基于Hilbert-Huang变换的极端气温时间序列的尺度分析

极端气温时间序列作为非常复杂的非线性非平稳信号由多个不同频率的信号组成,本身频谱中包含多个不同尺度特征波.本文应用Hilbert-Huang变换方法分析了2005年-2014年上海市奉贤区10年间最高气温时间序列和最低气温时间序列.通过该分析展示了Hilbert-Huang变换对非线性非稳定信号具有良好的自适应性;通过分析极端气温的时间序列原始数据来判断极端事件频率和强度变化特征;结果表明,最高气温和最低气温都有不同程度的升高.通过周期性分析,模态数和平均周期之间存在着一定的关系,各模态的平均周期变化呈现渐近的质数增长;结果还显示,最高最低气温时间序列所表现出来的平均周期性和模态能量分布大体相同.通过多尺度观察极端气温的时间序列探寻了其内在的发展规律及时空变化关系,得到了原始信号中时-频-能之间的联系.     

基于OAET和HHT的混凝土AE源损伤识别方法

针对混凝土材料中所产生的声发射(AE)信号复杂的特点,采用正交异性声发射传感器(OAET)提取结构中特定方向的AE信号。运用Hilbert-Huang变换(HHT)对AE信号进行分析,通过循环应用经验模态分解的方法,将复杂的原始数据序列分解为有限数目的固有模态函数及一个残余项,进而采用Hilbert变换,得到以时间为自变量的信号幅度和瞬时频率函数。文章探讨了基于幅度和瞬时频率函数的损伤识别方法,形成了一种混凝土中复杂AE信号处理及损伤识别的新途径,有助于AE技术的发展与推广应用。     

动脉中非平稳流动壁面剪切力及其Hilbert-Huang变换

本文通过数值方法求解均匀动脉中的非平稳脉动流,给出了通过测量非平稳脉动血流量确定壁面切应力的方法.作为算例,采用实测的大鼠颈总动脉流量信号,求出了均匀动脉壁面切应力波形.进一步对求得的切应力波形进行经验模态分解(EMD),得到了切应力波形的各内在模态(IMF),以及Hilbert幅值谱.从切应力波形经Hilbert-Huang变换得到的IMF和Hilbert谱图可以明显地看出切应力各频率成分的物理意义.所得结果为进一步深入研究非平稳脉动切应力与血管重建的关系提供了一种方法学基础.     

旋转运动中弹性梁耦合振动的辛方法

研究旋转梁结构的弹性耦合振动问题。通过引入对偶体系，建立了解决该类问题的辛方法。在辛体系中描述旋转梁纵向和横向耦合振动控制方程，即哈密顿正则方程。进一步求解得到结构的固有振动频率及相应的振动模态，发现固有振动频率随转动角速度先升后降以及模态之间的某种转化规律。     

自适应摄动法在失谐叶盘受迫振动分析中的应用

针对自适应摄动法在失谐叶盘受迫振动分析中,选择接近激振力频率的相应模态数目难于控制的问题,基于质量-弹簧模型,提出一种自动选择模态的方法。该方法可根据激振力频率与基系统固有频率集的关系,自动选择最接近激振力频率的相应模态个数。计算结果显示,对失谐叶盘系统,特别是在弱耦合情况下,该方法比人为选择模态更为可靠,可以使用较少机时,获得较高的求解精度。     

基于Hilbert-Huang变换理论的结构振动主动变刚度频率控制

在主动变刚度(AVS)控制策略的基础上,提出一种新的结构振动控制主动变刚度频率控制算法。首先利用Hilbert-Huang变换理论将地震信号分解为有限数量的固有模态函数(IMF),再对这些IMF求解瞬时频率,进而获得信号的时频谱。由地震信号的瞬时频率与结构固有频率构造AVS控制切换准则,当两者频率接近时,AVS装置改变结构的刚度以抑制地震激励下的结构响应。选取两个建筑结构的Benchmark模型作为算例给出仿真分析,结果表明该方法能有效地控制受控结构的地震响应。     

环形陀螺敏感结构的平面振动分析

在薄壁圆环振动特性基础上,研究了振动环式微机械陀螺的支撑梁对环的振动模态及自然频率的影响。对一种外支撑式环形微机械陀螺敏感结构进行了ANSYS模态仿真,得到工作振动模态的变形量。以薄壁环2节点变形模态函数为参考函数对仿真变形量用最小二乘法拟合,拟合误差在4.5%以内,各函数系数一致性误差小于1.5%。基于支撑梁对环结构的模态函数影响较小的条件,用能量法和速度积分法得到结构的应变能和动能函数,进一步得到具有支撑梁环结构自然频率的近似解。选取4组支撑梁尺寸,其近似解与仿真结果的相对误差在±3%以内。     

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通过Hilbert-Huang变换得到地震波的时间-频率-振幅分布图,并对地震动动力特性进 行分析,创造性地提出了用地震动峰值能量的最大值(即时频密度函数的最大值)和峰值系 数作为评估地震动震动效应强弱的定量指标,初步建立了地震动震动效应评估的判据;并用实 例验证了该判据的可行性和可靠性.     

