｇ（侯赣生）（Ｄｅｐｌ．ｏｆＰｈｙｓｉｃｓ,Ｊｉａｎｇｘ...     

EAPPROXIMATE INERTIAL MANIFOLDS FOR THE SYSTEM OF THE J-J EQUATIONS

ＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＴＨＥＪ－ＪＥＱＵＡＴＩＯＮＳＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＴＨＥＪ－ＪＥＱＵＡＴＩＯＮＳ￥ＣａｉＲｉｚｅｎｇ（...     

AN ITERATIVE METHOD FOR THE DISCRETE PROBLEMS OF A CLASS OF ELLIPTICAL VARIATIONAL INEQUALITIES

ＡＮＩＴＥＲＡＴＩＶＥＭＥＴＨＯＤＦＯＲＴＨＥＤＩＳＣＲＥＴＥＰＲＯＢＬＥＭＳＯＦＡＣＬＡＳＳＯＦＥＬＬＩＰＴＩＣＡＬＶＡＲＩＡＴＩＯＮＡＬＩＮＥＱＵＡＬＩＴＩＥＳＺｈｅｎｇＴｉｅ－ｓｈｅｎｓ（郑铁生）ＬｉＬｉ（李立）ＸｕＱｉｎｇ－ｙｕ（许庆余）（Ｄ...     

THE ASYMPTOTIC EXPRESSION OF THE SOLUTION OF THE CAUCHY’S PROBLEM FOR A HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WHEN THE LIMIT EQUATION HAS SINGULARITY

ＴＨＥＡＳＹＭＰＴＯＴＩＣＥＸＰＲＥＳＳＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＯＦＴＨＥＣＡＵＣＨＹ’ＳＰＲＯＢＬＥＭＦＯＲＡＨＩＧＨＥＲＯＲＤＥＲＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＨＥＮＴＨＥＬＩＭＩＴＥＱＵＡＴＩＯＮ...     

THE SLIDING SURFACE ALGORITHMSINTHREE－DIMENSIONAL DYNAMIC FINITE ELEMENT CODE

ＴＨＥＳＬＩＤＩＮＧＳＵＲＦＡＣＥＡＬＧＯＲＩＴＨＭＳＩＮＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＤＹＮＡＭＩＣＦＩＮＩＴＥＥＬＥＭＥＮＴＣＯＤＥＳｏｎｇＳｈｕｎ－ｃｈｅｎｇ（宋顺成）（ＩｎｎｅｒＭｏｎｇｏｌｕａＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅｏｆＭｅｔ...     

Dynamic snapping of a suddenly loaded elastica with fixed end slopes

In this paper we study the dynamic snapping of an elastica with fixed end slopes. Both ends of the elastica are clamped, with one fixed in space and the other allowed to slide along a linear track. An edge thrust is applied suddenly on the sliding clamp, causing the elastica to undergo a snap-through jump. This setup can be used as a bistable device. The interest of this paper is to determine the critical value of the suddenly applied edge thrust causing snap-through, termed dynamic snapping load. With use of deformation potentials, the equations of motion of the elastica-slider assembly are rearranged, taking into account the effects of both the slider mass and damping. Finite difference method is adopted to discretize the resulted equations. In order to ensure the convergence of the numerical scheme, a linearization approach has to be adopted when the slider mass is non-zero. It is observed that for the setup studied in this paper, the dynamic snapping load is about 90% of its static counterpart. The viscous damping associated with the end slider in general has a favorable tendency of raising the dynamic snapping load. Somewhat unexpectedly, although the slider mass affects the transient response of the elastica-slider assembly significantly, it has no effect on the dynamic snapping load.     

ANALYSIS ON THE MAGNETO-ELASTIC-PLASTIC BUCKLING/SNAPPING OF CANTILEVER RECTANGULAR FERROMAGNETIC PLATES

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented.Based on the expression of magnetic force from the variational principle of ferromagnetic plates,the buckling and bending theory of thin plates,the Mises yield criterion and the increment theory for plastic deformation,we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method.Along with the phenom- ena of buckling/snapping and bending,or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed,the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads,the plastic regions expanding with the magnitude of applied magnetic field,as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.     

Buckling and post-buckling analysis for magneto-elastic–plastic ferromagnetic beam-plates with unmovable simple supports

This paper presents an analysis of buckling/snapping, bending and post-buckling/snapping behaviors of magneto-elastic–plastic interaction and coupling for soft ferromagnetic beam-plates with geometrically nonlinear deformation and unmovable simple supports at the ends of the plates. Based on the expression of magnetic force from the variational principle of ferromagnetic plates, the theory of thin plates with the nonlinear deformation of van Karman’s type, and the Mises yield criterion and the increment theory for plastic deformation, here, we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-coupling problems by the finite element method. Along with that the phenomena of buckling, bending, and post-buckling/snapping, or the characteristic curve of deflection versus magnitude of applied magnetic fields are numerically displayed, the critical values of buckling/snapping and yield magnetic fields, and the expansibility of plastic region after the plates undergo plastic deformation with increasing of the applied magnetic fields, as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.     

