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This paper deals with the lower order (first four) nonstationary statistical moments of the response of linear systems with random stiffness and random damping properties subject to random nonstationary excitation modeled as white noise multiplied by an envelope function. The method of analysis is based on a Markov approach using stochastic differential equations (SDE). The linear SDE with random coefficients subject to random excitation with deterministic initial conditions are transformed to an equivalent nonlinear SDE with deterministic coefficients and random initial conditions subject to random excitation. In this procedure, new SDE with random initial conditions, deterministic coefficients and zero forcing functions are introduced to represent the random variables. The joint statistical moments of the response are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vectors and the random variables of the structural system. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. The statistical moment equations are ordinary nonlinear differential equations where hierarchy of moments appear. The hierarchy is closed by the cumulant neglect closure method applied at the fourth order statistical moment level. General formulation is given for multi-degree-of-freedom (MDOF) systems and the performance of the method in problems with nonstationary excitations and large variabilities is illustrated for a single-degree-of-freedom (SDOF) oscillator. 相似文献
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Kinematic effects at the head of a flexible vertical pile embedded in a two‐layer soil deposit are investigated by means of rigorous three‐dimensional elastodynamic finite‐element analyses. Both pile and soil are idealized as linearly viscoelastic materials, modelled by solid elements, without the restrictions associated with the use of strength‐of‐materials approximations. The system is analyzed by a time‐Fourier approach in conjunction with a modal expansion in space. Constant viscous damping is considered for each natural mode, and an FFT algorithm is employed to switch from frequency to time domain and vice versa in natural or generalized coordinates. The scope of the paper is to: (a) elucidate the role of a number of key phenomena controlling the amplitude of kinematic bending moments at the pile head; (b) propose a simplified semi‐analytical formula for evaluating such moments; and (c) provide some remarks about the role of kinematic bending in the seismic design of pile foundations. The results of the study provide a new interpretation of the interplay between interface kinematic moments and corresponding head moments, as a function of layer thickness, pile‐to‐soil stiffness ratio, and stiffness contrast between the soil layers. In addition, the role of diameter in designing against kinematic action, with or without the presence of an inertial counterpart, is discussed. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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H.U. Köylüo?lu S.R.K. Nielsen A.?. Çakmak 《Soil Dynamics and Earthquake Engineering》1996,15(6):359-368
A semi-analytical forward-difference Monte Carlo simulation procedure is proposed for the determination of the lower order statistical moments and the joint probability density function of the stochastic response of hysteretic non-linear multi-degree-of-freedom structural systems subject to nonstationary gaussian white noise excitation, as an alternative to conventional direct simulation methods. The method generalizes the so-called Ermak-Allen algorithm developed for simulation applications in molecular dynamics to structural hysteretic systems. The proposed simulation procedure rely on an assumption of local gaussianity during each time step. This assumption is tantamount to various linearizations of the equations of motion. The procedure then applies an analytical convolution of the excitation process, hereby reducing the generation of stochastic processes and numerical integration to the generation of random vectors only. Such a treatment offers higher rates of convergence, faster speed and higher accuracy. The procedure has been compared to the direct Monte Carlo simulation procedure, which uses a fourth-order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process. The considered system was a multi-dimenensional hysteretic shear frame, where the constitutive equation of the hysteretic shear forces are described by a bilinear hysteretic model. The comparisons show that significant savings in computer time and accuracy can be achieved. 相似文献
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The dynamic response of offshore wind turbines is affected by the properties of the foundation and the subsoil. The aim of this paper is to evaluate the dynamic soil–structure interaction of suction caissons for offshore wind turbines. The investigations include evaluation of the vertical and coupled sliding–rocking vibrations, influence of the foundation geometry and examination on the properties of the surrounding soil. The soil is simplified as a homogenous linear viscoelastic material and the dynamic stiffness of the suction caisson is expressed in terms of dimensionless frequency‐dependent coefficients corresponding to different degrees of freedom. The dynamic stiffness coefficients for the skirted foundation are evaluated using a three‐dimensional coupled boundary element/finite element model. Comparisons with known analytical and numerical solutions indicate that the static and dynamic behaviours of the foundation are predicted accurately using the applied model. The analysis has been carried out for different combinations of the skirt length, Poisson's ratio of the subsoil and the ratio of the soil stiffness to the skirt stiffness. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Passive and semi‐active tuned mass damper (PTMD and SATMD) building systems are proposed to mitigate structural response due to seismic loads. The structure's upper portion self plays a role either as a tuned mass passive damper or a semi‐active resetable device is adopted as a control feature for the PTMD, creating a SATMD system. Two‐degree‐of‐freedom analytical studies are employed to design the prototype structural system, specify its element characteristics and effectiveness for seismic responses, including defining the resetable device dynamics. The optimal parameters are derived for the large mass ratio by numerical analysis. For the SATMD building system the stiffness of the resetable device design is combined with rubber bearing stiffness. From parametric studies, effective practical control schemes can be derived for the SATMD system. To verify the principal efficacy of the conceptual system, the controlled system response is compared with the response spectrum of the earthquake suites used. The control ability of the SATMD scheme is compared with that of an uncontrolled (No TMD) and an ideal PTMD building systems for multi‐level seismic intensity. