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1.
Shuenn-Yih Chang 《地震工程与工程振动(英文版)》2009,8(1):77-86
Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm (Chang, 2003) are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom (SDOF) system, can be applied to a nonlinear multiple degree of freedom (MDOF) system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing. 相似文献
2.
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
3.
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
4.
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
5.
A structure may exhibit a severe strain-softening behaviour when subjected to strong earthquake excitation. Pseudodynamic testing of such structures using an implicit time-integration algorithm may be conceived of as a problem, since the Newton-type iterations, which are often required when structural non-linearity develops, may not converge under these circumstances. An unconditionally stable implicit time-integration algorithm implemented with Newton-type iterations is analysed to provide an insight into this problem. A simple convergence condition is derived to detect possible divergence. The condition is shown to be a sufficient criterion for convergence for general multiple-degree-of-freedom structures, and it is used later on to develop an adaptive time-stepping strategy to avoid divergence under severe strain-softening conditions. The implementation of this technique for pseudodynamic testing is presented. As demonstrated by numerical examples, the algorithm proves to be effective and reliable. 相似文献
6.
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
7.
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
8.
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
9.
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
10.
Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real‐time hybrid simulation. The implicit HHT α‐algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real‐time hybrid simulation. Consequently, the HHT α‐algorithm has been implemented for real‐time hybrid simulation using a fixed number of substep iterations. The resulting HHT α‐algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT α‐algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT α‐algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time‐step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT α‐algorithm with a fixed number of substep iterations. Both numerical and real‐time hybrid simulations are conducted to verify the modified algorithm. The experimental results demonstrate the effectiveness of the modified algorithm for real‐time testing. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
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
12.
William Blumen 《地球物理与天体物理流体动力学》2013,107(4):265-272
Abstract The process of wave steepening in Long's model of steady, two-dimensional stably stratified flow over orography is examined. Under conditions of the long-wave approximation, and constant values of the background static stability and basic flow, Long's equation is cast into the form of a nonlinear advection equation. Spectral properties of this latter equation, which could be useful for the interpretation of data analyses under mountain wave conditions, are presented. The principal features, that apply at the onset of convective instability (density constant with height), are: i) a power spectrum for available potential energy that exhibits a minus eight-thirds decay, in terms of the vertical wavenumber k z -; ii) a rate of energy transfer across the spectrum that is inversely proportional to the wavenumber for large k z -; iii) an equipartition between the kinetic energy of the horizontal motion and the available potential energy, under the longwave approximation, although all the disturbance energy is kinetic at the point where convective instability is initiated. It is also shown that features i) and ii) apply to more general conditions that are appropriate to Long's model, not just the long-wave approximation. Application to fully turbulent flow or to conditions at the onset of shearing instability are not considered to be warranted, since the development only applies to conditions at the onset of convective instability. 相似文献
13.
由于在变形和累积耗能的建筑地震受损程度评估模型,是将建筑划分为五个状态水平,未研究建筑环境性能,评估结果误差较大。因此设计基于BIM的建筑地震受损程度评估模型,采用基于BIM的建筑环境研究与评估方法,考虑建筑环境性能,基于这个思路,依据混凝土单轴Mazars损伤模型,获取三轴状态中的损伤演化方程,得到应变大于损伤阈值时损伤演化方程增量形式,构建混凝土损伤评估模型。经实验证明,所设计模型在地震峰值加速度小于0.31g时,建筑结构大致无缺,在峰值加速度是0.61g时,建筑地震受损指数超过0.8,建筑倒塌;所设计模型评估的平均误差低于0.03,平均评估时间是2.86 s,说明所设计模型能够有效评估建筑地震受损程度,且精度和效率较高。 相似文献
14.
The “earthquake nucleation” is discussed in this paper. The acceleration is a property of the nucleation phase and is a necessary
condition of earthquake instability too. If the acceleration property of this nucleating process is described by the equation
dΘ/dt=C/(t
f−t)
n
, the process can be summarized briefly that the rate of cumulative seismic release is proportional to the inverse power of
the remaining time to failure. Based on this principle, the foreshock sequence of the 1975 Haicheng earthquake withM
S7.3, was analysed backward. It is stated clearly that the time-to-failure and magnitude of the mainshock can be predicted
successfully if the coefficientr
2 attains to the maximum. In the estimation of mainshock time, the error can generally be less than, or far less than, one-half
the remaining time between the time of the last used data point and the mainshock.
Contribution No. 95A0024, Institute of Geophysics, SSB, China.
This study is the "Eighth-Five" contract project ofSSB. 相似文献
15.
The convergence and energy-dissipation characteristics of an unconditionally stable implicit time integration scheme that has been adopted for pseudodynamic testing are examined in this paper. A convergence criterion is derived for general multiple-degree-of-freedom softening systems. Furthermore, it is shown that undesired loading and unloading cycles can be avoided in numerical iterations by scaling down the incremental corrections. Finally, it is proved that the total energy dissipation introduced by the residual convergence errors and proposed numerical correction is always positive for any softening structures. 相似文献
16.
