Winkler地基上有限长梁联合共振分析

为进一步完善弹性地基上梁的非线性振动理论以及满足实际工程的需要,本文对三种联合共振情况进行了研究。文中基于已建立的Winkler地基上有限长梁的非线性振动方程,运用Galerkin离散法以及多尺度法推导其稳态运动方程组,分析了主/次联合共振时,结构参数及初始条件对系统幅频响应曲线、调谐-相位曲线的影响,初步探讨了主/超联合共振、次/超联合共振的基本性质。研究结果表明:当且仅当两个激励频率是可公度关系时,联合共振才存在稳态响应;对于一个给定的调谐参数,系统最多存在七个解,而解的最终形式是由初始条件决定;系统参数及初始条件的微小变动,可能会激烈地改变系统的响应;工程中为了较好地抑制结构的振动,必须选择合适的方法提高系统的刚度。     

Incremental time—space finite strip method for non-linear structural vibrations

Based on an incremental Hamilton's principle a versatile and systematic computer method for analysing non-linear structural vibrations is developed in this paper. The essence of the proposed method can be regarded as an incremental harmonic balance method associated with a finite strip procedure in the time-space domain. Only linearized equations in terms of frequency increment, amplitude increments, etc. have to be formulated and solved in each incremental step. This method is applicable to highly non-linear problems and may be generalized to related non-linear periodic structural motions such as dynamic stability, flutter and some motions of a rotating body, etc. To show the effectiveness and versatility of this method, a typical time-space finite strip for beam problems is worked out and examples for a wide variety of vibration problems including free and forced vibrations, super- and sub-harmonic resonances, and complicated phenomena such as internal resonance are computed. Comparisons with previous results are also made.     

Verification of two-dimensional non-linear analysis of sand-structure system by examining the results of the shaking-table test

The verification of a two-dimensional non-linear analysis based on a hybrid constitutive model, which consists of the Ramberg-Osgood model extended to two-dimensional problems and a dilatancy model, is discussed through a comparison of the shaking-table test results for a one-storey structure standing on a dry sandy deposit with those for the same on a saturated sandy deposit. Since the relationships G vs. γ and h vs. γ for shear strains of 10^?5?10^?3 can be obtained accurately by an inversion analysis of the resonance curve of the sandy deposit the proposed non-linear method can represent well the observed non-linear response of the dry or the saturated sandy deposit including the structure. This method, however, should be applied carefully to assess the response of a soil-structure system when the three-dimensional interaction affects significantly the response of the model. An equivalent linear analysis using a sway-rocking model is applied to simulate the non-linear ground motion including the three-dimensional interaction, and it is found that the sway-rocking model can also represent well the non-linear response of the system.     

Continuous pulse control of structures with material non-linearity

A control method is presented for reducing the dynamic response of structures in the inelastic material range using a control force from an active bracing system. Recent full-scale experiments have verified the feasibility of implementing active control systems for control of seismic structures with existing technology. The proposed method of continuous pulse control uses closed-loop feedback control as a combination of two algorithms. The first is the instantaneous optimal algorithm which was derived assuming linear material behaviour, and the second is pulse control which applies a corrective pulse when a prespecified structural displacement, velocity, or acceleration threshold is exceeded. The three criteria of displacement, velocity, and acceleration lead to three pulse control schemes. Each of the three schemes is used in conjunction with the instantaneous optimal control to yield three continuous pulse algorithms, the displacement continuous pulse, velocity continuous pulse and acceleration continuous pulse. Comparisons between the three continuous pulse algorithms and the pulse control for seismic structures in the inelastic range show that the continuous pulse algorithms use less control energy and reduce the response better than pulse control. A comparison between the velocity continuous pulse and the non-linear optimal algorithm shows that the velocity continuous pulse uses a larger control force but is more adaptable than the non-linear optimal algorithm, in the sense that it can reduce the response of a given structure to various probable earthquakes. The non-linear optimal algorithm is more effective than the velocity continuous pulse for a single specific earthquake but is not as effective for other earthquakes which may occur in the life of the structure.     

Is a chaotic multi‐fractal approach for rainfall possible?

