State Space Formulation for Linear Viscoelastic Dynamic Systems with Memory

A dynamic system with memory is a system for which knowledge of the equations of motion, together with the state at a given time instant t0 is insufficient to predict the evolution of the state at time instants t>t0. To calculate the response of systems with memory starting from an initial time instant t0, complete knowledge of the history of the system for t相似文献   

Multivariate Extreme Value Distributions for Random Vibration Applications

The problem of determining the joint probability distribution of extreme values associated with a vector of stationary Gaussian random processes is considered. A solution to this problem is developed by approximating the multivariate counting processes associated with the number of level crossings as a multivariate Poisson random process. This, in turn, leads to approximations to the multivariate probability distributions for the first passage times and extreme values over a given duration. It is shown that the multivariate extreme value distribution has Gumbel marginal and the first passage time has exponential marginal. The acceptability of the solutions developed is examined by performing simulation studies on bivariate Gaussian random processes. Illustrative examples include a discussion on the response analysis of a two span bridge subjected to spatially varying random earthquake support motions.     

Dynamics of Nonviscously Damped Linear Systems

This paper is aimed at extending classical modal analysis to treat lumped-parameter nonviscously damped linear dynamic systems. It is supposed that the damping forces depend on the past history of velocities via convolution integrals over some kernel functions. The traditional restriction of symmetry has not been imposed on the system matrices. The nature of the eigenvalues and eigenvectors is discussed under certain simplified but physically realistic assumptions concerning the system matrices and kernel functions. A numerical method for calculation of the right and left eigenvectors is suggested. The transfer function matrix of the system is derived in terms of the right and left eigenvectors of the second-order system. Exact closed-form expressions for the dynamic response due to general forces and initial conditions are presented. The proposed method uses neither the state-space approach nor additional dissipation coordinates. Suitable examples are given to illustrate the derived results.     

Stochastic Averaging of Preisach Hysteretic Systems

The sustained progress in the study of the hysteretic behavior of structural and mechanical systems has led to the adoption of increasingly sophisticated and reliable mathematical representations. Models based on the distributed elements (hysterons) appear to be quite versatile. Among these, the Preisach hysteretic model has received considerable attention in the field of engineering mechanics. In this paper, the stochastic response of a Preisach hysteretic system driven by a white noise process is investigated. In this regard, the method of stochastic averaging is modified to be applicable for the determination of the probability density of the stationary system response envelope. Remarkably, this probability density expression in conjunction with the response of an auxiliary linear system can also be used to determine the power spectrum of the system response. The approximate theoretical solutions are validated by data derived by a pertinent Monte Carlo study.     

Surface Loading of a Multilayered Viscoelastic Pavement: Semianalytical Solution

In this paper a new method is proposed to analyze the mechanical response of a linear viscoelastic pavement. The material parameters of the asphalt concrete are characterized by the relaxation modulus and creep compliance, which are further represented by the Prony series. By virtue of the Laplace transform and the correspondence principle, the solution in the Laplace domain is first derived. The interconversion between the relaxation modulus and creep compliance is then applied to treat the complicated inverse Laplace transform. The displacement, strain, and stress fields are represented concisely in terms of the convolution integral in the time domain, which is subsequently solved analytically. Therefore, responses of the viscoelastic pavement are finally expressed analytically in the time domain and numerically in space domain, called a semianalytical approach. Since both the relaxation modulus and creep compliance are used simultaneously, instead of only one parameter in the conventional methods, the present method is also called a dual-parameter method. The present formulation is verified at both the short- and long-term time limits analytically and at the other finite time numerically, as compared to the conventional numerical methods. We clearly show that the present dual-parameter and semianalytical method can predict accurately the time-dependent responses of the viscoelastic pavement, especially at the long-term time. The present formulation could also be employed to validate the widely used collocation method.     

Seismic Analysis of Structures with Viscoelastic Dampers

Viscoelastic dampers are being used in structures to mitigate dynamic effects. The models of varying complexities from simple maxwell element to differential models with fractional and complex order derivatives have been used to represent their frequency-dependent force deformation characteristics. More complex models are able to capture the frequency dependence of the material properties better, but are difficult to use in analyses. However, the classical models consisting of assemblies of Kelvin and/or Maxwell elements with an adequate number of parameters can be formed to capture the frequency dependence as accurately as the more sophisticated fractional derivative models can do. The main advantage in adopting these classical models is a simpler and smaller system of equations, which can be conveniently analyzed for nonlinear and linear systems. In this study, the two classical mechanical models consisting of Kelvin chains and Maxwell ladder are used. It is shown that these mechanical models are as effective as the fractional derivative model in capturing the effect of the frequency dependence of the material properties in response calculations and are more convenient to use in dynamic response analyses.     

New General Principle of Mechanics and Its Application to General Nonideal Nonholonomic Systems

In this paper we develop a general minimum principle of analytical dynamics that is applicable to nonideal constraints. The new principle encompasses Gauss’s Principle of Least Constraint. We use this principle to obtain the general, explicit, equations of motion for holonomically and/or nonholonomically constrained systems with non-ideal constraints. Examples of a nonholonomically constrained system where the constraints are nonideal, and of a system with sliding friction, are presented.     

