Dynamic Behavior of Stay Cables with Rotational Dampers

Vibration reduction in stay cables by means of viscous dampers is of great interest in cable damage prevention and serviceability of structural system supported by such cables. The paper presents a study on the effectiveness, as well as the limits, of rotational viscous dampers and springs inserted at the two ends of a bending-stiff taut cable; influence of rotational stiffness of the springs is also investigated. After a nondimensional expression of the equation of motion has been obtained, as in other cases of nonproportionally damped continuous structures, complex modal analysis is pursued, obtaining complex eigenvalues and eigenfunctions. Comparison with intermediate dampers, widely used in bridge engineering, is performed showing the range of nondimensional parameters for which the proposed approach is of interest. Finally, a numerical technique based on complex mode superposition is presented in order to evaluate time domain responses for transversal distributed excitation. As an example, the procedure is applied to a wind-exposed cable.     

Nonlinear Vibration of Composite Shell Subjected to Resonant Excitations

Analysis of the vibration of a shallow, simply supported, nonsymmetric unbalanced cross-ply laminated, circular cylindrical composite shell is presented. The subject is particularly relevant, considering the widespread use of cylindrical shell structures in engineering applications. This research applies the discretized Lagrangian∕method of multiple scales solution technique. The Donnell shallow shell strain-displacement relations and the single-mode displacement field from the linear eigenvalue problem are applied. The system Lagrangian is developed and integrated over the spatial domain and then substituted into Lagrange's equation. The resulting equation of motion is a second-order temporally nonlinear ordinary differential equation in the form of the Duffing oscillator. The natural frequency, the coefficient of the cubic nonlinearity, and the strength of the nonlinearity are investigated. The method of multiple scales is applied to the nonlinear equation of motion in order to analyze the frequency response. Primary resonance, subharmonic resonance, and superharmonic resonance are analyzed.     

Response of an Elastic Structure Subject to Air Shock Considering Fluid-Structure Interaction

Shock-wave interaction with an elastic structure is investigated using a coupled numerical analysis approach, which considers solid-fluid interaction within an arbitrary Lagrangian-Eulerian framework. The analysis is performed considering a compressive shock wave, where the shock front is followed by constant pressure. An analysis procedure, which considers the change in the fluid domain due to the deformation of the solid and changes in the overpressure due to the movement of the elastic structure, is developed. Approximate numerical procedures for solving the Riemann problem associated with the shock are implemented within the Godunov finite volume scheme for the fluid domain. The influences of parameters such as structural stiffness and mass of the system on the displacement, velocity, and energy of the elastic structure following the shock-wave incidence are investigated. Immediately after the contact of the shock wave with the solid surface the pressure at the face of the elastic solid rises to a value which is equal to that obtained off of a fixed rigid wall. Subsequently, the motion of the piston produces changes in the applied pressure. The overpressure applied to the elastic system does not have a fixed profile but it depends on its elastic stiffness and structure mass. It is shown that there is a continuous exchange of energy between the air and the moving elastic structure, which produces a damped motion of the solid. The effect of damping is considerable for the cases of low elastic stiffness and low structural mass, where the resulting motion of the solid is nonoscillatory. The conventional analysis procedure, which ignores the energy exchange between the air and the moving solid, predicts an undamped oscillatory response of the structure for all cases considered. It is shown that neglecting the interaction between the air and solid can produce significant error in the total energy of the structure and the dynamic load factor when the resulting motion is nonoscillatory.     

Analysis of Class of Nonlinear System under Deterministic and Stochastic Excitations

In this paper, some analysis techniques of nonlinear dynamics are applied to physical systems which may be modeled by the Duffing nonlinear differential equation. The response of the Duffing oscillator to both deterministic sinusoidal and stochastic loadings is investigated and distinct regimes of the response motion are discerned and discussed. The stochastic input to the system is low-pass Gaussian white noise. The efficacy of studying the variation in time of the probability density of one or more of the system output states to determine the type of motion of the system is examined. Attractors in phase space are defined via Poincaré mapping and bounds on motion which serve as signatures for particular types of motion (e.g., chaotic, periodic) are identified by a hypervolume measurement technique. An accepted method for adapting one measured output state into a higher dimensional space by using time-delayed coordinates is used in conjunction with correlation dimension calculation to supply a lower-bound estimate of the fractal dimension and insight into the character of the motion of a nonlinear dynamic system.     

