APPLICATION OF WAVELET TRANSFORM TO BIFURCATION AND CHAOS STUDY

I.IntroductionThetypesofmotionforanonlinearvibrationsystemmaybeperiodic,quasiperiodicorchaotic.Foragivensetofparametersofthesystem,Poincarkmap,powerspectral,waveformandLyapunovexponentareusuallyutilizedtoseewhethertheresponseofthesystemischaoticornot,butitisdiftlculttodeterminepreciselytheexistingdomainsorattractingbasinsofdifferenttypesofmotionsinparametricspaceorinitialvaluespaceonlyfromgraphicsstudy,andcomputingLyapunovexponentistimeconsuming.Aswavelettransformcanreveallocalpropertyinboth…     

用积分变换及边界积分方法求解多层地基的静力问题

本文利用积分变换及矩阵递推方法得到了任意n层弹性体平面应变及轴对称问题的Mindlin解。再把此解作为基本解,利用Somigliana关系式,得到计算多层弹性体内部任意点位移的简便方法。利用此法很容易编制程序,且具有较高的计算精度与速度。     

一种新的摄动粘弹性边界元法

本文在拉普拉斯变换空间中,运用摄动理论和“弹性-粘弹性”对应性原理,提出了一种新的粘弹性问题边界元求解法。文中结合广义变分原理,导出了摄动粘弹性边界元方程,并给出了摄动粘弹性问题的基本解。最后,详述了一阶摄动的求解过程,并给出了算例。     

Wave propagation in multi-wire strands by wavelet-based laser ultrasound

Methods based on guided ultrasonic waves are gaining increasing attention for the non-destructive inspection and condition monitoring of multi-wire strands used in civil structures such as prestressing tendons and cable stays. In this paper we examine the wave propagation problem in seven-wire strands at the level of the individual wires comprising the strand. Through a broad-band, laser ultrasonic setup and a time—frequency wavelet transform processing, longitudinal and flexural waves are characterized in terms of dispersive velocity and frequency-dependent attenuation. These vibrating frequencies propagating with minimal losses are identified as they are suitable for long-range inspection of the strands. In addition, the wave transmission spectra are found to be sensitive to the load level, suggesting the potential for continuous load monitoring in the field.     

Chaos and Shadowing Lemma for Autonomous Systems of Infinite Dimensions

For finite-dimensional maps and periodic systems, Palmer rigorously proved Smale horseshoe theorem using shadowing lemma in 1988 [20]. For infinite-dimensional maps and periodic systems, such a proof was completed by Steinlein and Walther in 1990 [30], and Henry in 1994 [9]. For finite-dimensional autonomous systems, such a proof was accomplished by Palmer in 1996 [17]. For infinite-dimensional autonomous systems, the current article offers such a proof. First we prove an Inclination Lemma to set up a coordinate system around a pseudo-orbit. Then we utilize graph transform and the concept of persistence of invariant manifold, to prove the existence of a shadowing orbit.     

孔隙压力作用下圆形巷道围岩的蠕变分析

在原有的岩土流变理论基础上,与渗流力学原理相结合,考虑孔隙压力及孔隙度在岩石蠕变过程中对于岩体变形的影响,在弹性解答的基础上,通过Laplace变换(对应性原理)得出解析解．在一定的假设条件下,利用弹性力学基本方程、蠕变方程及有效应力原理(Terzaghi有效应力方程),采用H-K体模型作为本构方程,将孔隙压力引入到围岩蠕变方程中．给出在孔隙压力作用下的蠕变曲线,并与不考虑孔隙压力和定孔隙压力条件下蠕变曲线相比,其更接近于实际．     

Effective properties of elastic periodic composite media with fibers

A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites.     

小波分析技术在陀螺故障诊断中的应用研究

小波分析是一种全新的时一频两维分析技术，其对高频突变信号和低频缓变信号的分析有其独特的优点。本文分析了小波分析技术的原理，提出了将其引入机械设备故障诊断中的方法。通过对有故障陀螺振动信号的多尺度分析，研究故障信号小波变换轴心轨迹分量图，建立典型故障特征模型，从而对单故障及多故障问题进行分析与诊断。     

三维运动接触问题的广义Галин定理

本文给出了求解一类相当普遍的三维运动接触问题的分析解法,并且把仅仅对静态接触问题成立的 定理推广到动力学情形,作了严格证明。作为例子,对接触区为椭圆的情形给出了积分形式的解,并且作了数值计算,由这些结果可以看出运动压体速度的效应。     

Fourier Transform in Bounded Domains

The functional analysis, the concept of distributionsu in the sense of Schwartz [7] andtheir extension given by Gelfand and Shilov [5]to ultradistributions u ,enables us to find by the means of the Fourier transform a secondlanguage to characterize physical behaviour. Almost any expressionwith physical meaning can be transformed, even if it isformulated in domains with complicated boundaries and evenif it is not integrable.Numerical procedures in the transformed space can bedeveloped in analogy to those well known in engineeringmechanics like the methods of Finite or BoundaryElements (FEM or BEM). Basis of the approaches presentedhere is the analytical representation of characteristicdistribution of a domain and the theorem of Parseval whichstates the invariance of energy in respect to thetransformation. In addition, the concept of thecharacteristic distribution leads to a very simplederivation of the Green-Gauss formulas fundamental for theBoundary or Finite Elements (e.g. [6]).