具有重特征值的阻尼线性系统振动

本文在复模态理论基础上引入系统传递函数矩阵及其留数矩阵的概念,推证了传递函数矩阵展式,通过展式导出系统振动响应的实数表达式可用于计算具有重特征值的阻尼线性系统振动响应,从而解决了涉及重特征值的振动求解问题,文中对特征值、特征向量及留数矩阵做了探讨,并给出了算例.     

Application of Differential Operator with Servo-Order Function in Model of Viscoelastic Deformation Process

The aim of the present paper is the application of a differential operator of variable order in constitutive relations for viscoelastic material. The dependence of the order function on the strain and strain rate is evaluated on the basis of known experimental results on deformation of polymeric materials. Established dependences are used for studying the vibrations of a 1-degree-of-freedom oscillator, in which the viscoelastic deformation is governed by a servo order function.     

Earthquake Response of Elastic Single-Degree-of-Freedom Systems with Nonlinear Viscoelastic Dampers

Investigated are the steady-forced and earthquake responses of single-degree-of-freedom (SDF) systems with a nonlinear viscoelastic damper (VED), which consists of a nonlinear fluid viscous damper (FVD) connected in series to a linear elastic bracing element (chevron or inverted V-shaped braces). For a wide range of bracing stiffness, nonlinear dampers are advantageous because they achieve essentially the same reduction in system responses but with a significantly reduced force. Damper nonlinearity has little influence on the structural response in the velocity-sensitive region of the spectrum even if the bracing is fairly flexible, but differences up to 16% were observed in other spectral regions. As expected, supplemental damping reduces structural response and the response reduction depends on the bracing stiffness, with this dependence varying with the spectral regions. For practical applications, a procedure is presented to estimate the design values of structural deformation, structural force, foundation shear, and damper force directly from the earthquake design (or response) spectrum. Finally, a procedure is presented to determine the damper and bracing properties necessary to limit the structural deformation to some design value or to the structural capacity.     

备件寿命的计算机随机模拟

运用蒙特卡罗方法，在计算机上对备件寿命进行模拟仿真，从而为优化备件的储备提供了一套科学的、有效的方法，并对最终的计算精度进行了分析。     

Adaptive Predictive Functional Control for Networked Control Systems with Random Delays

Nowadays, more and more field devices are connected to the central controller through a serial communication network such as fieldbus or industrial Ethernet.Some of these serial communication networks like controller area network (CAN) or industrial Ethernet will introduce random transfer delays into the networked control systcms (NCS), which causes control performance degradation and even system instability.To address this problem, the adaptive predictive functional control algorithm is derived by applying the concept of predictive functional control to a discrete state space model with variable delay.The method of estimating the networkinduced delay is also proposed to facilitate the control algorithm implementing.Then, an NCS simulation research based on TrueTime simulator is carried out to validate the proposed control algorithm. The numerical simulations show that the proposed adaptive predictive functional control algorithm is effective for NCS with random delays.     

Effect of Internal Moment Release on the Eigenfrequencies of Combined Linear Systems

A method for analyzing the free vibration of complex structural systems, consisting of a simple oscillator attached to a beam with an internal hinge, is presented. A mathematical model possessing important features of singularity functions with their higher order derivatives is proposed to account for the effect of internal hinge and spring force interacting between the oscillator and supporting structure. The particular integral approach together with Laplace transformation is proved to be an efficient alternative to solve the generalized differential equation for the normal modes of dynamically combined systems. Exact vibration frequencies for clamped–pinned and pinned–pinned boundaries are determined. The results are extended to the cases in which the oscillator or internal hinge is removed from the structure. It is shown that the presence of internal hinge does not alter the generalized orthogonality relation for the combined system. The search for the optimal location of the internal hinge, which maximizes the desired natural frequency, is discussed. It is concluded that a combined system with an optimally positioned hinge vibrates with the same natural frequency as an equivalent system without a hinge.     

Simulation of Binary Random Fields with Applications to Two-Phase Random Media

This paper introduces a methodology for simulation of binary random fields according to their prescribed autocorrelation function. It starts with a brief outline of the essential features of binary random fields and their implications in modeling two-phase random media. The exposition of the proposed methodology is done in two steps. In the first step, an algorithm is introduced to obtain samples of a binary field from generated realizations of a Gaussian field, using the theory of zero crossings of Gaussian fields. This mapping constitutes essentially a nonlinear transformation with memory of the Gaussian sample functions. In the second step, an iterative algorithm is introduced that allows the determination of the probabilistic characteristics of the underlying Gaussian field, so that the resulting binary field obtained through the proposed nonlinear transformation has a prescribed autocorrelation function. Several numerical examples are provided to demonstrate the capabilities of the methodology, especially in modeling two-phase random media. The methodology is shown to have a wide range of applicability and its computational cost is small, especially when a large number of realizations is needed.     

