Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufcient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive diferential equations with "supremum" and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the efectiveness of the obtained results.     

Erratumon“Shear beammodel for interface failure underantiplane shear (Ⅰ )——fundamental behaviour”

Ｄｕｅｔｏｔｈｅｒｅｓｐｏｎｓｉｂｉｌｉｔｙｏｆｔｈｅｆｉｒｓｔａｕｔｈｏｒ,Ｆｉｇ .1ｉｎｔｈｅｐａｐｅｒｅｎｔｉｔｌｅｄ“Ｓｈｅａｒｂｅａｍｍｏｄｅｌｆｏｒｉｎｔｅｒｆａｃｅｆａｉｌｕｒｅｕｎｄｅｒａｎｔｉｐｌａｎｅｓｈｅａｒ (Ⅰ )———ｆｕｎｄａｍｅｎｔａｌｂｅｈａｖｉｏｕｒ” ,ｐｕｂｌｉｓｈｅｄｏｎＩｓｓｕｅ2 0 0 0 ,2 1 ( 1 1 ) :1 2 2 1 -1 2 2 8,ｉｓｉｎｃｏｒｒｅｃｔａｎｄｃｏｒｒｅｃｔｉｏｎｓｈｏｕｌｄｂｅｍａｄｅａｓｆｏｌｌｏｗｓ :Ｉｎｃｏｒｒｅｃｔｏｎｅ :Ｆｉｇ.1　Ｄｏｕｂｌｅ＿ｓ…     

Comments on “Particle swarm optimization with fractional-order velocity”

In this paper, some comments on the paper Solteiro Pires et al. (Nonlinear Dyn. 67:893–901, 2010) are presented. We demonstrate that the authors of the above paper have deduced the incorrect formula about the velocity updating strategy of the fractional-order particle swarm optimization algorithm. This paper deduces the modified updating formula, and verified experiments are also conducted.     

Comment on “Particle swarm optimization with fractional-order velocity”

This comment points out to a mistake in the main equation of Solteiro Pires et al. (Nonlinear Dyn. 61:295–301, 2010) concerning the fractional velocity in particle swarm optimization. The correct fractional velocity equation is provided and simulation experiments are redone in the comment.     

Numerical investigation of interactions between shock waves and thermal inhomogeneities after “multipoint” energy emission

This paper discusses a possible mechanism for the various anomalous phenomena induced by spatially inhomogeneous energy emission. Two gas-dynamical models of multipoint energy emission in an ideal compressible gas have been numerically investigated using a second-order difference scheme. It is shown that qualitatively different scenarios are possible depending on the initial parameters.     

Discussion on “Rectangular Plates with Free Edges on Elastic Foundations”

This paper points out the former work does not fulfill the boundary conditions that the concentrated force at the four corner points should not exist. Therefore, Ritz method adopted by the author concerned in the illustrative example will not be convergent in the best way. Moreover, Garlerkin method which is illustrated in this paper may carry out incorrect results if we apply its formulae. We have proved that the boundary conditions which govern the concentrated force equal to zero at the four corner points are indispensable if the problem is properly set.     

Discussion on“Rectangular Plates with Free Edges on Elastic Foundations”

This paper points out the former work does not fulfill the boundaryconditions that the concentrated force at the four corner points should notexist.Therefore,Ritz method adopted by the author concerned in the illus-trative example will not be convergent in the best way.Moreover,Garlerkinmethod which is illustrated in this paper may carry out incorrect results ifwe apply its formulae.We have proved that the boundary conditions whichgovern the concentrated force equal to zero at the four corner points areindispensable if the problem is properly set.     

Reprint of “Multi-scale cohesive laws in hierarchical materials” [In. J. Solids Struct. 44 (2007) 8177–8193]

Motivated by the observations that natural materials such as bone, shell, tendon and the attachment system of gecko exhibit multi-scale hierarchical structures, this paper aims to develop a better understanding of the effects of structural hierarchy on flaw insensibility of materials from the viewpoint of multi-scale cohesive laws. We consider two idealized, self-similar models of hierarchical materials, one mimicking gecko’s attachment system and the other mimicking the mineral–protein composite structure of bone, to demonstrate that structural hierarchy leads to multi-scale cohesive laws which can be designed from bottom up to enable flaw tolerance from nanoscale to macroscopic length scales.     

Comparison of integrated characteristics and shapes of profiled contours of laval nozzles with “smooth” and “abrupt” contractions

The influence of the selection of the generator of subsonic sections of plane and axisymmetric Laval nozzles on the integrated characteristics and on the shapes of their profiled supersonic parts is investigated in the approximation of an ideal (inviscid and nonheat-conducting) gas. Nozzles with a smooth entrance and with an abrupt contraction are compared for the same flow rates and size restrictions on the whole nozzle, not only to its supersonic part. In such a formulation, in accordance with [1], nozzles with abrupt contractions in the flow of ideal gas in them should be expected to have the best characteristics. This is confirmed by the results of the calculations performed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 129–137, July–August, 1986.The authors are grateful to V. A. Vostretsova for her help in the work.     