Nonlinear Dynamics of a Harmonically-Excited Inelastic Inverted Pendulum

Issues of dynamic stability for a single-degree-of-freedom system subjected to a time-varying axial load are presented. The linearized differential equation of motion for the model structure is given by the well-known Mathieu equation. Parametric resonance leading to dynamic instability is known to occur for such a system. This paper examines the response of the geometrically exact model for two inelastic constitutive models—an elastic-perfectly plastic model and a cyclic Ramberg-Osgood model. Damage evolution, represented by degradation of the elastic stiffness, is also considered. Analysis results demonstrate behavior that is counterintuitive to what would be expected under static or monotonic loading conditions. Though simple, this structural model helps illustrate the complex features in the response of an inelastic dynamical system.     

Probabilistic Solutions to Nonlinear Random Ship Roll Motion

The probability density function (PDF) and the mean up-crossing rate of the responses for nonlinear ship roll oscillations excited by random sea waves are examined. The excitation of random sea waves is approximated as white noise. The ship roll motion is described by a nonlinear stochastic differential equation that includes a nonlinear wave drag force and a nonlinear restoring moment. The PDF and mean up-crossing rate solution of the nonlinear oscillator are investigated with a new approximate method that expressed the PDF as an exponential function with an exponent in the form of a polynomial in the response variable and its derivative. A special measure is taken such that the Fokker-Planck-Kolmogorov equation is satisfied in the weak sense of integration with the assumed PDF. Numerical examples and a comparison with Monte Carlo simulation are given to show the effectiveness of the method in the study of randomly excited nonlinear ship roll motion.     

1D Time-Domain Solution for Seismic Ground Motion Prediction

A full time-domain solution for predicting earthquake ground motion based on the 1D viscoelastic shear-wave equation is presented. The derivation results in a time-domain equation in the form of an infinite impulse response filter. A solution in the time domain has several advantages including causality, direct modeling of impulsive and transient processes, and ease of inclusion of nonlinear soil behavior. The method is applicable to any arbitrarily layered silhouette presented as SH-wave velocity, damping coefficient, and mass density profiles for designated soil intervals. For nonlinear evaluations, an equivalent-linear formulation is incorporated and the standard modulus and damping degradation curves become part of the input set. Input motion can be either rock-outcrop or body-wave motions measured or estimated at the bottom of the geologic profile, and the output is the estimated ground motion time history. Application of the method to vertical array strong motion records from Garner Valley, and Wildlife Site, Calif., shows that predicted surface (and interval) ground motion is virtually identical to that measured. The differences between the results of linear and nonlinear analyses are negligible for most cases. A comparison of the time-domain model with SHAKE shows that SHAKE fails to accurately predict time histories in some situations, whereas the time-domain solution always yields satisfactory predicted surface ground motions.     

Human Jumping and Bobbing Forces on Flexible Structures: Effect of Structural Properties

The behavior of humans jumping and bobbing on flexible structures has become a matter of some concern for both structural integrity and human tolerance. The issue is of great importance for a number of structure types including stadia terraces. A unique test rig has been developed for exploring the forces, accelerations, and displacements that occur when a human subject jumps or bobs on a flexible structure where motion can be perceived. In tests reported earlier, it was found that the subject is able to generate near resonant structural response but it is extremely difficult, if not impossible, to jump or bob at or very near to the natural frequency of the structure when its vertical motion is significant. Also, under such near-resonant conditions, the force developed by the subject was found to drop significantly. In this paper, the effect of altering the subject-to-structure mass ratio and the damping ratio of the structure on these phenomena is presented. As would be expected, it is shown that as the structure becomes more massive and more highly damped it moves less for nominally the same excitation. In this situation, it becomes easier to jump and bob near to resonance and the degree of force dropout reduces, although it is still significant for even the most massive and highly damped case considered. A method for including these effects of human-structure interaction in a load model for dynamic response calculations is then proposed.     

