A model of imperfect interface with damage

In this paper two models of damaged materials are presented. The first one describes a structure composed by two adherents and an adhesive which is micro-cracked and subject to two different regimes, one in traction and one in compression. The second model is a model of interface derived from the first one through an asymptotic analysis, and it can be interpreted as a model for contact with adhesion and unilateral constraint. Simple numerical examples are presented.     

粘弹性介质中逆散射问题的求解方法

本文讨论了一维粘弹性介质中的逆散问题,给出了两种反演粘弹性介质松弛模量的方法。这两种方法只利用了介质层一侧波的反射数据,其中一种方法只需已知一个走时来回时间内的反射数据就可以确定介质的松弛模量在任意时刻的值。文中最后给出了数值算例,可以看出,数值反演的结果与初始给定的松驰模量吻合得很好。     

On the problem of slow seismic waves

The use of vector eigenfunctions in the block method permits one one to simplify the construction of solutions of some boundary value problems and decrease the order of the systems of pseudodifferential equations. Because of this possibility, one can reveal some general properties of the stress-strain state of bounded deformable bodies. This result makes us closer to the explanation of certain behavior of block structures, including lithosphere plates, under seismic actions and allows one to study phenomena of the existence of slow seismic waves propagating in the Earth’s crust along the so-called “seismic traces.”     

Non-linear modal analysis of a rotating beam

The free non-linear vibration of a rotating beam has been considered in this paper. The von Karman strain-displacement relations are implemented. Non-linear equations of motion are obtained by Hamilton’s principle. Results are obtained by applying the method of multiple scales to a set of discretized ordinary differential equations which obtained by using the Galerkin discretization method. This set contains coupling between transverse and axial displacements as quadratic and cubic geometric non-linearities. Non-linear normal modes and non-linear natural frequencies with or without internal resonance are observed. In the internal resonance case, the internal resonance between two transverse modes and between one transverse and one axial mode are explored. Obtained results in this study are compared with those obtained from literature. The stability and some dynamic characteristics of the non-linear normal modes such as the phase portrait, Poincare section and power spectrum diagrams have been inspected. It is shown that, for the first internal resonance case, the beam has one stable or degenerate uncoupled mode and either: (a) one stable coupled mode, (b) one unstable coupled mode, (c) two stable and one unstable coupled modes, (d) three stable coupled modes, and (e) one stable coupled mode. On the other hand, for the second internal resonance case, the beam has one stable or unstable or degenerate uncoupled mode and either: (a) two stable coupled modes, (b) two unstable coupled modes, and (c) one stable coupled mode depending on the parameters.     

On the diffusion of load from a stiffener into an infinite wedge-shaped plate

Summary The stress-distribution in a wedge-shaped plate with a stiffener upon one of the edges is considered. The stiffener is loaded by an axial force. The problem leads to the solution of a biharmonic equation with one mixed boundary condition. The problem is reduced to the standard problem of the stress-distribution in a wedge. The reduction has been executed by the solution of a difference equation for the transform of the shear-stress along the stiffened edge. For this solution we give two representations: one by means of an infinite product and one by means of an integral. Full discussion is given on asymptotic behaviour and on the numerical aspects.     

Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension

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Energy transfer in double plate system dynamics

The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.     

Shock induced Richtmyer-Meshkov instability in the presence of a wall boundary layer

An experimental investigation on gaseous mixing zones originated from the Richtmyer-Meshkov instability has been undertaken in a square cross section shock tube. Mass concentration fields, of one of the two mixing constituents, have been determined within the mixing zone when the shock wave passes from the heavy gas to the light one, from one gas to an other of close density, and from the light gas to the heavy one. Results have been obtained before and after the coming back of the reflected shock wave. The diagnostic method is based on the infrared absorption of one of the two constituents of the mixing zone. It is shown that the mixing zone is strongly deformed by the wall boundary layer. The consequence is the presence of strong gradients of concentration in the direction perpendicular to the shock wave propagation. Finally, it is pointed out that the mixing goes more homogeneous when the Atwood number tends to zero.     

Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique

In this paper, active backstepping design technique is applied to achieve reduced-order hybrid combination synchronization and reduced-order projective hybrid combination synchronization of three chaotic systems consisting of: (i) two third-order chaotic Josephson junctions as drives and one second-order chaotic Josephson junction as response system; (ii) one third-order chaotic Josephson junction as the drive and two second-order chaotic Josephson junctions as the slaves. Numerical simulations are performed to verify the feasibility and effectiveness of the analytical results. Reduced-order combination synchronization has more valuable practical applications to information processing in physical, biological, and social systems than the normal one master system and one slave system synchronization scheme.     

The reconstruction of a wave equation from one side measurement

We are concerned with the reconstruction of a one dimensional wave equation, where the potential is known in a neighborhood of one of the end points of the boundary. We show then the sought potential can be determined by one single measurement of the solution at that end. We also show that the solution can be evaluated at the other end without the need of solving the wave equation.     