弹性连接旋转柔性梁动力学分析

采用Chebyshev 谱方法对考虑根部连接弹性的平面内旋转柔性梁动力学特性进行研究. 基于Gauss-Lobatto 节点与Chebyshev 多项式方法对柔性梁变形场进行离散,通过投影矩阵法施加固定及弹性连接边界条件. 利用Chebyshev 谱方法获得了系统固有频率和模态振型数值解,通过与有限元方法及加权残余法的比较,验证了方法的有效性. 分析了弹性连接刚度、角速度比率、系统径长比及梁的长细比等参数对系统固有频率及模态振型的影响. 研究发现:由于系统弯曲模态、拉伸模态的频率随各参数的变化规律不一致,将出现频率转向与振型转换现象;随着弹性连接刚度、角速度比率及系统径长比的增大,低阶弯曲模态频率增大并超过高阶拉伸模态频率,随着梁的长细比的增大,低阶拉伸模态频率增大并超过高阶弯曲模态频率.      

汽车动力总成悬置系统振动解耦计算方法研究

目前,汽车发动机动力总成悬置系统设计的主要任务是选择悬置元件的刚度、位置和角度,使悬置系统自由振动模态频率避开发动机怠速激励力频率与车身自振频率,并尽量提高各模态振型的解耦程度,从而提高悬置系统隔振效果。悬置系统按预定频率严格解耦设计是使设计出的悬置系统模态频率完全等于按汽车设计频率规划预定的频率,并使各模态的振型严格解耦,即各向振动能量的解耦度等于1。本文从悬置系统的自由振动方程出发给出了对悬置系统按预定频率严格解耦设计的方程组,通过方程组构造函数进而求出该方程组的解,从而提供比当前的悬置系统模态优化设计更为简便高效的优化设计方法。相应的算例验证了本文提出的按预定频率严格解耦设计方程和求解方法的正确性。     

多跨梁离散系统的频谱和模态的定性性质

采用差分法建立了两端任意支承多跨梁的差分离散模型,对只具有两端支承的单跨梁是正系统的情形,导出了对应的多跨梁差分离散系统的柔度系数;从单跨梁正系统的刚度矩阵的符号振荡性出发,通过引入辅助系统,讨论了多跨梁的柔度矩阵的振荡性,确定了对应于单跨梁正系统的多跨梁差分离散系统的频谱和模态的一系列定性性质.      

Investigation of Mechanisms of Excitation and Growth of Unstable Perturbations in Pulsating Flows

General laws of the processes of generation and amplification of secondary perturbations in oscillating viscous fluid flows are studied theoretically. The stability and receptivity are analyzed with reference to perturbations generated by fluctuations of the flow rate of Poiseuille flow induced by small two-dimensional roughnesses of the channel walls. It is shown that the presence of roughness leads to excitation in the flow of perturbations at all multiples of the main flow oscillation frequency. Using the Fourier transform along the streamwise coordinate, the problem of calculating the frequency harmonics is reduced to a system of equations of the Orr-Sommerfeld type interrelated via the oscillatory component of the main flow. On the basis of an investigation of the analytic properties of the Fourier-image it is shown that upstream and downstream of the roughness the perturbation can be represented in the form of a superposition of modes of the time-dependent Poiseuille flow. The modes are classified and their spectrum is calculated. The structure of the mean-square fluctuations generated by free perturbations is investigated. Examples of calculating the evolution of forced perturbations are given for cases in which the scattering of the oscillations of the main flow on the roughness leads to the generation of one or two modes growing downstream.     

Vortex dynamics simulation of interacting vortex rings and filaments

Interaction between a vortex ring and a vortex filament of the same strength has been simulated by a three-dimensional vortex method which employs vortex arrows with the Rosenhead-Moore core structure. The power spectrum of the velocity field and the enstrophy spectrum are obtained in a closed form whose limit of the core radius tending to zero is equivalent to that given be Aksman et al. (1985) Phys. Rev. Lett. 54. 2410. Four basic modes of the interaction are shown to exist. Temporal evolution of the spectrum during the interaction is also obtained for the basic modes: the energy of the velocity field is generally transferred to the high-wavenumber range as the interaction proceeds.     