The use of unconditionally stable implicit time integration techniques for pseudodynamic tests has been recently proposed and advanced by several researchers. Inspired by such developments, a pseudodynamic test scheme based on an unconditionally stable implicit time integration algorithm and dual displacement control is presented in this paper. The accuracy of the proposed scheme is proved with error-propagation analysis. It is shown by numerical examples and verification tests that the error-correction method incorporated can eliminate the spurious higher-mode response, which can often be excited by experimental errors. The practicality of the proposed scheme lies in the fact that the implementation is as easy as that of explicit schemes and that the convergence criteria required are compatible with the accuracy limits of ordinary test apparatus. 相似文献
17.
John H. Cushman Moongyu Park Monica Moroni Natalie Kleinfelter-Domelle Daniel O��Malley 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(1):1-10
When formulated properly, most geophysical transport-type process involving passive scalars or motile particles may be described
by the same space–time nonlocal field equation which consists of a classical mass balance coupled with a space–time nonlocal
convective/dispersive flux. Specific examples employed here include stretched and compressed Brownian motion, diffusion in
slit-nanopores, subdiffusive continuous-time random walks (CTRW), super diffusion in the turbulent atmosphere and dispersion
of motile and passive particles in fractal porous media. Stretched and compressed Brownian motion, which may be thought of
as Brownian motions run with nonlinear clocks, are defined as the limit processes of a special class of random walks possessing
nonstationary increments. The limit process has a mean square displacement that increases as tα+1 where α > −1 is a constant. If α = 0 the process is classical Brownian, if α < 0 we say the process is compressed Brownian while
if α > 0 it is stretched. The Fokker–Planck equations for these processes are classical ade’s with dispersion coefficient
proportional to tα. The Brownian-type walks have fixed time step, but nonstationary spatial increments that are Gaussian with power law variance.
With the CTRW, both the time increment and the spatial increment are random. The subdiffusive Fokker–Planck equation is fractional
in time for the CTRW’s considered in this article. The second moments for a Levy spatial trajectory are infinite while the
Fokker–Planck equation is an advective–dispersive equation, ade, with constant diffusion coefficient and fractional spatial
derivatives. If the Lagrangian velocity is assumed Levy rather than the position, then a similar Fokker–Planck equation is
obtained, but the diffusion coefficient is a power law in time. All these Fokker–Planck equations are special cases of the
general non-local balance law. 相似文献
18.
Structural modal parameter identification and damage diagnosis based on Hilbert-Huang transform 总被引：1，自引：1，他引：0
Traditional modal parameter identifi cation methods have many disadvantages,especially when used for processing nonlinear and non-stationary signals.In addition,they are usually not able to accurately identify the damping ratio and damage.In this study,methods based on the Hilbert-Huang transform(HHT) are investigated for structural modal parameter identifi cation and damage diagnosis.First,mirror extension and prediction via a radial basis function(RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition(EMD),which is a crucial part of HHT.Then,the approaches based on HHT combined with other techniques,such as the random decrement technique(RDT),natural excitation technique(NExT) and stochastic subspace identifi cation(SSI),are proposed to identify modal parameters of structures.Furthermore,a damage diagnosis method based on the HHT is also proposed.Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure.The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure.Finally,acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches.The results show that the proposed approaches based on HHT for modal parameter identifi cation and damage diagnosis are reliable and practical. 相似文献
19.
地震是诱发边坡失稳的主要因素之一,重力式挡土墙作为一种广泛采用的岩土支挡结构,有必要对其地震稳定性问题进行深入的研究.为有效评估地震作用下非饱和填土的主动土压力,基于极限分析上限原理和拟动力法,提出一种半解析水平片分法,计算具有非线性分布特征的非饱和土重力和地震惯性力所做外功率,并构建功能平衡方程,得到非饱和填土主动土压力显示半解析解.通过与解析解对比,验证该方法的合理性,并通过算例分析,揭示吸力效应的强化机制和非饱和填土主动土压力的地震响应规律.结果表明:忽略吸力效应会高估填土的主动土压力,吸力的强化作用不仅取决于填土类型,还与地震动特性密切相关;水平和竖向地震动对土压力有较大影响, 土压力系数峰值随土剪切模量的增加略有增加并向负方向移动,随地震周期的增加略有增加并向正方向移动;填土倾角较大时,坡顶附加荷载的影响更加显著;对于倾角大于100°的填土,墙G土界面摩擦角较大时,土压力相对较高. 相似文献
20.
The pseudodynamic test method provides a means of inexpensive seismic performance testing for laboratories that do not have a shaking table. However, most pseudodynamic tests to date have used planar portions of structures subjected to a single lateral component of base excitation, mimicking the type of testing that would occur on a shaking table. There has been little work on the extension of the pseudodynamic test method to three-dimensional testing of structures under multiple components of base excitation. In this paper a three-dimensional specimen is tested under a multicomponent fixed base excitation and the response is compared to shaking table tests. The paper presents an overview of the pseudodynamic test method, including non-planar extensions, and highlights many physical problems that occurred during the testing process. Many of these problems apply to any pseudodynamic test, not just non-planar tests, but the results show that very accurate non-planar tests can be achieved with careful error control. 相似文献