车辆-轨道系统垂向随机振动的辛方法分析

将轨道视为无限长的周期结构,建立车辆轨道垂向耦合模型. 使用虚拟激励法将随机的轨道不平顺激励转化为确定性的简谐激励,再用辛数学方法求解轨道结构的频率响应特性和耦合系统的响应功率谱. 整个计算模型只有26个自由度,求解过程快速而精确.数值算例中,将该方法与常规有限元方法进行了比较,验证了方法的高效性和正确性,讨论了车辆速度对系统随机响应的影响.      

Principal Trajectories of Forced Vibrations for Discrete and Continuous Systems

Principal trajectories of forced vibration of linear and nonlinear continuous systems are introduced as such motions in which the system is equivalent to a Newtonian particle in the function space of the system configurations. The corresponding 'effective mass' of the particle gives physical characteristics of the system response, so that zero effective mass is associated with resonance. The methodology can be viewed as a complementary tool to the method of normal modes, when considering the class of forced vibrating systems, since the related basis accounts for the system physical properties as well as the external forcing factor. In particular, it is shown that a two degrees of freedom system can possess an infinite discrete set of in-phase and out-of-phase forced vibrations of the normal modes type. The corresponding forcing vector-functions obey the second Newton law due to the definition of principal trajectories.     

Ergodic theorem for infinite iterated function systems

1IntroductionandProblem IteratedFunctionSystems(IFS)theorycanbesaidtobethecontinuationanddevelopment ofdynamicalsystemtheory.DynamicalsystemstheorydealswithiterationofonemapbutIFS theorydealswithiterationofmanymaps. IFStheory’srootwasveryearlybutthebeginningofactivedevelopmentwasHutchinson’s paper(1981).Heresearchedselfsimilarityoffractalsetsusingsystemoffinitenumberofsimilar contractionmapsofRn.Barnsleycalledafinitesetofcontractionmappsasaniteratedfunction systemsandsystemizedIFStheo…     

Integrodifferential equations for plane filtration in the presence of cracks

A system of singular integr Differential equations is derived for the plane problem of steady-state filtration in a plate cut by a system of cracks. We consider an arbitrary set of cracks, and also monoperiodic and biperiodic systems of cracks, in an infinite plane. In the case of a system of infinite parallel rectilinear cracks, the general solution is obtained in explicit form-in quadratures. As an example, we find the complex potential and the formula for the output from a borehole for a linear system of tiered, flooded plates, cut by a system of rectilinear parallel cracks.     

Quasiperiodic oscillations in robot dynamics

Delayed robot systems, even of low degree of freedom, can produce phenomena which are well understood in the theory of nonlinear dynamical systems, but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm which leads to an infinite dimensional dynamical system. Restricting the dynamics to a four dimensional center manifold, we show that the system undergoes a codimension two Hopf bifurcation for an infinite set of parameter values. This provides a mechanism for the creation of two-tori in the phase space and gives a theoretical explantion for self-excited quasiperiodic oscillations of force controlled robots. We also compare our results with experimental data.     

多自由度振动系统的一类凸集响应

对激励用凸集合建模的线性时不变振动系统定义了响应集的概念，将多自由度振动系统的凸集响应问题转化成寻求响应集的问题，从而降低了求解的难度．并提出了求解一类凸集载荷的响应集的支撑超平面法．对有限时刻的响应集，导出了求任意方向边界点的解析解，而对无限时刻的响应集，建议了一种求任意精度的凸多胞形近似的方法．最后给出了一个实例，得到了不同时刻的响应集，并将凸集响应与谐波响应及非平稳随机响应作了对照     

Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method

The scattering of flexural wave by multiple circular holes in an infinite thin plate is analytically solved by using the multipole Trefftz method. The dynamic moment concentration factor (DMCF) along the edge of circular holes is determined. Based on the addition theorem, the solution of the field represented by multiple coordinate systems centered at each circle can be transformed into one coordinate system centered at one circle, where the boundary conditions are given. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived as an analytical model for the scattering of flexural wave by multiple holes in an infinite plate subject to the incident flexural wave. The formulation is general and is easily applicable to dealing with the problem containing multiple circular holes. Although the number of hole is not limited in our proposed method, the numerical results of an infinite plate with three circular holes are presented in the truncated finite system. The effects of both incident wave number and the central distance among circular holes on the DMCF are investigated. Numerical results show that the DMCF of three holes is larger than that of one, when the space among holes is small and meanwhile the specified direction of incident wave is subjected to the plate.     

