爆破地震地面运动的演变功率谱密度函数分析

按照Priestly提出的演变随机过程理论，对非平稳随机过程的演变功率谱密度函数进行了理论推导，并给出了定义。在此基础上，建立了基于均匀调制随机过程的爆破地震动演变功率谱密度函数。经对比发现，理论模型计算值与实验测试结果具有较好的一致性。     

全非平稳地震作用下地下空间结构随机反应及可靠度分析

为研究全非平稳地震作用下地下空间结构的随机地震反应特征及可靠度分析方法，本文基于非均匀调制演变随机过程，建立了一种同时考虑强度非平稳和频率非平稳的全非平稳随机地震动输入功率谱分析模型；利用频响函数和脉冲响应函数间的傅里叶变换关系，推导出了适用于地下空间结构随机反应分析的响应功率谱计算表达式，可结合有限元方法对全非平稳地震作用下地下空间结构进行随机反应分析．基于穿越过程为泊松过程假定，采用分部积分方法，进一步推导出了适用于首次超越破坏可靠度计算的互相关函数解析表达式．然后，本文以上海某两层三跨地铁车站为工程背景，建立土-地铁车站结构相互作用体系有限元模型，对全非平稳地震作用下地铁车站结构进行了随机反应分析和中柱可靠度分析．结果表明：在非均匀调制演变功率谱作用下，结构的响应功率谱也具有明显的演变特征；利用文中给出的互相关函数计算公式，可避开调制函数的数值微分，提高计算精度．     

非平稳地震动的双调制模型研究

地震动是工程结构地震反应研究与抗震设计的基础,要分析工程系统的性能,必须要把地震动作为随机过程来建立可靠的模型。本文通过对非平稳过程演变谱的研究,给出双调制函数,建立了双调制非平稳地震地面运动模型。结合双调制函数和三角级数法生成人工地震波,通过对人工波频率和强度的非平稳性研究验证了双调制模型的有效性。同时本文给出了双调制非平稳地震激励的结构响应虚拟激励算法,得到响应的时变功率谱。分析表明,该模型具有明确的物理意义,且更符合实际,为结构抗震可靠性分析提供了一种较好的地震动模型。     

基于虚拟激励法的大跨度桥梁非平稳随机振动分析闭合解

针对大跨度结构考虑地面空间运动的非一致地震响应分析问题,结合虚拟激励法,应用傅里叶分析建立了结构非平稳随机振动响应演变功率谱分析的频域方法。建立的方法完全基于频域执行,给出了响应演变功率谱的闭合解表达式。由于实现了确定性调制过程与随机过程的有效分离,应用离散傅里叶变换进行计算不需要较高的采样分析频率就可以获得较好精度的数值结果。数值算例研究了某斜拉桥的考虑地面运动空间效应非平稳随机地震响应,与通常时频分析方法进行对比,验证了本文频域方法的正确性和有效性。     

受非均匀调制演变随机激励结构响应快速精确计算

本文假定结构受到非均匀调制的演变随机激励，亦即其调制函数是时间与频率二者的函数，导出了有关的虚拟激励算法，并采用精细逐步积分格式，进行时变功率谱计算，获得了很高的计算效率和精度。     

相关演变随机激励下响应演变谱矩阵的表达式

引入演变频率响应矩阵的概念,时不变线性系统在矢量演变随机激励下的响应演变功率谱矩阵有十分简洁的形式,与平稳随机响应-激励功率谱矩阵的关系式十分相似.实质不同在于:此处的演变频率响应理应定义为零初始条件下、系统对演变复谐和激励的确定性瞬态响应.因此,演变随机响应问题就归结为相关演变复谐和激励下的确定性瞬态响应问题.响应演变谱矩阵的一般表达式覆盖了非均匀调制与均匀调制随机激励两种情形的结果.而同源演变随机激励情形只是其特例.     

关于虚拟激励法的一个注记

从具有随机频率与随机相位的随机谐和函数出发,证明了当随机频率与相位均为均匀分布而随机幅值与功率谱密度平方根成正比时,该随机过程的功率谱即精确地等于目标功率谱.进而表明:只需遍历频率区间,即可由单一谐和函数激励下的响应幅值给出响应的功率谱密度,从而揭示了虚拟激励法的物理意义.研究还表明:为了给出结构响应的功率谱密度,实际...     

关于功率谱密度与风速谱的注记

探讨了随机过程中双边功率谱密度负频率引入的原因,实际的频谱函数应将负频率项与相应正频率项成对合并起来而直流分量保持不变,此即单边功率谱所表达的含义.对目前文献中给出的单边功率谱的表达式和单边功率谱与双边功率谱的关系式进行了修正,并对维纳-辛钦公式的变换形式也做了相应的修正,指出其修正前后在不同风速谱实际应用中的区别.算例证明了本文所给公式的正确性.     