高层建筑标准模型风洞测压和测力试验研究

CAARC高层建筑标准模型是国际上通用的风工程标准模型之一,用来检验各个模拟自然风的风洞试验结果,以确保风洞试验测量数据的可信度。本研究使用缩尺比为1：300的CAARC模型,在同济大学TJ-2建筑风洞中进行了B类和D类地面粗糙度风场下的刚性测压试验和高频动态天平试验。在刚性测压试验中测量了建筑模型表面在不同风速和风向角下的平均风压系数,并与国外风洞机构的试验数据进行了对比分析。在高频动态天平试验中,不同风向角下的结构气动力系数和顶点位移被给出,并同样与国外风洞机构进行了对比。风洞试验结果表明：TJ-2风洞能较好地模拟大气边界层风场,且风场品质较好;试验技术可靠,所测得的试验数据具有较高的精度。     

Optimization of Forced Convection Heat Transfer in a Composite Porous Medium Channel

The optimization of heat transfer for forced convection in a composite porous channel was studied. We investigated the question where should one place, in the core or in the sheath, the material with high permeability and high-thermal conductivity and where should one place the material with low permeability and low-thermal conductivity, to maximize heat transfer from the walls. We also investigated the optimal heat transfer situation when one has the freedom to vary the relative volumes of the core and the sheath.     

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

Nonlinear Dynamics - The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of...     

平面突扩流动非稳定性的大涡模拟

用ＴＧ有限元法求解二维大涡模拟的非定常Ｎ－Ｓ方程，数值模拟了平面突扩流动，计算结果展示了回流区内流动的多涡结构及其不稳定的周期振荡过程，而该振荡过程的周期时间历程平均，恰好与诸多湍流模型的计算结果及实验结果相吻合，证明了数值模拟的正确性。     

Numerical analysis of pressure drop oscillations in parallel channels

In this study pressure drop oscillations in two parallel channels are analyzed taking into account the thermal capacity of the pipes. A different limit cycle than the one that takes place in a single channel system is found. During the instability one channel always follows the typical pressure drop oscillations limit cycle while the other channel oscillates always in the superheated vapor region. This behavior leads to very high wall temperatures at the outlet of the heated pipe. This undesirable situation with one channel operating in the superheated vapor region takes place also for the maldistributed stable solutions.     

Fringe multiplication by reflection

A new method of fringe multiplication is presented in this paper.The method is simpleand applicable.Only one polarizer and one quarter-wave plate are adopted to get fringemultiplication by reflection.     

Regularity Criteria of MHD System Involving One Velocity and One Current Density Component

We study a regularity criteria of the three-dimensional magnetohydrodynamics system. In particular, we obtain a regularity criteria that involves one velocity component and one current density component. Its immediate consequence is a regularity criteria in terms of one velocity component and two entries from the Jacobian matrix of the magnetic vector field, in contrast to many previous results that involve three entries all from the Jacobian matrix of the velocity vector field. Moreover, the conditions on the current density component is in the norm with scaling dimension zero; i.e. Serrin-class.     

On the stability of plane wave and soliton solutions to the Zakharov equations

Plane wave and soliton solutions of the two types of Zakharov equation (two dimensional and simplified one directional) are considered. Stability properties in one dimensional space are seen to be similar. This is interesting, as the first type of equation is not solvable whereas the second is. The soliton solutions of both are one dimensionally stable but those of the full Zakharov equations are unstable with respect to perpendicular perturbations. Regions of stability of nonlinear wave and shock wave solutions in parameter space as well as growth rates of instabilities are given.     

Nonlinear Normal Modes of Buckled Beams: Three-to-One and One-to-One Internal Resonances

Nonlinear normal modes of a fixed-fixed buckled beam about its first post-buckling configuration are investigated. The cases of three-to-one and one-to-one internal resonances are analyzed. Approximate solutions for the nonlinear normal modes are computed by applying the method of multiple scales directly to the governing integral-partial-differential equation and associated boundary conditions. Curves displaying variation of the amplitude of one of the modes with the internal-resonance-detuning parameter are generated. It is shown that, for a three-to-one internal resonance between the first and third modes, the beam may possess one stable uncoupled mode (high-frequency mode) and either (a) one stable coupled mode, (b) three stable coupled modes, or (c) two stable and one unstable coupled modes. For the same resonance, the beam possesses one degenerate mode (with a multiplicity of two) and two stable and one unstable coupled modes. On the other hand, for a one-to-one internal resonance between the first and second modes, the beam possesses (a) two stable uncoupled modes and two stable and two unstable coupled modes; (b) one stable and one unstable uncoupled modes and two stable and two unstable coupled modes; and (c) two stable uncoupled and two unstable coupled modes (with a multiplicity of two). For a one-to-one internal resonance between the third and fourth modes, the beam possesses (a) two stable uncoupled modes and four stable coupled modes; (b) one stable and one unstable uncoupled modes and four stable coupled modes; (c) two unstable uncoupled modes and four stable coupled modes; and (d) two stable uncoupled modes and two stable coupled modes (each with a multiplicity of two).     

Planar non-linear free vibrations of an elastic cable

Continuum non-linear equations of free motion of a heavy elastic cable about a deformed initial configuration are developed. Referring to an assumed mode technique one ordinary equation for the cable planar motion is obtained via a Galerkin procedure, an approximate solution of which is pursued through a perturbation method. Suitable nondimensional results are presented for the vibrations in the first symmetric mode with different values of the cable properties. Which procedure is the proper one to account consistently for the non-linear kinematical relations of the cable in one ordinary equation of motion is discussed.