Mathematical Formulation and Validation of a Mixed Finite Element–Finite Difference Model for Simulating Phreatic Surfaces

The phreatic surface in an unconfined aquifer exists as a movable interface between the saturated and unsaturated zones. The movement of the phreatic surface depends on recharge, hydraulic conductivity, porosity, and horizontal and vertical flows. The location of the phreatic surface helps define the variably saturated flow domain in the subsurface. The variably saturated flow process in the subsurface is described by a parabolic partial differential equation. In this equation, the hydraulic conductivity and soil moisture capacity are used as the subsurface characteristics. The location of the phreatic surface is governed by a first-order partial differential equation. The governing parabolic partial differential equation is solved using a variational finite element formulation. The first order phreatic surface equation is then solved by loosely coupling with the governing parabolic partial differential equation describing the variably saturated flow. In the present study, a two-dimensional space is used to investigate the movement of the phreatic surface in a variably saturated unconfined flow domain. Based on the time-varying solutions of hydraulic heads, the location of the phreatic surface is simulated in a finite two-dimensional space.     

Considerations of Multimode Structural Response for Near-Field Earthquakes

This paper presents an investigation of multimode effects of tall buildings idealized as a continuous shear-beam model subjected to near-field pulse-like ground motion. The investigation is based on three analytical approaches: a damped wave solution approach, a fundamental-mode approach, and a modal summation approach. In the modal summation approach, all modal damping ratios are assumed to be equal and a set of Green’s functions for the shear strain response is explicitly derived. The multimode effects on the base-level shear strain/force demands are compared by using an effective response spectrum for shear-beam systems. The study results show that the occurrence of major spectral differences is conditioned on the ratio of the fundamental structural period to the duration of the predominant excitation pulse. Seismic analyses for a set of recorded near-field earthquake data indicate a strong correlation between the characteristics of effective response spectra and the ground pulse parameters.     

增量型AGC模型稳定性研究

采用误差分析方法导出增量型自动厚度控制(AGC)模型设定序列的差分方程.根据该差分方程的特征值表达式讨论了AGC模型设定序列的稳定区域和稳态误差与AGC模型参数之间的关系.     

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.     

Numerical Modeling of Contaminant Transport through Soils: Case Study

This paper presents the development and validation of a numerical model for simulation of the flow of water and air and contaminant transport through unsaturated soils. The governing differential equations include two mass balance equations for the water phase and air phase together with a balance equation for contaminant transport through the two phases. In the model the nonlinear system of the governing differential equations was solved using a finite-element method in the space domain and a finite difference scheme in the time domain. The governing equation of the miscible contaminant transport including advection, dispersion-diffusion and adsorption effects are presented. The mathematical framework and the numerical implementation of the model are described in detail. The model is validated by application to standard experiments on contaminant transport in unsaturated soils. The application of the model to a case study is then presented and discussed. Finally, the merits and limitations of the model are highlighted.     

On a stochastic theory of grain growth

A theory of isothermal grain growth in polycrystalline solids, which treats grain growth as a statistical or stochastic process, is presented. In this treatment deterministic equation for the rate of grain growth is made stochastic by the addition of a “noise” term. The noise or fluctuations are used to model the effect of complex topologically connected structure of the specimen on grain boundary motion, in addition to such motion directed by surface tension forces. Such considerations lead to a second order partial differential equation (Fokker-Planck equation) for the grain size distribution. Many of the major attributes of grain growth are shown to be a natural consequence of this equation. The solution obtained for this equation is a modified form of Rayleigh distribution which in many respects is similar of log normal distribution. Grain size distribution is also obtained from independent statistical consideration and is shown to be approximately log normal. Extension of the mathematical analysis to the case of Ostwald ripening is indicated.     

