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1.
Shuenn-Yih Chang 《地震工程与工程振动(英文版)》2011,10(3):437-451
Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropriate time step before performing a pseudodynamic test. Therefore, a novel parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change at the end of a time step, and can thus be used to evaluate numerical and error propagation properties for nonlinear systems. Based on these properties, it is possible to select an appropriate time step to conduct a pseudodynamic test in advance. This possibility is very important in pseudodynamic testing, since the use of an arbitrary time step might lead to unreliable results or even destroy the test specimen. In this paper, guidelines are proposed for choosing an appropriate time step for accurate integration of nonlinear systems. These guidelines require estimation of the maximum instantaneous degree of nonlinearity and the solution of the initial natural frequency. The Newmark explicit method is chosen for this study. All the analytical results and the guidelines proposed are thoroughly confirmed with numerical examples. 相似文献
2.
It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems. 相似文献
3.
It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation
for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation
techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by
introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics
of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found
that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree
of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only
for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical
dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses
are almost unaffected for both linear elastic and nonlinear systems.
Supported by: National Science Council, Chinese Taipei, Under Grant No. NSC-92-2211-E-027-015 相似文献
4.
In pseudodynamic tests, experimental feedback errors are accumulated in the step-by-step integration procedure. In this paper, the growth of cumulative experimental errors is examined. Approximate cumulative error bounds are derived for linear single- and multi-degree-of-freedom systems, based on realistic models of random and systematic feedback errors. These studies show that the rate of cumulative error growth with respect to the integration time step increases rapidly with the natural frequency of the specimen and the integration time interval used. Hence, the higher modes of a multi-degree-of-freedom system are more sensitive to experimental errors than the lower ones. Furthermore, it is shown that some systematic errors are extremely undesirable. Rational criteria for assessing the reliability of pseudodynamic test results are presented. 相似文献
5.
Real‐time pseudodynamic (PSD) and hybrid PSD test methods are experimental techniques to obtain the response of structures, where restoring force feedback is used by an integration algorithm to generate command displacements. Time delays in the restoring force feedback from the physical test structure and/or the analytical substructure cause inaccuracies and can potentially destabilize the system. In this paper a method for investigating the stability of structural systems involved in real‐time PSD and hybrid PSD tests with multiple sources of delay is presented. The method involves the use of the pseudodelay technique to perform an exact mapping of fixed delay terms to determine the stability boundary. The approach described here is intended to be a practical one that enables the requirements for a real‐time testing system to be established in terms of system parameters when multiple sources of delay exist. Several real‐time testing scenarios with delay that include single degree of freedom (SDOF) and multi‐degree of freedom (MDOF) real‐time PSD/hybrid PSD tests are analyzed to illustrate the method. From the stability analysis of the real‐time hybrid testing of an SDOF test structure, delay‐independent stability with respect to either experimental or analytical substructure delay is shown to exist. The conditions that the structural properties must satisfy in order for delay‐independent stability to exist are derived. Real‐time hybrid PSD testing of an MDOF structure equipped with a passive damper is also investigated, where observations from six different cases related to the stability plane behavior are summarized. Throughout this study, root locus plots are used to provide insight and explanation of the behavior of the stability boundaries. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
6.
There is a significant motivation to implement an unconditionally stable scheme in the pseudodynamic test method. As more complex experiments with many degrees of freedom are tested, explicit time integration methods limit the size of time step on the basis of the highest natural frequency of the system. This is true even though the response of the structure may be dominated by a few lower frequency modes. The limit on step size is undesirable because it physically increases the duration of a test, but more importantly, because the number of steps to completion increases and error propagation problems increase with the number of steps in a test. In addition, incremental displacements within each step become smaller, introducing the potential for problems associated with stress relaxation. An unconditionally stable algorithm allows the time step to be selected to give accurate response in the modes of interest without regard for higher mode characteristics. 相似文献
7.