Dissipation and Compact Attractors

We present an approach to the study of the qualitative theory of infinite dimensional dynamical systems. In finite dimensions, most of the success has been with the discussion of dynamics on sets which are invariant and compact. In the infinite dimensional case, the appropriate setting is to consider the dynamics on the maximal compact invariant set. In dissipative systems, this corresponds to the compact global attractor. Most of the time is devoted to necessary and sufficient conditons for the existence of the compact global attractor. Several important applications are given as well as important results on the qualitative properties of the flow on the attractor.     

Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

A method is proposed to investigate the behavior of an axisymmetric system consisting of an infinite thin elastic cylindrical shell immersed in an infinite elastic medium, filled with a perfect compressible fluid, and containing an oscillating spherical inclusion. The system is subjected to periodic excitation. The task is to detect so-called resonant phenomena, to establish conditions that cause them, and to examine the possibilities of using the characteristic parameters of such a hydroelastic system to influence these conditions. The method allows transforming the general solutions of mathematical physics equations from one coordinate system to another to obtain exact analytic solutions (in the form of Fourier series) to interaction problems for systems of rigid and elastic bodies __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 82–97, July 2006.     

Solution of the elastic boundary value problems for a layer with tunnel stress raisers

A novel procedure for solving three-dimensional problems for elastic layer weakened by through-thickness tunnel cracks has been developed and is presented in this paper. This procedure reduces the given boundary value problem to an infinite system of one-dimensional singular integral equations and is based on a system of homogeneous solutions for a layer. Integral representations of single- and double-layer potentials are used for metaharmonic and harmonic functions entering in the singular integral equations. These representations provide a continuous extendibility of the stress vector while allowing a jump in the displacement vector in the transition through the cut.Expanding the potential and biharmonic solutions in the Fourier series over the thickness coordinate yields the integral representations of the displacement vector and stress tensor. The problem of reducing a denumerable set of the integral equations of the given boundary value problem to one-to-one correspondence with the set of unknown densities appearing in the Fourier’s coefficient representations has been settled efficiently. Numerical investigations show a rapid convergence of the proposed reduction procedure as applied to the solution of the infinite system of one-dimensional integral equations. Numerical examples illustrate the proposed method and demonstrate its advantages.     

Projective synchronization between two different time-delayed chaotic systems using active control approach

In this paper, we investigate the projective synchronization between two different time-delayed chaotic systems. A suitable controller is chosen using the active control approach. We relax some limitations of previous work, where projective synchronization of different chaotic systems can be achieved only in finite dimensional chaotic systems, so we can achieve projective synchronization of different chaotic systems in infinite dimensional chaotic systems. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective synchronization between two different time-delayed chaotic systems. The validity of the proposed method is demonstrated and verified by observing the projective synchronization between two well-known time-delayed chaotic systems; the Ikeda system and Mackey–Glass system. Numerical simulations fully support the analytical approach.     

Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem

This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.     

一类偏微分方程的Hamilton正则表示

主要给出一系列关于力学中的偏微分方程的无穷维Ｈａｍｉｌｔｏｎ正则表示．其中包括变系数线性偏微分方程,ＫｄＶ方程,ＭＫｄＶ方程,ＫＰ方程,Ｂｏｕｓｉｎｅｓｑ方程等的无穷维Ｈａｍｉｌｔｏｎ正则表示．     

动态断裂力学的无限相似边界元法

对弹性动力学的相似边界元法进行了进一步研究,推导了相应的计算公式,并在此基础上提出了动态断裂力学的无限相似边界元法.与传统的边界元法相比,相似边界元法由于只需在少数单元上进行数值积分,大大减少了计算量.对动态断裂力学问题,无限相似边界元法由于在裂纹尖端的边界上设置了逼近于裂纹尖端的无限个相似边界单元,可直接得到裂纹尖端具有奇异性的应力,而不需要设置奇异单元,从而突破了奇异单元对应力奇异性阶次的局限.另外,还讨论了无限相似边界元法得到的无限阶的线性代数方程组的求解方法.     

