考虑弯曲刚度斜拉索面内面外内共振分析

本文研究桥梁工程中含弯曲刚度斜拉索的面内面外内共振问题．描述了工程中斜拉索变形的三种状态,考虑弯曲刚度、大变形及垂度等因素,忽略斜拉索纵向惯性力的影响,运用Hamilton变分原理建立了含弯曲刚度的斜拉索面内面外耦合偏微分控制方程,采用Galerkin方法对偏微分方程离散,并运用多尺度摄动方法进行了求解,获得了斜拉索可能存在的内共振模式,以工程中一根斜拉索为例,运用有限元法对其进行动力特性分析,列出了斜拉索前10阶面内面外振动频率,找出面内面外可能产生内共振的模态,分别研究了主共振条件下斜拉索面内和面外1:1、2:1内共振情形,获得了有意义的结论．     

Random excitation of coupled oscillators with single and simultaneous internal resonances

The primary objective of this paper is to examine the random response characteristics of coupled nonlinear oscillators in the presence of single and simultaneous internal resonances. A model of two coupled beams with nonlinear inertia interaction is considered. The primary beam is directly excited by a random support motion, while the coupled beam is indirectly excited through autoparametric coupling and parametric excitation. For a single one-to-two internal resonance, we used Gaussian and non-Gaussian closures, Monte Carlo simulation, and experimental testing to predict and measure response statistics and stochastic bifurcation in the mean square. The mean square stability boundaries of the coupled beam equilibrium position are obtained by a Gaussian closure scheme. The stochastic bifurcation of the coupled beam is predicted theoretically and experimentally. The stochastic bifurcation predicted by non-Gaussian closure is found to take place at a lower excitation level than the one predicted by Gaussian closure and Monte Carlo simulation. It is also found that above a certain excitation level, the solution obtained by non-Gaussian closure reveals numerical instability at much lower excitation levels than those obtained by Gaussian and Monte Carlo approaches. The experimental observations reveal that the coupled beam does not reach a stationary state, as reflected by the time evolution of the mean square response. For the case of simultaneous internal resonances, both Gaussian and non-Gaussian closures fail to predict useful results, and attention is focused on Monte Carlo simulation and experimental testing. The effects of nonlinear coupling parameters, internal detuning ratios, and excitation spectral density level are considered in both investigations. It is found that both studies reveal common nonlinear features such as bifurcations in the mean square responses of the coupled beam and modal interaction in the neighborhood of internal resonances. Furthermore, there is an upper limit for the excitation level above which the system experiences unbounded response in the neighborhood of simultaneous internal resonances.     

Parametric random excitation of nonlinear coupled oscillators

The stochastic bifurcation and response statistics of nonlinear modal interaction under parametric random excitation are studied analytically, numerically and experimentally. Two basic definitions of stochastic bifurcation are first introduced. These are bifurcation in distribution and bifurcation in moments. bifurcation in moments is examined for the case of a coupled oscillator subjected to parametric filtered white noise. The center frequency of the excitation is selected to be close to either twice the first mode or second mode natural frequencies or the sum of the two. The stochastic bifurcation in moments is predicted using the Fokker-Planck equation together with gaussian and non-Gaussian closures and numerically using the Monte Carlo simulation. When one mode is parametrically excited it transfers energy to the other mode due to nonlinear modal interaction. The Gaussian closure solution gives close results to those predicted numerically only in regions well remote from bifurcation points. However, bifurcation points predicted by the non-Gaussian closure are in good agreement with those estimated by numerical simulation. Depending on the excitation level, the probability density of the excited mode is strongly non-Gaussian and exhibits multi-maxima as predicted by Monte Carlo simulation. Experimental tests are carried out at relatively low excitation levels. In the neighborhood of stochastic bifurcation in mean square the measured results exhibit different regimes of response characteristics including zero motion and occasional small random motion regimes. These two regimes are characterized by the phenomenon of on-off intermittency. Both regimes overlap and thus it is difficult to locate experimentally the bifurcation point.     

随机边界弹性约束空间预应力钢桁架随机内力摄动分析

本文在文献[2]-[4]的基础上,进一步建立了具有任意弹性约束的拉索式空间预应力钢桁架计算模型,其中所有弹性约束均由一组弹簧模拟,在此基础上考虑到边界弹性约束刚度的随机性,进一步建立了拉索式预应力空间钢桁架随机内力摄动分析的计算公式,并针对三角形立体钢桁架进行了分析,为预应力立体钢桁架的可靠性研究奠定了一定的理论基础。     

大型射电望远镜悬挂馈源的风振模拟

基于随机过程理论和数值模拟方法 ,提出了利用 MATL AB软件模拟生成随机风荷的一种新途径。分析了 5 0 0 m口径大型射电望远镜 ( FAST)悬挂馈源结构在随机风荷下的非线性动力响应 ,为设计馈源稳定平台的运动控制范围提供了依据。     

Response of Systems Under Non-Gaussian Random Excitations

The approach of nonlinear filter is applied to model non-Gaussian stochastic processes defined in an infinite space, a semi-infinite space or a bounded space with one-peak or multiple peaks in their spectral densities. Exact statistical moments of any order are obtained for responses of linear systems jected to such non-Gaussian excitations. For nonlinear systems, an improved linearization procedure is proposed by using the exact statistical moments obtained for the responses of the equivalent linear systems, thus, avoiding the Gaussian assumption used in the conventional linearization. Numerical examples show that the proposed procedure has much higher accuracy than the conventional linearization in cases of strong system nonlinearity and/or high excitation non-Gaussianity. An erratum to this article is available at .     

Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input

A method for the evaluation of the probability density function (p.d.f.) of the response process of non-linear systems under external stationary Poisson white noise excitation is presented. The method takes advantage of the great accuracy of the Monte Carlo simulation (MCS) in evaluating the first two moments of the response process by considering just few samples. The quasi-moment neglect closure is used to close the infinite hierarchy of the moment differential equations of the response process. Moreover, in order to determine the higher order statistical moments of the response, the second-order probabilistic information given by MCS in conjunction with the quasi-moment neglect closure leads to a set of linear differential equations. The quasi-moments up to a given order are used as partial probabilistic information on the response process in order to find the p.d.f. by means of the C-type Gram-Charlier series expansion.     

Deterministic and Stochastic Response of Nonlinear Coupled Bending-Torsion Modes in a Cantilever Beam

The purpose of this study is to understand the main differences between the deterministic and random response characteristics of an inextensible cantilever beam (with a tip mass) in the neighborhood of combination parametric resonance. The excitation is applied in the plane of largest rigidity such that the bending and torsion modes are cross-coupled through the excitation. In the absence of excitation, the two modes are also coupled due to inertia nonlinearities. For sinusoidal parametric excitation, the beam experiences instability in the neighborhood of the combination parametric resonance of the summed type, i.e., when the excitation frequency is in the neighborhood of the sum of the first bending and torsion natural frequencies. The dependence of the response amplitude on the excitation level reveals three distinct regions: nearly linear behavior, jump phenomena, and energy transfer. In the absence of nonlinear coupling, the stochastic stability boundaries are obtained in terms of sample Lyapunov exponent. The response statistics are estimated using Monte Carlo simulation, and measured experimentally. The excitation center frequency is selected to be close to the sum of the bending and torsion mode frequencies. The beam is found to experience a single response, two possible responses, or non-stationary responses, depending on excitation level. Experimentally, it is possible to obtain two different responses for the same excitation level by providing a small perturbation to the beam during the test.     

Transport of phosphate in a heterogeneous field

A model for the transport of P in an ensemble of vertical homogeneous columns is given. For a single column, the dimensionless concentration of P sorbed to the solid phase, , as a function of dimensionless depth, is approximated with a piston profile. The velocity of the P-front within a column depends on the application rate of P and the retention capacity of the soil. For a field, represented by an ensemble of columns differing with respect to P applied (A _T ) and retention capacity (F _T ), the field average dimensionless concentration , at fixed depth and time, is related to A _T and F _T using probability theory. F _T and A _T are expressed in terms of easily measured variables: oxalate extractable P and Fe + Al. With the probability density functions of these random variables the field-averaged profile is calculated. Experimental and computed profiles are reasonably in agreement and differences can be explained by assuming correlation of F _T and A _T . A parameter analysis shows the increase in field-scale dispersion if the coefficients of variation of the random variables are increased. Negative correlation of A _T and F _T or a positive correlation of successive applications A _i cause an increase in field-scale dispersion. Trends observed for A _T and F _T must be taken into consideration if the model is used for predictive purposes.Notation of variables and parameters A _T Total amount of phosphate (P) applied [mmol/m²] - A Annually applied amount of P [mmol/m²] - C Covariance - CV Coefficient of variation - D Coefficient of molecular diffusion and hydrodynamic dispersion [m²/yr] - D ^* Effective dispersion coefficient for adsorbing solute, D/R [m²/yr] - E Expectation - F Functional relationship of sorption with time and concentration [mmol/xxx - F _m Maximal sorption based on (Fe + Al) _ox [mmol/xxx - F _T Total sorption capacity for P of soil layer with thickness L [mmol/m²] - K Kolmogorov-Smirnov statistic - L Length of column [m] - M Number of applications - N Number of sample locations - P _m Maximal sorption based on P _ox + P _R [mmol/xxx - P _R Extrapolated measured sorption [mmol/xxx - Q Adsorbed amount [mmol/xxx - R Retardation factor - S Precipitated amount [mmol/xxx - VAR Variance - X Generic notation of a random variable - c Concentration of P in solution [mmol/m³] - c ⁰ Feed solution concentration of P [mmol/m³] - f Probability density function - h Separation vector - l _infD ^supf Field scale dispersivity [m] - m Mean, - m Ratio of means, m/m ^R with m ^R for reference situation - t Time [yr] - t ₁ Period in time between successive applications [yr] - t ^* Time required to dissolve solid P [yr] - v Interstitial water velocity [m/yr] - v ^* Effective interstitial water velocity for adsorbing solute, v/R [m/yr] - Time averaged propagation velocity of front [m/yr] - x, y, z Coordinates [m] - Ratio between P _m and (Fe + Al) _OX - Semivariogram - Dimensionless concentration of P in the solid phase - Variable - Coefficient of correlation - _s Soil bulk density [kg/m³] - Standard deviation, (VAR)^1/2 - Ratio of standard deviations, / _R with _R for reference situation - Total time [yr] - Volumetric water content - Coordinate [m] - Dimensionless depth - _p Dimensionless front penetration depth