Although it has been shown that the implementation of the HHT-α method can result in improved error propagation properties in pseudodynamic testing if the equation of motion is used instead of the difference equation to evaluate the next step acceleration, this paper proves that this method might lead to instability when used to solve a nonlinear system. Its unconditional stability is verified only for linear elastic systems, while for nonlinear systems, instability occurs as the step degree of convergence is less than 1. It is worth noting that the step degree of convergence can frequently be less than 1 in pseudodynamic testing, since a convergent solution is achieved only when the step degree of convergence is close to 1 regardless of whether its value is greater or less than 1. Therefore, the application of this scheme to pseudodynamic testing should be prohibited, since the possibility of instability might incorrectly destroy a specimen. Consequently, the implementation of the HHT-α method by using the difference equation to determine the next step acceleration is recommended for use in pseudodynamic testing. 相似文献
8.
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
9.
A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a structure does not need to be considered. This is because this subfamily is unconditionally stable for any instantaneous stiffness softening system, linear elastic system and instantaneous stiffness hardening system that might occur in the pseudodynamic testing of a real structure. In addition, it also offers good accuracy when compared to a general second-order accurate method for both linear elastic and nonlinear systems. 相似文献
10.
Converting the second-order differential equation to a first-order equation by integrating it with respect to time once as the governing equation of motion for a structural system can be very promising in the pseudodynamic testing. This was originally found and developed by Chang. The application of this time-integration technique to the Newmark explicit method is implimented and investigated in this paper. The main advantages of using the integral form of Newmark explicit method instead of the commonly used Newmark explicit method in a pseudodynamic test are: a less-error propagation effect, a better capability in capturing the rapid changes of dynamic loading and in eliminating the adverse linearization errors. All these improvements have been verified by theoretical studies and experimental tests. Consequently, for a same time step this time-integration technique may result in less-error propagation and achieve more accurate test results than applying the original form of Newmark explicit method in a pseudodynamic test due to these significant improvements. Thus, the incorporation of this proposed time-integration technique into the direct integration method for pseudodynamic testings is strongly recommended. © 1998 John Wiley & Sons, Ltd. 相似文献
11.
The error-propagation characteristics of an implicit time integration algorithm in pseudodynamic testing are examined. It is shown that the implicit algorithm is superior to explicit integration algorithms in terms of experimental error amplification. The influence of systematic experimental errors is studied and methods for controlling these errors are examined. In spite of the fact that the implicit algorithm is unconditionally stable, it is shown that the integration time interval in a pseudodynamic test is limited by the calibration range of the electronic hardware as well as the degree of participation of the higher modes. Furthermore, the tolerance for experimental errors decreases as the integration time interval increases. 相似文献
12.
Shuenn-Yih Chang 《地震工程与工程振动(英文版)》2009,8(3):329-340
Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing.Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However,their numerical properties in the solution of a nonlinear system are not apparent.Therefore,the performance of both algorithms for use in the solution... 相似文献
13.
In the most recent seismic codes, the assessment of the seismic response of structures may be carried out by comparing the displacement capacity, provided by nonlinear static analysis, with the displacement demand. In many cases the code approach is based on the N2 method proposed by Fajfar, which evaluates the displacement demand by defining, as an intermediate step, a single degree‐of‐freedom (SDOF) system equivalent to the examined structure. Other codes suggest simpler approaches, which do not require equivalent SDOF systems, but they give slightly different estimation of the seismic displacement demand. The paper points out the differences between the methods and suggests an operative approach that provides the same accuracy as the N2 method without requiring the evaluation of an equivalent SDOF system. A wide parametric investigation allows an accurate comparison of the different methods and demonstrates the effectiveness of the proposed operative approach. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
14.