Receptivity of the Flat-Plate Boundary Layer to Free-Stream Turbulence

The linear problem of generation of perturbations of a flat-plate boundary layer by external turbulence is solved. The turbulence is represented in the form of a set of space- and time-periodic vortex modes. It is shown that the boundary layer is most receptive to low-frequency longitudinal vorticity modes. The mean-square velocity fluctuations in the boundary layer and their spectrum are found for isotropic turbulence with a spectrum satisfying the Kolmogorov-Obukhov law.     

Tangential oscillations of a differentially rotating spherical fluid layer

The natural harmonic oscillations of a differentially rotating fluid layer under the action of a potential force are considered. The rise in the layer level is assumed to be negligible. The oscillations satisfy an ordinary second-order differential equation with singular coefficients that depend on the spatial coordinate. This equation is solved by the method of local separation of singularities based on the use of the properties of the Fuchs series for a bounded solution. Various laws for the latitude dependence of the angular rate of ocean rotation and the effect of these laws on the problem spectrum are considered. An equation is obtained for the streamlines of the oscillations investigated. Two cases in which the latitude dependence of the base flow velocity coincides with the real dependence for a celestial body are considered and the corresponding modes are found.     

Fluctuation characteristics of bubbly liquid flow in converging-diverging nozzle

The pressure fluctuation characteristics in bubbly liquid flow in a converging-diverging nozzle are interpreted on the basis of the previous theoretical results concerning the possible wave modes in bubbly liquid flow and their properties. The experiment is performed in a visual blowdown facility using water and nitrogen gas. The intensity and power spectrum density of the pressure fluctuations are measured, as well as the velocities of liquid and bubbles, the void fraction and the chord length of bubbles. All the fluctuation characteristics and their relation with the main stream condition are compatible with the theoretical predictions. The instability of the convection mode in the presence of the velocity slip and the cut off of the propagation modes in moderate frequency are demonstrated.     

Laboratory experiments on internal wave interactions with a pycnocline

Laboratory experiments have been performed to investigate the interaction of internal waves with a pycnocline. An oscillating cylinder generated internal wave beams, which were observed using the synthetic schlieren technique. Internal waves incident on the pycnocline layer excited higher-frequency modes. In the absence of shear, a discrete spectrum of harmonic modes was generated due to nonlinear effects. These harmonic modes might play a role in the formation of internal solitary waves which have been observed in ocean pycnoclines. With shear, a continuous spectrum of excited modes was found.     

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.     

Parametric pulse excitation in distributed mechanical systems with nonstationary boundaries

In a distributed system whose parameters vary with time the natural oscillation modes are interconnected and so it is possible to get parametric excitation of several synchronized harmonic modes simultaneously. If the natural oscillation spectrum of such a system consists of almost equally spaced lines, then a periodic change of the parameters with time can lead to the excitation of pulse-type oscillations [1]. This phenomenon can occur both in systems whose size varies with time and in systems whose boundary properties are nonstationary. The present paper is devoted to a study of the instability in these systems.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 145–151, July–August, 1976.     

Surface adapted partial waves for the description of elastic vibrations in bilayered plates

An approach is proposed in which the form of the partial waves in the decomposition of the displacement field is chosen in such a way that boundary conditions on the outer surfaces of a layered structure are matched exactly. So found basis functions are further used to solve for the remaining boundary conditions. Explicit analytic expressions for the vibration spectrum and normalized amplitudes of a free plate in the long wavelength regime are derived and their behavior in the full space of material parameters is discussed. Thus, it is found that properties of the fundamental flexural mode change in a strongly non-monotonous way. In particular, by increasing the thickness of added layer one may observe the same propagation velocity for up to three different values of layer thicknesses ratio. Existence of an important criterion based on the relative signs taken by the amplitudes on the outer surfaces in this regime is revealed. It allows to establish a clear correspondence between symmetric and antisymmetric solutions for a single layer and those for a bilayered plate. It is suggested that the criterion is not limited to case of two layers. Branches of the spectrum are classified accordingly and their evolution from long to short wavelength is discussed. Analysis of a specific example which includes volume and surface modes (Rayleigh and Stoneley) is presented. The results demonstrate the efficiency of the proposed scheme and possible extensions are suggested.