论同源随机激励及其响应的特点

本文从一般情形出发，为同源随机激励提出一个含义较广的定义。同源随机激励的特点是其功率谱矩阵可表示为一个列阵与其共轭行阵的乘积。在同源激励作用下，常参数线性系统的响应仍保持激励的上述特点，充分利用这一特点可以节约计算工作量。文中还借助模态分析给出了在同源平稳随机激励下响应功率谱矩阵的解析式，以及在同源演变随机激励下非平稳响应的演变谱表示式。     

随机过程的随机谐和函数表达

研究了随机过程的随机谐和函数表达及其性质. 首先证明了当随机谐和函数的频率分布与目标功率谱密度函数形状一致时, 随机谐和函数过程的功率谱密度函数等于目标功率谱密度函数. 进而, 证明了随机谐和函数过程的渐进正态性, 讨论了趋向正态分布的速率, 并采用Pearson分布研究了一维概率密度函数的性质. 与已有的随机过程谱表达方式相比, 采用随机谐和函数表达, 仅需要很少的展开项数, 即可获得精确的目标功率谱密度函数, 从而大大降低了与之相关的随机动力系统分析的难度. 最后, 以多自由度体系的线性和非线性响应分析为例, 验证了随机谐和函数模型的有效性和优越性.      

On model equations for particle dispersion in inhomogeneous turbulence

Comparisons are made between the Advection–Diffusion Equation (ADE) approach for particle transport and the two-fluid model approach based on the PDF method. In principle, the ADE approach offers a much simpler way of calculating the inertial deposition of particles in a turbulent boundary layer than that based on the PDF approach. However the ADE equations that have recently been used are only strictly valid for a simple Gaussian process when particle inertia is small. Using a prescribed, but in general non-Gaussian random particle velocity field, it is shown that the net particle mass flux contains a drift term in addition to that from the mean velocity of the particle velocity field, associated with the compressibility of the velocity field. Furthermore the diffusive flux in general depends not only upon the gradient of the mean concentration (true only for a Gaussian random flow field) but also upon higher order derivatives whose relative contribution depends on diffusion coefficients D_ijk… etc. These coefficients depend upon the statistical moments associated with random displacements and compressibility of the particle flow field along particle trajectories which in turn depend upon particle inertia. In contrast the PDF approach offers the advantage of using a simple gradient (Gaussian) approximation in particle phase space which can lead to a non-Gaussian spatial dispersion process when particle inertia is important. Conditions based on the particle mean free path are derived for which a simple ADE is appropriate. Some of the features of particle transport in an inhomogeneous turbulent flow are illustrated by examining particle dispersion in a random flow field composed of pairs of counter rotating vortices which has an rms velocity which increase linearly from a stagnation point.     

基于P-S-N曲线的强度退化随机模型

强度退化一般具有随机性和不可逆性,而Gamma过程是一个独立非负的增量过程,具有描述强度退化特性的基本属性。由于强度退化过程中,表征退化状态(磨损、裂纹、腐蚀等)的数据很难直接测量,属于典型的缺失数据,而表征材料疲劳性能的P-S-N曲线一般易于获得。因此,本文假定Gamma过程的形状参数为线性函数,并利用材料的P-S-N曲线对Gamma过程的特征参数进行估计,由此建立基于P-S-N曲线的强度退化随机模型。最后,利用20CrMnTi钢的疲劳试验数据对所建模型的有效性进行验证和分析。结果表明,所建模型能够有效描述材料强度退化的宏观趋势。     

Global modes and superdirective acoustic radiation in low-speed axisymmetric jets

Global linear stability theory is used to study the resonances in a slowly diverging axisymmetric jet. The absolute frequency ω₀ is calculated as a function of slow axial position X , and analytic continuation into the complex X -plane allows a saddle point in ω₀ to be identified. A key element in the analysis is the approximation of ω₀(X) by rational functions which identifies a well-defined saddle point and leading-order global frequency. A preferred-mode Strouhal number, S_D=0.44 , is calculated which compares well with existing experimental values. The global frequency has negative imaginary part and the jet is interpreted as being marginally globally stable, so that forcing in the vicinity of the resonance frequency produces a large response above background, rather like that of a slightly damped linear oscillator. The axial shape of the global-mode amplitude is Gaussian and yields a superdirective acoustic field.     

Nonlinear dynamics between two differentially heated vertical plates in the presence of stratification

We consider the numerical simulation of the flow between infinite, differentially heated vertical plates with positive stratification. We use a two-dimensional Boussinesq approximation, with periodic boundary conditions in the vertical direction. The relative stratification parameter ${\gamma=(\frac{1}{4}Ra S)^{1/4}}$ , where Ra is the Rayleigh number and S the adimensional stratification, is kept constant and equal to 8. The Prandtl number is 0.71. We derive a complex Ginzburg-Landau equation from the equations of motion. Coefficients are computed analytically, but we find that the domain of validity of these coefficients is small and rely on the numerical simulation to adjust the coefficients over a wider range of Rayleigh numbers. We show that the Ginzburg-Landau equation is able to accurately predict the characteristics of the periodic solution at moderate Rayleigh numbers. Above the primary bifurcation at Ra = 1.63 × 10⁵, the Ginzburg-Landau model is found to be Benjamin-Feir unstable and to be characterized by modulated traveling waves and phase-defect chaos, which is supported by evidence from the DNS. As the Rayleigh number is increased beyond Ra = 2.7 × 10⁵, nonlinearities become strong and the flow is characterized by cnoidal waves.     