An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381–2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono‐fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi‐fractal approaches. The assumption behind multi‐fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi‐fractals. However, it has been observed recently that multi‐fractal approaches might provide positive evidence of a multi‐fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi‐fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi‐fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi‐fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi‐fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessment of the seismic non-linear behavior of ductile wall structures due to synthetic earthquakes

In this paper, different methods for generating synthetic earthquakes are compared in terms of related non-linear seismic response of ductile structures. The objective of the investigation is to formulate recommendations for the use of synthetic earthquakes for reliable seismic analysis. The comparison is focused on the accuracy of the reproduction of the characteristics of the structural non-linear response due to recorded earthquakes. First the investigations are carried out for non-linear single-degree-of-freedom systems. Later, the results are validated for a set of realistic buildings modelled as multi-degree-of-freedom systems. Various options of the classical stationary simulation procedure of SIMQKE and a non-stationary simulation procedure proposed by Sabetta and Pugliese are examined and compared. The adopted methodology uses a set of recorded earthquakes as a reference. Hundred synthetic accelerograms are generated for each examined simulation option with the condition that the related elastic responses are similar to those of the reference set. The non-linear single-degree-of-freedom systems are defined using six recognized hysteretic models and four levels of increasing non-linearity. The non-linear responses computed for the reference set and the studied simulation options are then statistically compared in terms of displacement ductility and energy. The results show that the implementation of the classical stationary procedure always leads to a significant underestimation of the ductility demand and a significant overestimation of the energy demand. By contrast, non-stationary time histories produce much better results. The results with the multi-degree-of-freedom systems are shown to confirm these conclusions.     

Temporal scaling in river flow: can it be chaotic? / L’invariance d’échelle de l’écoulement fluvial peut-elle être chaotique?

Abstract

Abstract Identification of the presence of scaling in the river flow process has been a challenging problem in hydrology. Studies conducted thus far have viewed this problem essentially from a stochastic perspective, because the river flow process has traditionally been assumed to be a result of a very large number of variables. However, recent studies employing nonlinear deterministic and chaotic dynamic concepts have reported that the river flow process could also be the outcome of a deterministic system with only a few dominant variables. In the wake of such reports, a preliminary attempt is made in this study to investigate the type of scaling behaviour in the river flow process (i.e. chaotic or stochastic). The investigation is limited only to temporal scaling. Flow data of three different scales (daily, 5-day and 7-day) observed in each of three rivers in the USA: the Kentucky River in Kentucky, the Merced River in California and the Stillaguamish River in Washington, are analysed. It is assumed that the dynamic behaviour of the river flow process at these individual scales provides clues about the scaling behaviour between these scales. The correlation dimension is used as an indicator to distinguish between chaotic and stochastic behaviours. The results are mixed with regard to the type of flow behaviour at individual scales and, hence, to the type of scaling behaviour, as some data sets show chaotic behaviour while others show stochastic behaviour. They suggest that characterization (chaotic or stochastic) of river flow should be a necessary first step in any scaling study, as it could provide important information on the appropriate approach for data transformation purposes.     

Non-linear steady state vibration and dynamic snap through of shallow arch beams

The non-linear steady state vibration of shallow arch beams is studied by a finite element method based on the principle of virtual work. Both the free and forced periodic vibrations are considered. The axial and flexural deformations are coupled by the induced axial force along the beam element. The spatial discretization is achieved by the usual finite element method and the steady state nodal displacements are expanded into a Fourier series. The harmonic balance method gives a set of non-linear algebraic equations in terms of the vibrating frequency and the Fourier coefficients of nodal displacements. The non-linear algebraic equations are solved by the Newtonian algorithm iteratively. The combined algorithm is called the incremental harmonic balance method. The importance of the conditions of completeness and balanceability is presented. Since the non-linearity is essentially softening, different orders of internal resonances between two modes can occur repeatedly. Isolated response curves are possible and are connected to the bifurcation of a particular excited mode.     

Deterministic uncertainty in landscapes

Deterministic complexity (chaos) may be common in geomorphic systems, but traditional definitions may have limited practical utility for empirical geomorphology. These definitions are based on sensitivity to initial conditions, which in geomorphology are both unknown and unknowable. Further, chaos analysis depends on distinguishing deterministic complexity from stochastic complexity. This is problematic in geomorphology because some stochastic complexity is virtually always present in addition to any chaos that may be present. While it is important to recognize that some complex, apparently random patterns may derive from inherent non-linear system dynamics, this is of limited use in explaining process–response relationships or mechanics of landscape evolution. A more general term, which subsumes chaos, is deterministic uncertainty, i.e. uncertainty associated with an identifiable but unknown or uncertain source. An analysis of landscape entropy shows that such underlying constraints produce spatial patterns which are apparently chaotic. For the case of geologic controls, the apparent contribution of deterministic chaos to the landscape entropy is a direct non-linear function of the extent of geologic constraints. However, the underlying constraints and their contribution to observed spatial patterns can also be interpreted in non-chaotic terms. Examples are given, involving geologic constraints on stream channel networks and parent material control of surface soil textures. Because both randomness and chaos may be more apparent than real, the concept of deterministic uncertainty is more useful in process geomorphology than that of chaos.     