Non-linear and failure behaviour of spotwelds: a “global” finite element and experiments in pure and mixed modes I/II

The paper deals with joint element model used in crashworthiness simulations. The first part of the paper is dedicated to the formulation of a new “global” finite element for spotweld modelling. The mechanical behaviour of the joint is elastic–plastic type and damage is taken into account to model the failure of the welded area. The second part of the paper concerns a new experimental procedure for joint strength analysis in pure and mixed modes I/II and for joint model characterisation. Experiment is based on Arcan principle and results are compared to open literature. In the last part of the paper, the parameters of the new joint model are identified using experiments and used for several shapes of spot-welded specimens. The model predicts reasonably the elastic–plastic part of the response but is unable to predict the post-peak response observed especially in the case of pure shear.     

Comment on “Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers”

It is noted that the evaluation of the mean free path of ions by Park et al. [HEDP 8 (2012), 38–45] is incomplete without taking into account ion–electron collisions for colliding streams of high-speed laser-produced plasmas. As a result, the calculated scale of their interaction, ～few mm, can be explained by Coulomb collisions rather than as claimed in the paper, by the formation of a laboratory collisionless shock that simulates astrophysical shocks mediated by a Weibel-like instability. Advantages of CO₂-laser's irradiation and plane targets for such kind of experiments are discussed.     

Thermo-fluid-dynamic analysis of the flow in a rotating channel with a sharp “U” turn

Infrared thermography has been employed to carry out a detailed convective heat transfer measurements at Re?=?20,000 in a two-pass square channel both for the static case (absence of channel rotation) and for the rotating case (Ro?=?0.3). At the same time, the main and secondary flow fields have been measured by means of particle image velocimetry with the aim to investigate how the flow behavior affects the local distributions of the convective heat transfer coefficient for the two cases. The normal-to-wall velocity component (w) and the turbulent kinetic energy, both measured close to the heat exchanging wall, have been used to formulate an empirical heat transfer correlation within an attempt to identify the role performed by these two quantities on the convective heat transfer coefficient distributions. The latter ones have been reported in terms of normalized Nusselt number (Nu/Nu*) maps, where Nu* is the Nusselt number evaluated with the classical Dittus-B?lter correlation.     

Comments on “Adaptive fuzzy H ∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems” [Nonlinear Dyn. 69 (2012) 1639–1650]

In this paper, it is shown that the closed-loop system stability analysis in the main theorem of the paper (Lin et al. in Nonlinear Dyn. 69:1639?C1650, 2012) contains two essential errors. We demonstrate that the authors of the above paper have carelessly dealt with the derivation and integration procedures of the fractional-order equations as common ordinary differential equations.     

Comments on “Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays”

In this note some points for paper [Huabin Chen, Chuanxi Zhu, Peng Hu, Yong Zhang, Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays, Nonlinear Dyn. (2012), doi:10.1007/s11071-012-0324-3] are presented.     

Wave‐field structure in active bubble systems in shock tubes with “discontinuities” in cross section

The wave structure in active bubble media in shock tubes with sudden changes of profiles in the form of discontinuities in cross section and a onephase liquid waveguide is analyzed numerically. In axisymmetric formulation, the paper studies wave amplification due to reflection from a wall and focusing at the buttend of a rigid rod aligned coaxially with the channel. In this configuration, the amplification effect results from twodimensional cumulation of the shock wave after it leaves the annular channel and reaches the buttend of the rod. A Mach configuration forms in the focus spot. The geometrical characteristics of the shock tube allow one to control (to some extent) the amplification coefficient and the coordinates of the focus spot. In particular, it is shown that the wave can be focused near the second discontinuity of cross section — a rigid wall (in the region of passage through the interface to the waveguide) — and intensified upon reflection. If the waveguide radius is equal to the height of the Mach stem, the reflected wave has a maximum amplitude.     

“Thermal layer” effect in MHD: Interaction of a parallel shock with a layer of decreased density

Interaction of a parallel fast MHD shock with a layer of decreased density is discussed using ideal MHD approach. This is an extrapolation of gas dynamic thermal layer effect on ideal MHD. Computer simulations show that a magnetic field of a moderate intensity ( 1) may change the character of the flow for intermediate Mach numbers (M 5) and a new raking regime may occur which is not observed in the absence of a magnetic field. Self similar precursor analogous to that in gas dynamics may develop in the case of highM and low density in the layer but magnetic forces essentially decrease its growth rate. This problem appears in connection with cosmical shock propagation where planetary magnetic tails play the role of the thermal layer, and it may also be observed in the laboratory when the shock is strong enough to heat the walls ahead of it.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Investigation of quasi-periodic response of a buckled beam under harmonic base excitation with an “unexplained” sideband structure

Nonlinear Dynamics - The aim of this paper is to investigate quasi-periodic response of a fixed–fixed buckled beam experimentally studied in detail by Kreider and Nayfeh (Nonlinear Dyn...