Influence of rotatory inertia and transverse shear on stochastic instability of the cross-ply laminated beam

The stochastic instability problem associated with an axially loaded cross-ply laminated beam is formulated. The effects of shear deformation and rotatory inertia are included in the present formulations. The beam is subjected to time-dependent deterministic and stochastic forces. By using the direct Liapunov method, bounds for the almost sure instability of beams as a function of viscous damping coefficient, variance of the stochastic force, ratio of principal lamina stiffnesses, shear correction factor, number of layers, mode numbers and geometrical ratio, are obtained. Numerical calculations are performed for the Gaussian process with a zero mean and variance σ² as well as for harmonic process with an amplitude A.     

Asymptotics of the Solutions of the Random Schrödinger Equation

We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then the Fourier transform \({\hat\zeta_\epsilon(t,\xi)}\) of the appropriately scaled solution converges point-wise in ξ to a stochastic complex Gaussian limit. On the other hand, when the two-point correlation function decays slowly, we show that the limit of \({\hat\zeta_\epsilon(t,\xi)}\) has the form \({\hat\zeta_0(\xi){\rm exp}(iB_\kappa(t,\xi))}\) where B _κ (t, ξ) is a fractional Brownian motion.     

Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil

The effects of asymmetric sinusoidal motion on pitching airfoil aerodynamics were studied by numerical simulations for 2-D flow around a NACA0012 airfoil at Re=1.35×10⁵. Various unsteady parameters (amplitude of oscillation, d; reduced frequency, k) were applied to investigate the effect of asymmetry parameter S on the instantaneous force coefficients and flow patterns. The results reveal that S has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficient, maximum lift and drag coefficient, hysteresis loops and the flow structures.     

Evolutionary behavior of induced discontinuities behind one dimensional shock waves in non-linear elastic materials

The governing differential equation of induced discontinuities behind one dimensinal shock waves in non-linear elastic materials has been derived. This equation depends, in particular, on the shock amplitude itself. Therefore, its solution depends on the solution of the governing equation of the shock amplitudes which, in turn, depend on the induced discontinuities. It is shown in the special case pertaining to a first-order approximation that there exists a critical shock amplitude S _c such that the evolutionary behavior of the induced discontinuities depends on the relative magnitudes of the shock amplitudes and S _c. However, in the special case pertaining to a second-order approximation the evolutionary behavior of the induced discontinuities is monotone.     

Transient heat and mass transfer in a natural circulation loop

Comprehensive work has been performed by theoretical and numerical methods in order to study the steady state, transient and stability characteristics of a double diffusive natural circulation loop. It was found that the behavior of the flow in the system depends on the initial conditions and on the location of the state in the seven-parameter space of the thermal and saline Rayleigh numbers,Ra _T ,Ra _S , the modified Prandtl and Schmidt numbers,Pr, Sc, the dimensionless heat and mass transfer coefficients,H _T ,H _S , and the “aspect ratio” (between the height and width) of the loop, γ. Numerical results are presented here, showing the flow in each of the five regions formed in the stability chart. The steady state solutions include convection (constant velocity flow), conduction (no-flow) and periodic with constant amplitude and frequency. Two main new results were obtained: long term periodic oscillations where the amplitude is not symmetric around the conduction solution, and an overshoot of the velocity in transients before reaching the stable convection solutions. In the monotonic instability region of the conduction solution, convection solutions (constant velocity flow) develop, and in the global stability region the flow decays to the conduction solution (no flow), regardless of the initial conditions.     

Effect of flow regime change from subsonic to transonic on the air loads of an oscillating airfoil

In this research, the effect of flow regime change from subsonic to transonic on the air loads of a pitching NACA0012 airfoil is investigated. To do this, the effect of change in flow regime on the lift and pitching moment coefficients hysteresis cycles is studied. The harmonic balance approach is utilized for numerical calculation due to its low computational time. Verifications are also made with previous works and good agreements are observed. The assessment of flow regime change on the aforementioned hysteresis cycles is accomplished in the Mach number range of M=0.65–0.755. The reduced frequency and pitch amplitude also vary from k=0.03 to 0.1 and α₀=1–2.51°, respectively. Results show that the effect of increase in Mach number is to increase and decrease the lift coefficient during downstroke and upstroke, respectively, whereas at low reduced frequencies, the effect of increase in Mach number may lead to a reverse manner when airfoil moves toward its extremum angle of attack. Results also reveal that as the pitch amplitude varies, the shape of lift coefficient hysteresis cycle depends more on the pitch amplitude than on the appearance of shock. It is shown that as the Mach number increases, the incidence angles correspond to the extremum pitching moment, and depending on the reduced frequency, lie between zero and extremum angle of attack. These incidence angles shift toward the extremum angle of attack as the reduced frequency decreases. Results also show that the increase in pitch amplitude at low Mach number, in such a way that leads to the formation of shock around the extremum angle of attack, causes the extremum pitching moment to appear around these angles and at high Mach number, depending on the reduced frequency, the extremum pitching moment incidence angles would be between zero and extremum incidence angle.