Seismic resonances of spherical acoustic cavities

We study the interaction of a seismic wavefield with a spherical acoustic gas‐ or fluid‐filled cavity. The intention of this study is to clarify whether seismic resonances can be expected, a characteristic feature that may help in detecting cavities in the subsurface. This is important for many applications, in particular the detection of underground nuclear explosions, which are to be prohibited by the Comprehensive Test Ban Treaty. To calculate the full seismic wavefield from an incident plane wave that interacts with the cavity, we considered an analytic formulation of the problem. The wavefield interaction consists of elastic scattering and the wavefield interaction between the acoustic and elastic media. Acoustic resonant modes caused by internal reflections in the acoustic cavity show up as spectral peaks in the frequency domain. The resonant peaks coincide with the eigenfrequencies of the un‐damped system described by the particular acoustic medium bounded in a sphere with stiff walls. The filling of the cavity could thus be determined by the observation of spectral peaks from acoustic resonances. By energy transmission from the internal oscillations back into the elastic domain, the oscillations experience damping, resulting in a frequency shift and a limitation of the resonance amplitudes. In case of a gas‐filled cavity, the impedance contrast is still high, which means low damping of the internal oscillations resulting in very narrow resonances of high amplitude. In synthetic seismograms calculated in the surrounding elastic domain, the acoustic resonances of gas‐filled cavities show up as persisting oscillations. However, due to the weak acoustic–elastic coupling in this case, the amplitudes of the oscillations are very low. Due to a lower impedance contrast, a fluid‐filled cavity has a stronger acoustic–elastic coupling, which results in wide spectral peaks of lower amplitudes. In the synthetic seismograms derived in the surrounding medium of fluid‐filled cavities, acoustic resonances show up as strong but fast decaying reverberations.     

An incremental mode-superposition for non-linear dynamic analysis

This paper uses an incremental mode-superposition procedure to compute the inelastic dynamic response of multi-degree-of-freedom systems. A damping matrix proportional to the instantaneous properties is used throughout the analysis. The non-linear response of several shear type plane and space frames with elastic-plastic and bilinear column properties subjected to ground excitation was computed by both the incremental mode-superposition and the direct integration of the coupled equations of motion. When all modes are considered, the responses computed by the incremental mode-superposition are identical to those from the direct integration. Fewer modes can also be used to compute the response with reasonable accuracy by performing the modal truncation for each time increment. The study shows that incorporating instantaneous damping in non-linear dynamic analysis is relatively simple and requires less computational time than the direct integration.     

Alfvén intermittency in space plasmas

The onset of Alfvén intermittent chaos in space plasmas is studied by numerically solving the derivative non-linear Schrödinger equation (DNLS) under the assumption of stationary Alfvén waves. We describe how the Alfvénic fluctuations of the magnetic field can evolve from periodic to chaotic behavior through a sequence of bifurcations as the plasma dissipation is varied. The collision of a chaotic attractor with an unstable periodic orbit leads to the generation of strongly chaotic behavior, in an event known as interior crisis. We also show that in the DNLS equation, chaotic attractors coexist with nonattracting chaotic sets responsible for transient chaotic behaviors. After the interior crisis point, a wide chaotic attractor can be decomposed into two coupled nonattracting chaotic sets, resulting in intermittent chaotic time series. Understanding transient chaos is a key to understand intermittency in space plasmas.     

基础隔震结构的耗能分析

采用Bouc-wen模型,利用状态空间迭代法,对基础隔震结构进行了多质点的弹塑性时程分析,并根据此结果,利用能量方程,求得隔震结构的各项能量,绘制了各能量项时程曲线。以一实际工程为例,求得隔震结构的各项耗能情况,说明了基础隔震结构以减少地震输入和隔震层滞回耗能来减小对上部结构的损坏。     

Coupling between waveguide modes and field line resonances

WKBJ methods are often used to study the excitation of waveguide modes and field line resonances in the magnetosphere. In this paper, these methods are used to study the nature of the reflection and transmission process at a turning point when conditions are favourable for strong excitation of the field line resonance. The accuracy and region of validity of such WKBJ solutions are discussed. In regions where they are not valid, a series solution of the relevant equations is given. The wave fields can be found to great accuracy by matching WKBJ solutions across the turning point and resonance using this series solution. This allows the calculation of the Stokes constant which does not show Airy function behaviour as often assumed. The Stokes constant is effectively a reflection coefficient referred to the turning point. Its phase, when the transmission to the resonance is strong, is nearer to 180° than 90° as often assumed. Its magnitude allows the fraction of incident energy which is transmitted to the resonance to be calculated. These results are expected to be useful in studying the behaviour of waveguide modes.     