Schlieren imaging of loud sounds and weak shock waves in air near the limit of visibility

A large schlieren system with exceptional sensitivity and a high-speed digital camera are used to visualize loud sounds and a variety of common phenomena that produce weak shock waves in the atmosphere. Frame rates varied from 10,000 to 30,000 frames/s with microsecond frame exposures. Sound waves become visible to this instrumentation at frequencies above 10 kHz and sound pressure levels in the 110 dB (6.3 Pa) range and above. The density gradient produced by a weak shock wave is examined and found to depend upon the profile and thickness of the shock as well as the density difference across it. Schlieren visualizations of weak shock waves from common phenomena include loud trumpet notes, various impact phenomena that compress a bubble of air, bursting a toy balloon, popping a champagne cork, snapping a wooden stick, and snapping a wet towel. The balloon burst, snapping a ruler on a table, and snapping the towel and a leather belt all produced readily visible shock-wave phenomena. In contrast, clapping the hands, snapping the stick, and the champagne cork all produced wave trains that were near the weak limit of visibility. Overall, with sensitive optics and a modern high-speed camera, many nonlinear acoustic phenomena in the air can be observed and studied.     

Energy method solution for the postbuckling response of an axially loaded bilaterally constrained beam

Bistable and multistable structures have shown great usefulness in many applications such as MEMS actuation and energy harvesting. Bistability of structures can be achieved through buckling. Confining a buckled beam between two lateral constraints allows it to buckle into higher modes as the axial load increases. This paper presents a theoretical study of the postbuckling response of a bilaterally constrained elastica subjected to gradually increased axial load. Equilibrium states are determined using an energy method. Under small deformation assumptions, the total potential energy is minimized under the defined constraints. The presented model allows for an accurate representation of the flatting behavior and the increase in the length of contact areas with the lateral constraints before the sudden snapping between equilibrium states. Mode transitions are manifested by jumps in the response curves. Previously developed models based on geometry and symmetries overestimate the required forces for higher equilibrium modes and do not match experimental observations. Results are validated with experimental force–displacement measurements under both force- and displacement-control. The kinetic energy released during buckling mode transitions is determined by a dynamic analysis.     

On the unsymmetrical deformation and reverse snapping of a spinning non-flat disk

In this paper we study the steady state deflection and reverse snapping phenomenon of a spinning non-flat disk. Both the initial and the deformed shapes of the disk are allowed to have axisymmetrical and unsymmetrical components. For the analysis of a rotating axisymmetrical disk, we conclude that there is no need to include the unsymmetrical assumed modes in the solution because all the unsymmetrical steady state deformations are unstable. In addition, the stability of the axisymmetrical positions will not be affected by the inclusion of the unsymmetrical assumed modes. In the case when the initial shape of the disk contains a dominant axisymmetrical component and a smaller unsymmetrical component, attention is focused on the effect of this unsymmetrical component on the overall deformation and stability of the spinning disk. It is found that the unsymmetrical component with one nodal diameter tends to slightly defer the occurrence of the reverse snapping phenomenon. On the other hand, all other unsymmetrical components with more than one nodal diameter tend to reduce dramatically the reverse snapping speed. Experiment is conducted on a non-flat brass disk containing an axisymmetrical component and an unsymmetrical component with two nodal diameters. The experimental measurement confirms the theoretical prediction.     

Snapping of an elastica under various loading mechanisms

This paper studies the snap-through buckling of a hinged elastica subject to a midpoint force. The focus is placed on how different load models affect the deformation and snapping load. Three different load models are considered. In the first model, the point force is fixed onto a midpoint of the elastica. In the second model, the point force is fixed on a central line in space. In the third model, the external force is applied through a rigid bar, which is allowed to slide along the central line in space. When the loaded elastica deforms symmetrically, as in the case when the magnitude of the point force is small, there is no difference between these three load models. However, when the elastica deforms unsymmetrically, the three load models produce different results. Vibration method is used to determine the stability of the equilibrium configurations. It is found that the elastica may snap via either a sub-critical pitchfork bifurcation or a limit-point bifurcation. If the elastica snaps via a sub-critical pitchfork bifurcation, the pre-snapping deformation is symmetric. If the elastica snaps via a limit-point bifurcation, on the other hand, the pre-snapping deformation is unsymmetric. For a specified initial shape of the elastica, different load models predict different snapping loads and pre-snapping deformations. The theoretical predictions are confirmed by experimental observations.     

弧长控制类方法使用中若干问题的探讨与改进

在结构非线性跟踪分析中，弧长控制类方法和能量控制类方法是两类最主要的方法。近年来，各类弧长方法由于概念简单明了、计算方便可靠而广为采用。本文首先对几种主要弧长方法的使用进行回顾和比较，并就跟踪失败的可能情况作简单探讨，进而针对部分可能失败的情况提出改进措施。再以一个同时存在跳跃及跳回现象且具有分枝路径的问题为例，将这几种弧长方法用于其变形全过程的跟踪分析，来验证所提出的改进措施，比较这几种弧长方法的跟踪能力。最后给出使用这些弧长方法的几点结论。     

Point attractors and dynamic buckling of autonomous systems under step loading

In this study the dynamic response of autonomous mainly dissipative multi D.O.F. systems under step loading is re-examined. Based on the geometrical point of view of the theory of non-linear dynamical systems and the rapidly developing theory of attractors, the investigation focuses on limit point like systems, with snapping as their salient feature. It is found that dynamic buckling (through a saddle or its neighborhood) , although leading to a large amplitude motion, may be associated with a point attractor response on the pre-buckling fixed point, depending on the amount of damping considered in close conjunction with the motion channel geometry and the total potential characteristics of all (stable and complementary) equilibria. For such systems, only a straightforward fully non-linear dynamic analysis can provide valid information on the global dynamic stability, since the shape of the total potential hypersurface may become very complicated, rendering energy aspects practically not applicable. A 2-D.O.F. model, simulating an asymmetric suspended roof is comprehensively analyzed to capture the above findings, and a parametric investigation is carried out, revealing a variety of new dynamic response types and leading to a more accurate insight of the stability of motion in the large.