Construction of an infinite-dimensional invariant torus of a countable system of linear differential-difference equations by the method of its reduction in the angular variable

We use the method of reduction in the angular variable to construct an infinite-dimensional invariant torus for a linear system of differential-difference equations that depends on an infinite set of constant deviations of arguments of different signs. This means that the function that defines the torus is represented in the form of the limit of a sequence of functions, each of which defines an invariant torus for the initial system reduced in the angular variable, as the order of reduction tends to infinity.     

Biharmonic Problem in a Rectangle

This paper addresses the fascinating long history of the classical two-dimensional biharmonic problem for a rectangular domain. Among various mathematical and engineering approaches, the method of superposition is effective for solving mechanical problems concerning creeping flow of viscous fluid set up in a rectangular cavity by tangential velocities applied along its walls, an equilibrium of an elastic rectangle, and bending of a clamped thin rectangular elastic plate by a normal load. The object of this paper is both to clarify some purely mathematical questions connected with the solution of the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm. The method is illustrated by several examples of steady Stokes flow in a square cavity.     

一种求解含振子及弹性支承圆板振动的新方法

将富里叶－贝塞尔级数引入积分方程[1],推导出一种研究含振子及弹性支承圆板振动特性的新方法,根据积分方程和富里叶－贝塞尔级数理论,首先用第一类贝塞尔函数构造圆板的格林函数,然后由叠加原理将圆板的自由振动问题转化为积分方程的特征值问题;进面将积分方程形式的特征值问题转化为无穷阶矩阵的标准特征值问题,计算时根据精度的要求,截取无穷阶矩阵的标准特征值为有限阶矩阵的标准特征值问题,采用Q－R算法,计算实践表明,本方法不仅具有运算简捷,精度高,适用性强的特点,而且能从整体上对系统的动态性加以研究,从而为这类系统的优化设计提供有;力的 工具。     

Stress concentrations in the particulate composite with transversely isotropic phases

The accurate series solution have been obtained of the elasticity theory problem for a transversely isotropic solid containing a finite or infinite periodic array of anisotropic spherical inclusions. The method of solution has been developed based on the multipole expansion technique. The basic idea of method consists in expansion the displacement vector into a series over the set of vectorial functions satisfying the governing equations of elastic equilibrium. The re-expansion formulae derived for these functions provide exact satisfaction of the interfacial boundary conditions. As a result, the primary spatial boundary-value problem is reduced to an infinite set of linear algebraic equations. The method has been applied systematically to solve for three models of composite, namely a single inclusion, a finite array of inclusions and an infinite periodic array of inclusions, respectively, embedded in a transversely isotropic solid. The numerical results are presented demonstrating that elastic properties mismatch, anisotropy degree, orientation of the anisotropy axes and interactions between the inclusions can produce significant local stress concentration and, thus, affect greatly the overall elastic behavior of composite.     

On the existence of infinite-dimensional invariant tori of nonlinear countable systems of difference-differential equations

In the space of bounded number sequences, we establish sufficient conditions for the existence of invariant tori for nonlinear countable systems of difference-differential equations defined on infinite-dimensional tori and containing an infinite set of constant deviations of a scalar argument.     

On the existence of invariant tori of countable systems of difference-differential equations defined on infinite-dimensional tori

In the space of bounded number sequences, we establish sufficient conditions for the existence of invariant tori for linear and quasilinear countable systems of differential-difference equations defined on infinitedimensional tori and containing an infinite set of constant deviations of a scalar argument.