双线性单自由度体系强迫动力反应的Hilbert谱与本征振动模态:输入简谐波频率的影响

系统地研究了双线性单自由度体系在简谐波输入下表现出非线性力学行为时,输入简谐波频率对体系动力响应的Hilbert谱、Hilbert边缘谱及Fourier幅值谱的影响.研究结果表明,如果体系输入简谐波频率为f,那么体系动力响应Hilbert边缘谱的能量分布在f附近一个较宽的频带上,该频带的产生是体系动力响应Hilbert谱中所蕴含的波内调制的必然结果,它源自于体系某个本征振动模态瞬时频率的波动,而这种瞬时频率的波动描述了体系屈服与卸载的非线性力学行为;体系动力响应的Fourier幅值谱自3f起,每隔2f就会出现一个幅值明显高出周围其它分量的Fourier“伪”谐波分量,这也是体系非线性力学行为所造成的结果.     

Chaotic axisymmetrical spherical convection and large-scale mantle circulation

This paper presents a study of high Rayleigh number (up to 200 times supercritical) axisymmetrical convection in a spherical shell with an aspect ratio relevant for the Earth's lower mantle. Both bottom-heated and internal heated cases have been considered. Computations have been carried out for an infinite Prandtl number isoviscous fluid with free slip isothermal boundary conditions. The first part of the paper is devoted to the influence of the resolution on the accuracy of the numerical results. It is shown that the resolution strongly influences the onset of time dependence. Recent methods of non-linear physics have been used to prove that the time dependence and the chaotic behaviors of the solutions are real ones. From these results we can confirm that convection is chaotic, in this particular geometry, even for Rayleigh numbers 200 times critical. Aperiodic boundary layer instabilities are found to be incapable of breaking up the large-scale flow, owing to the shear of the global circulation. Spectral analysis of the power associated with the thermal anomalies shows that there is an upward cascade of energy, due to small-scale chaotic instabilities, from l = 2 to l = 4–6 at the bottom boundary, in agreement with new seismic observations at the core-mantle boundary [1–3].     

A study on chaotic behaviour of equatorial/low latitude ionosphere over Indian subcontinent,using GPS-TEC time series

The deterministic chaotic behaviour of ionosphere, over Indian subcontinent falling under equatorial/low latitude region, ?0.3 to 22.19°N (geomagnetic), was studied using GPS-TEC time series. The values of Lyapunov exponent are low at Thiruvananthapuram and Agatti (?0.30 and 2.38°N, geomagnetic, respectively), and thereafter increase through Bangalore and Hyderabad (4.14 and 8.54°N, geomagnetic, respectively), and attain maximum at Mumbai (10.09°N, geomagnetic), which is near/at the edge of an anomaly crest. The values of correlation dimension computed for TEC time series are in the range 3.1–3.6, which indicate that equatorial/low latitude ionosphere can be described with four variables. Entropy values estimated for TEC time series show no appreciable latitudinal variabilites. The values of non-linear prediction error exhibit a trough, around the latitude sector, 4.14–16.15°N (Geomagnetic). Based on the values of the above quantifiers, the features of chaotic behaviour of equatorial/low latitude ionosphere are briefly discussed.     

用随机共振理论解释地震孕育过程与地震发生现象中的一个显著特征

地震孕震体是一个非线性双稳整系统,具备发生随机共振的条件。而地震的孕震过程与发生现为有量输入和大功率的能量输出。本用随机共振理论,解释了这一特征。     

Dynamic behaviour of rocking two-block assemblies

The dynamic behaviour of systems consisting of two blocks, one placed on the top of the other, and free to rock without sliding, is examined in this analysis. The equations of motion for each ‘mode’ of vibration are derived and criteria for the initiation of rocking and the transition between modes are given. During vibration, the system continuously changes from one mode to another and this makes the response non-linear. This transition may be accompanied by impact, in which case dissipation of energy occurs, the amount of which depends on the relative velocities and the dimensions of the blocks. Also, redistribution of the kinetic energy of the system in the blocks happens. In most cases, the fractional contribution from the upper block to the system energy increases, which results in a larger and longer response of the top block, compared to the vibration of the lower one.