Generalization of behavioral and psychostimulant treatment of attention-deficit/hyperactivity disorder (ADHD): discussion and examples

Assessment and treatment of attention-deficit/hyperactivity disorder (ADHD) are reviewed in order to highlight the importance of examining individual differences in treatment response. It is emphasized that treatment response in children often varies as a function of the domain measured, the setting evaluated, and intensity of the treatment. Three case studies are presented to illustrate this point. The first case study is an example of a child who showed a consistent response to medication across settings and domains and treatment intensities. The second case study is an example of a child who showed differential treatment response as a function of setting and/or treatment intensity, but was consistent across domain. The third case study is an example of a child who showed a differential response to treatment as a function of domain, but was consistent across settings and treatment intensities. These case studies highlight the need for systematic, comprehensive, individualized treatments for children with ADHD.     

高炉焦炭负荷的分布规律

 焦炭负荷和焦炭在风口前的失碳率随着煤比的提高而增大,而焦炭强度则随着失碳率的提高而降低,因而焦炭在高炉内各部位所承受的压力,成为进一步研究极限煤比的基础。根据高炉炉料的散料特性,采用微元平衡法,对散料体中的任意微元体应用守恒定律,建立连续方程和运动方程,并结合状态方程,建立二维炉料压力数学模型。然后采用数值差分法对流函数和压力函数进行差分推导,设定流场和压力场的边界条件,对高炉内各点进行迭代计算,并用VC++进行程序代码设计得出了压力场分布规律。     

Response of Damped Oscillators to Cycloidal Pulses

In this paper, the transient response of a damped oscillator subjected to cycloidal pulses is investigated. The response is computed analytically by considering viscous and friction damping, and response spectra for relative and absolute quantities are presented for the linear viscous and sliding oscillator. The study complements the list of numerous shock spectra mostly published for the undamped linear oscillator. Subsequently, a numerical procedure based on a state-space formulation is developed to compute the response of damped oscillators when subjected to ground motions recorded near the source of strong earthquakes. It is found that although in several occasions such motions resemble to cycloidal pulses, the response of structures with low to moderate periods is substantially affected by the high-frequency fluctuations that often override the long duration pulse.     

Site-Specific Validation of Random Vibration Theory-Based Seismic Site Response Analysis

Seismic site response analysis is typically performed using a suite of rock acceleration-time histories prescribed at the base of a soil column and propagated to the ground surface. To develop statistically stable estimates of the site response, a large number of input motions are required. Alternatively, random vibration theory (RVT) can be used to predict statistically stable estimates of the surface response spectrum in one analysis without the need to prescribe the input rock motion in the time domain. Thus, the critical and time consuming activity of choosing appropriate input ground motions and fitting them to a target spectrum is avoided. This paper describes the RVT approach, its analytical background and input requirements, and provides a site-specific validation of the procedure against traditional site response predictions. The single-corner frequency Brune source spectrum is used in the RVT procedure to describe the input motion in the frequency domain. RVT site response predictions using the Brune spectrum as input are compared with those from traditional site response analyses that incorporate different suites of input rock motions. Results indicate that RVT site response analysis can provide a response spectrum that is similar to the median response spectrum from analyses performed using a suite of input rock motions. However, the favorable comparison is obtained only when the seismological parameters used to describe the RVT input motion are carefully chosen to be consistent with the suite of input rock motions.     

Moment Equation Analysis of Base-Isolated Buildings Subjected to Support Motion

The stationary response of base-isolated buildings subjected to support motion is studied. The isolation device consists of a friction device, while the ground motion is assumed to be a stationary Gaussian white noise random process. The moment equation approach is preferred in this study to characterize the structural response statistically. A non-Gaussian closure is adopted to reveal the degree of non-Gaussianness of the response. The proposed approach is compared with the stochastic equivalent linearization and the numerical simulation, resulting in more accuracy when predicting the moments of the response which is markedly non-Gaussian. The models of cascaded and coupled system for the base isolator and the building are also compared, finding the former to be quite in error.