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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A non-Gaussian closure scheme based on the Edgeworth expansion of the probability density function is used to study the response of a hysteretic structure under random parametric excitation. The system considered consists of a weightless mass supporting a concentrated mass and it is subjected to the vertical and horizontal components of the ground acceleration modeled as nonstationary Gaussian white noise processes. The material of the structure exhibits bilinear hysteretic behaviour. The equation governing the motion of the system is transformed into an Itô stochastic differential equation. A set of ordinary differential equations governing the response statistics are obtained. These form an infinite hierarchy of equations which must be truncated in order to solve for moments of any order. The Edgeworth expansion of the joint density is used to truncate this infinite hierarchy. Such a closure scheme appears desirable since for hysteretic systems an explicit expression of the probability density is required. A frequently used closure scheme based on Gaussian assumption underestimates the response. The non-Gaussian density can be used in reliability studies. 相似文献
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The parameter estimation methods of (1) moments, (2) maximum‐likelihood, (3) probability‐weighted moments (PWM) and (4) self‐determined PWM are applied to the probability distributions of Gumbel, general extreme values, three‐parameter log‐normal (LN3), Pearson‐3 and log‐Pearson‐3. The special method of computing parameters so as to make the sample skewness coefficient zero is also applied to LN3, and hence, altogether 21 candidate distributions resulted. The parameters of these distributions are computed first by original sample series of 14 successive‐duration annual extreme rainfalls recorded at a rain‐gauging station. Next, the parameters are scaled by first‐degree semi‐log or log‐log polynomial regressions versus rainfall durations from 5 to 1440 min (24 h). Those distributions satisfying the divergence criterion for frequency curves are selected as potential distributions, whose better‐fit ones are determined by a conjunctive evaluation of three goodness‐of‐fit tests. Frequency tables, frequency curves and intensity–duration–frequency curves are the outcome. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems 
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下载免费PDF全文 Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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A frequency response function change (FRFC) method to detect damage location and extent based on the change in the frequency response functions of a shear building under the effects of ground excitation was proposed in this paper. The damage identification equation was derived from the motion equations of the system before and after the occurrence of the damage. Efforts to make the FRFC method less model‐dependent were made. Intact system matrices, which could be estimated using the measured data without the need for an analytical model, and the frequency response functions were required for the FRFC method. The effects of measurement noise and model parameter error in the FRFC method were studied numerically. The proposed FRFC method was validated by experimental studies of a six‐story steel building structure with single and multiple damage cases. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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According to theoretical analysis,a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands,which is verified by observations from the Xiangjiaba Hydropower Station.Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics,which significantly facilitate the isolation design.In order to obtain the response probabilistic distribution of a nonlinear system,the state space split technique is modified.As only a few degrees of freedom are subjected to the random noise,the probabilistic distribution of the response without involving stochastic excitation is represented by theδfunction.Then,the sampling property of theδfunction is employed to reduce the dimension of the Fokker-PlanckKolmogorov(FPK)equation and the low-dimensional FPK equation is solvable with existing methods.Numerical results indicate that the proposed approach is effective and accurate.Moreover,the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods. 相似文献
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Nonstationary stochastic response of structural systems equipped with nonlinear viscous dampers under seismic excitation 总被引：1，自引：0，他引：1 下载免费PDF全文
下载免费PDF全文 Nonlinear viscous dampers are supplemental devices widely used for enhancing the performance of structural systems exposed to seismic hazard. A rigorous evaluation of the effect of these damping devices on the seismic performance of a structural system should be based on a probabilistic approach and take into account the evolutionary characteristics of the earthquake input and of the corresponding system response. In this paper, an approximate analytical technique is proposed for studying the nonstationary stochastic response characteristics of hysteretic single degree of freedom systems equipped with viscous dampers subjected to a fully nonstationary random process representing the seismic input. In this regard, a stochastic averaging/linearization technique is utilized to cast the original nonlinear stochastic differential equation of motion into a simple first‐order nonlinear ordinary differential equation for the nonstationary system response variance. In comparison with standard linearization schemes, the herein proposed technique has the significant advantage that it allows to handle realistic seismic excitations with time‐varying frequency content. Further, it allows deriving a formula for determining the nonlinear system response evolutionary power spectrum. By this way, ‘moving resonance’ effects, related to both the evolutionary seismic excitation and the nonlinear system behavior, can be observed and quantified. Several applications involving various system and input properties are included. Furthermore, various response parameters of interest for the seismic performance assessment are considered as well. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed technique. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Semi‐active stiffness damper (SASD) is one of many semi‐active control systems with the capability to mitigate the dynamic response using only a small amount of external power. The system consists of a hydraulic damper connected to the bracing frame in a selected story unit. In this paper, study of a SASD in two building models of five‐stories under four benchmark earthquake records is reported. The purpose of this study is to evaluate the effectiveness of the control system against structure type and varying earthquake inputs. Various control laws are chosen to work with SASD, such as: resetting control, switching control, linear quadratic regulator (LQR) and modified LQR, and the results are compared with no control and passive control cases. Numerical results show that the use of a SASD is effective in reducing seismic responses. Control effectiveness is dependent on the type of structure and earthquake excitation. Passive control is less effective than other control cases as expected. Resetting control, switching control and LQR generally perform similarly in response reduction. While modified LQR is more efficient and robust compared with other control algorithms. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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John P. Wolf 《地震工程与结构动力学》2002,31(1):15-32