R. S. Jangid 《地震工程与结构动力学》2004,33(15):1417-1428
Earthquake excitation is often modelled by non‐stationary random process (i.e. uniformly modulated broad‐band excitation) for analysis of structural safety subjected to seismic hazards. In this paper, the non‐stationary response of a single‐degree‐of‐freedom (SDOF) system to non‐stationary earthquake motion is investigated for different shapes of modulating functions. The evolutionary power‐spectral density function (PSDF) of the displacement of the SDOF system is obtained using the time‐varying frequency response function and the PSDF of the earthquake excitation. The close form expressions for time‐varying frequency response function are derived for different shapes of the modulating functions. In order to study the effects of the shape of the modulating function, a comparison of the non‐stationary earthquake response of the SDOF system is also made for different modulating functions having the same energy content. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
Predictors of seismic structural demands (such as inter‐storey drift angles) that are less time‐consuming than nonlinear dynamic analysis have proven useful for structural performance assessment and for design. Luco and Cornell previously proposed a simple predictor that extends the idea of modal superposition (of the first two modes) with the square‐root‐of‐sum‐of‐squares (SRSS) rule by taking a first‐mode inelastic spectral displacement into account. This predictor achieved a significant improvement over simply using the response of an elastic oscillator; however, it cannot capture well large displacements caused by local yielding. A possible improvement of Luco's predictor is discussed in this paper, where it is proposed to consider three enhancements: (i) a post‐elastic first‐mode shape approximated by the deflected shape from a nonlinear static pushover analysis (NSPA) at the step corresponding to the maximum drift of an equivalent inelastic single‐degree‐of‐freedom (SDOF) system, (ii) a trilinear backbone curve for the SDOF system, and (iii) the elastic third‐mode response for long‐period buildings. Numerical examples demonstrate that the proposed predictor is less biased and results in less dispersion than Luco's original predictor. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
Jun Iyama 《地震工程与结构动力学》2005,34(15):1799-1815
The response of an elasto‐plastic single degree of freedom (SDOF) system to ground motion is estimated based on wavelet coefficients calculated by discrete wavelet transform. Wavelet coefficients represent both the time and frequency characteristics of input ground motion, and thus can be considered to be directly related to the dynamic response of a non‐linear system. This relationship between the energy input into an elastic SDOF system and wavelet coefficients is derived based on the assumption that wavelets deliver energy to the structure instantaneously and the quantity of energy is constant regardless of yielding. These assumptions are shown to be valid when the natural period of the system is in the predominant period range of the wavelet, the most common scenario for real structures, through dynamic response analysis of a single wavelet. The wavelet‐based estimation of elastic and plastic energy transferred by earthquake ground motion is thus shown to be in good agreement with the dynamic response analysis when the natural period is in the predominant range of the input. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
17.
Knowledge of maximum velocity is essential for the design of structures and especially those with supplementary dampers. Although the nonlinear time history analysis leads to reliable estimation of actual velocities, it seems to be complicated for the everyday engineering practice due to the increased computational cost. This paper proposes an alternative for single‐degree‐of‐freedom (SDOF) systems to estimate the actual velocity in a straightforward and effective manner. More specifically, this study examines the inelastic velocity ratio (IVR), i.e., the ratio of the maximum inelastic to the maximum elastic velocity of an SDOF system, the knowledge of which allows the computation of maximum inelastic velocity directly from the corresponding elastic counterpart. The proposed method is general and can be applied to both conventional structures and structures with supplementary dampers. Extensive parametric studies are conducted to obtain expressions for IVR in terms of the period of vibration, viscous damping ratio, force reduction factor, and soil class. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
18.
The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi‐directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi‐directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi‐directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
19.
J. L. Liu 《地震工程与结构动力学》2001,30(4):613-619
As an extension of the procedure in which an arbitrary dynamic loading is approximated by piecewise linear segments, the second‐ and third‐degree piecewise Lagrangian interpolating polynomials are employed to approximate an arbitrary dynamic loading in the Duhamel integral for the solution of dynamic response of a SDOF system. The related formulae are derived. The proposed method offers computational advantage over the traditional step‐by‐step solution techniques for comparable accuracy, and far better accuracy than the piecewise linear approximation procedure for comparable time interval when the loading cannot be represented by straight‐line segments. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
20.
A computational method of energy evaluation is derived to study the elastic responses and energy distribution of actively controlled single‐degree‐of‐freedom (SDOF) structures during earthquakes. Contrary to the common perception that applying active control force pumps energy into the structure, the applied control force can actually reduce the energy in the structure by reducing the input energy from earthquakes to the structure. In addition, applying control force can dissipate a large amount of energy in the structure when this control force is applied in the direction opposite to the displacement and velocity responses. To demonstrate this energy mechanism in active controlled structures, the two most popular control algorithms, optimal linear control (OLC) and instantaneous optimal control (IOC) algorithms, are used to calculate the control response and energy spectra. One‐step time delay is incorporated into the algorithms to take into consideration the practical aspect of active control. The effects of different earthquakes and damping ratios on control energy and response spectra are studied. These studies show that both OLC and IOC are very effective in reducing the structural displacement and velocity responses by reducing the input earthquake energy as well as dissipating a large amount of energy in the structure. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献