Fatigue Reliability of Multidimensional Vibratory Degrading Systems under Random Loading

In this paper, the basic methodology for the fatigue reliability assessment of randomly vibrating multidegree-of-freedom systems is presented within the coupled response-degradation model. The fatigue process in the system components is quantified by the fatigue crack growth equations which—via the stress range—are coupled with the system response. Simultaneously, the system dynamics is affected by fatigue process via its stiffness degradation so that it provides the actual stress values to the fatigue growth equation. In addition to the general coupled response-degradation analysis, its special case of noncoupled fatigue crack growth is treated as well for the wide-band stationary applied stress by the use of its first four spectral moments and the approximate, empirically motivated, Dirlik’s probability distribution for the stress range. Both, the general analysis and the illustrating exemplary problems elaborated in the paper provide the route to the fatigue reliability estimation in complex–hierarchical vibratory systems under random loading.     

Viscoelastic Model for Discrete Element Simulation of Asphalt Mixtures

This paper presents a viscoelastic model of asphalt mixtures with the discrete element method, where the viscoelastic behaviors of asphalt mastics (fine aggregates, fines, and asphalt binder) are represented by a Burger’s model. Aggregates are simulated with irregular shape particles consisting of balls bonded together by elastic contact models, and the interplaces between aggregates are filled with balls bonded with viscoelastic Burger’s model to represent asphalt mastic. Digital samples were prepared with the image analysis technique. The micromechanical model was developed with four constitutive laws to represent the interactions at contacts of discrete elements (balls) within an aggregate, within mastic, between an aggregate and mastic, and between two adjacent aggregates. Each of these constitutive laws consists of three parts: a stiffness model, a slip model, and a bonding model in order to provide a relationship between the contact force and relative displacement and also in order to describe slipping and tensile strength at a particular contact. The relationship between the microscale model input and macroscale material properties was derived, and an iterative procedure was developed to fit the dynamic modulus test data of asphalt mastic with Burger’s model. The favorable agreement between the discrete element prediction and the lab results on dynamic moduli and phase angles indicates that the viscoelastic discrete element model developed in this study is very capable of simulating constitutive behavior of asphalt mixtures.     

Simulation of Multidimensional Binary Random Fields with Application to Modeling of Two-Phase Random Media

This paper proposes a methodology for simulation of binary random fields with application to the problem of generating sample realizations of two-phase random media. The methodology is based on the concept of nonlinear transformations with memory of Gaussian random fields. The simulation is performed according to the autocorrelation function of the binary field which contains considerable information about the microstructural characteristics of the medium. The determination of the probabilistic characteristics of the underlying Gaussian field is achieved through an iterative procedure that was introduced in a previous paper by the same authors in one dimension and is extended here to multiple dimensions. Limiting cases and alternative mappings are also presented. The capabilities of the methodology are demonstrated in a series of examples.     

Viscoelastic Modeling and Field Validation of Flexible Pavements

The objective of this study was to characterize hot-mix asphalt (HMA) viscoelastic properties at intermediate and high temperatures and to incorporate laboratory-determined parameters into a three-dimensional finite element (FE) model to accurately simulate pavement responses to vehicular loading at different temperatures and speeds. Results of the developed FE model were compared against field-measured pavement responses from the Virginia Smart Road. Results of this analysis indicated that the elastic theory grossly underpredicts pavement responses to vehicular loading at intermediate and high temperatures. In addition, the elastic FE model could not simulate permanent deformation or delayed recovery, a known characteristic of HMA materials. In contrast, results of the FE viscoelastic model were in better agreement with field measurements. In this case, the average error in the prediction was less than 15%. The FE model successfully simulated retardation of the response in the transverse direction and rapid relaxation of HMA in the longitudinal direction. Moreover, the developed model allowed predicting primary rutting damage at the surface and its partial recovery after load application.     

线性奇异系统的特征结构配置

讨论了线性时不变奇异系统经纯状态反馈配置特征结构的问题.在系统是正则未及强能控的前提下,给出了可以配置给定特征结构的充分必要条件.由于采用了构造性方法的证明,当条件满足时,所需的反馈阵也是容易得到的.研究表明:可配置特征结构的\     

Identification of Viscoelastic Functions for Hot-Mix Asphalt Mixtures Using a Modified Harmony Search Algorithm

This study proposes a modified harmony search (MHS) algorithm for determining the time-domain viscoelastic function of hot-mix asphalt (HMA) concrete materials. This MHS technique, employing a global optimization technique as well as a Wiechert model for the relaxation function, substantially enhances accuracy and consistency in the determination of viscoelastic functions of several HMA mixtures. In addition, this study shows how to determine a time-domain Prony series representation from the complex modulus in the frequency domain using the MHS algorithm. This can be efficiently used for numerical analysis with techniques such as the finite-element method. The results from lab frequency sweep tests of unmodified and lime-modified HMA at various asphalt contents were consistent with the functions obtained from the MHS algorithm.