The scaled boundary finite‐element method is a powerful semi‐analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure–soil interface. This permits the analysis of dynamic soil–structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three‐dimensional vector‐wave equation of elasto‐dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high‐frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first‐order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure–soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half‐space with the results of the boundary‐element method is observed. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three‐dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre‐corrected fast Fourier transform (pFFT)‐accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre‐conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts. 相似文献
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Based on knowledge of a commutative group calculation of the rock stiffness and on some geophysical assumptions, the simplest fractured medium may be regarded as a fracture embedded in an isotropic background medium, and the fracture interface can be simulated as a linear slip interface that satisfies non‐welded contact boundary conditions: the kinematic displacements are discontinuous across the interface, whereas the dynamic stresses are continuous across the interface. The finite‐difference method with boundary conditions explicitly imposed is advantageous for modelling wave propagation in fractured discontinuous media that are described by the elastic equation of motion and non‐welded contact boundary conditions. In this paper, finite‐difference schemes for horizontally, vertically, and orthogonally fractured media are derived when the fracture interfaces are aligned with the boundaries of the finite‐difference grid. The new finite‐difference schemes explicitly have an additional part that is different from the conventional second‐order finite‐difference scheme and that directly describes the contributions of the fracture to the wave equation of motion in the fractured medium. The numerical seismograms presented, to first order, show that the new finite‐difference scheme is accurate and stable and agrees well with the results of previously published finite‐difference schemes (the Coates and Schoenberg method). The results of the new finite‐difference schemes show how the amplitude of the reflection produced by the fracture varies with the fracture compliances. Later, comparisons with the reflection coefficients indicate that the reflection coefficients of the fracture are frequency dependent, whereas the reflection coefficients of the impedance contrast interface are frequency independent. In addition, the numerical seismograms show that the reflections of the fractured medium are equal to the reflections of the background medium plus the reflections of the fracture in the elastic fractured medium. 相似文献
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Real‐time pseudodynamic (PSD) testing is an experimental technique for evaluating the dynamic behaviour of a complex structure. During the test, when the targeted command displacements are not achieved by the test structure, or a delay in the measured restoring forces from the test structure exists, the reliability of the testing method is impaired. The stability and accuracy of real‐time PSD testing in the presence of amplitude error and a time delay in the restoring force is presented. Systems consisting of an elastic single degree of freedom (SDOF) structure with load‐rate independent and dependent restoring forces are considered. Bode plots are used to assess the effects of amplitude error and a time delay on the steady‐state accuracy of the system. A method called the pseudodelay technique is used to derive the exact solution to the delay differential equation for the critical time delay that causes instability of the system. The solution is expressed in terms of the test structure parameters (mass, damping, stiffness). An error in the restoring force amplitude is shown to degrade the accuracy of a real‐time PSD test but not destabilize the system, while a time delay can lead to instability. Example calculations are performed for determining the critical time delay, and numerical simulations with both a constant delay and variable delay in the restoring force are shown to agree well with the stability limit for the system based on the critical time delay solution. The simulation models are also used to investigate the effects of a time delay in the PSD test of an inelastic SDOF system. The effect of energy dissipation in an inelastic structure increases the limit for the critical time delay, due to the energy removed from the system by the energy dissipation. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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This paper presents a new formulation for critical damping of structures with elastically supported visco‐elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco‐elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third‐order differential equation and the conventional method for defining the critical damping for second‐order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi‐infinite) for second‐order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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The scaled boundary finite‐element method is extended to simulate time‐harmonic responses of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. The unbounded domains and the elasticity matrices are transformed to the scaled boundary coordinates. The scaled boundary finite‐element equation in displacement amplitudes are derived directly from the governing equations of elastodynamics. To enforce the radiation condition at infinity, an asymptotic expansion of the dynamic‐stiffness matrix for high frequency is developed. The dynamic‐stiffness matrix at lower frequency is obtained by numerical integration of ordinary differential equations. Only the boundary is discretized yielding a reduction of the spatial dimension by one. No fundamental solution is required. Material anisotropy is modelled without additional efforts. Examples of two‐ and three‐dimensional non‐homogeneous isotropic and transversely isotropic unbounded domains are presented. The results demonstrate the accuracy and simplicity of the scaled boundary finite‐element method. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献