首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 437 毫秒
1.
Closed-form expressions are obtained to calculate the approximate complex eigenvalues and eigenvectors of a system composed of a non-classically damped primary structure and a single degree of freedom oscillator. The expressions are obtained through a systematic second order perturbation analysis of a transformed eigenvalue problem of the combined system. The possibility of tuning between the structure and equipment is considered. The dynamic properties of the combined system are derived in terms of the complex eigenvalues and eigenvectors of the supporting structure and the frequency, mass and damping ratio of the equipment. Examples demonstrating the accuracy of the expressions for the eigenvalues and eigenvectors are presented. These eigenproperties are used for generation of floor response spectra for non-classically damped structures to incorporate the dynamic interaction effects between the structure and equipment.  相似文献   

2.
For a proper response spectrum analysis of a secondary system with multiple supports, the seismic inputs are required to be defined in terms of the auto and cross floor response spectra. If no feed-back or interaction effect from the secondary system to its supporting primary structure is suspected, these inputs can be developed by a direct analysis of the supporting structure alone. However, sometimes the effect of the interaction on the secondary system response can be quite significant. Herein, a method is developed to incorporate the feed-back effect, through proper modification of the interaction-free floor spectrum inputs. The interaction coefficients are used to effect such modifications in different floor spectral quantities. A procedure for the calculation of the interaction coefficients is proposed. The modified floor spectra when used as inputs to the secondary system do introduce the interaction effect in the secondary system response. A successful application of this method is demonstrated by numerical examples of secondary systems with three different secondary-to-primary system mass ratios.  相似文献   

3.
The step-by-step modal time history integration methods are developed for dynamic analysis of non-classically damped linear structures subjected to earthquake-induced ground motions. Both the mode displacement and mode acceleration-based algorithms are presented for the calculation of member and acceleration responses. The complex-valued eigenvectors are used to effect the modal decoupling of the equations of motion. However, the recursive step-by-step algorithms are still in terms of real quantities. The numerical results for the acceleration response and floor response spectra, obtained with these approaches, are presented. The mode acceleration approach is observed to be decidedly better than the mode displacement approach in as much as it alleviates the so-called missing mass effect, caused by the truncation of modes, very effectively. The utilization of the mode acceleration-based algorithms is, thus, recommended in all dynamic analyses for earthquake-induced ground motions.  相似文献   

4.
A method is presented for generating floor response spectra for aseismic design of equipment attached to primary structures. The method accurately accounts for tuning, interaction and non-classical damping, which are inherent characteristics of composite oscillator-structure systems. Modal synthesis and perturbation techniques are used to derive the modal properties of the composite system in terms of the known properties of the structure and the oscillator. Floor spectra are generated directly in terms of these derived properties and the input ground response spectrum using modal combination rules that account for modal correlations and non-classical damping. The computed spectra, in general, are considerably lower than conventional floor response spectra due to the effect of interaction. They provide more realistic and economical criteria for design of equipment. The method is accurate to the order of perturbation and is computationally efficient, as it avoids time-history analysis and does not require numerical eigenvalue evaluation of the composite oscillator-structure system. The results of a parametric study demonstrate the accuracy of the method and illustrate several key features of floor response spectra.  相似文献   

5.
A method is proposed for the deterministic and stochastic non-stationary analysis of linear composite systems with cascaded secondary subsystems subjected to a seismic input. This method makes it possible to evaluate, by means of a unitary formulation, the deterministic and non-stationary stochastic response of both classically and non-classically damped subsystems and of secondary subsystems multiply supported on the primary one, as well as the ground. The proposed procedure is very efficient from a computational point of view, because of the Kronecker algebra systematically employed. Indeed, by using this algebra, it is possible to obtain in a very compact and elegant form the eigenproperties of the composite system as a function of the eigenproperties of the two subsystems taken separately. Moreover, it is possible to write the first order differential equations governing the evolution of the second order moments of the response and to solve them in a simple way.  相似文献   

6.
A mode synthesis-based direct approach is presented to calculate seismic response of equipment supported on structures. The approach incorporates the effect of the dynamic interaction between the equipment and the supporting structure. The modal properties of the combined structure–equipment system are obtained by synthesizing the modal properties of the individual structures. The seismic input defined in terms of smoothed ground response spectra can be directly utilized in this approach. Both heavy and light equipment can be considered by the approach equally effectively. Numerical examples demonstrating the effectiveness of the proposed approach are presented.  相似文献   

7.
This paper deals with floor acceleration spectra, which are used for the seismic design and assessment of acceleration‐sensitive equipment installed in buildings. In design codes and in practice, not enough attention has been paid to the seismic resistance of such equipment. An ‘accurate’ determination of floor spectra requires a complex and quite demanding dynamic response history analysis. The purpose of the study presented in this paper is the development of a direct method for the determination of floor acceleration spectra, which enables their generation directly from the design spectrum of the structure, by taking into account the structure's dynamic properties. The method is also applicable to inelastic structures, which can greatly improve the economic aspects of equipment design. A parametric study of floor acceleration spectra for elastic and inelastic single‐degree‐of‐freedom (SDOF) and multiple‐degree‐of‐freedom structures was conducted by using (non)linear response history analysis. The equipment was modelled as an elastic single‐degree‐of‐freedom system. The proposed method was validated by comparing the results obtained with the more accurate results obtained in a parametric study. Due to its simplicity, the method is an appropriate tool for practice. In the case of inelastic structural behaviour, the method should be used in combination with the N2 method, or another appropriate method for simplified nonlinear structural analysis. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

8.
A procedure is described to compute the lateral and rotational floor response spectra of an asymmetric reactor building structure without a time history analysis. The spectral values obtained by filtering the prescribed ground motion first through the structure and the resulting lateral-rotational motions through simple oscillators are equal to the maximum lateral-rotational responses of the structure developed when the order of filtration is reversed. Based on the preceding concept a deterministic method is presented to construct the lateral-rotational floor response spectra utilizing the response spectrum technique.  相似文献   

9.
In stochastic analysis the knowledge of cross-correlation coefficients is required in order to combine the response of the modal Single-Degree-Of-Freedom (SDOF) oscillators for obtaining the nodal response. Moreover these coefficients play a fundamental role in the seismic analysis of structures when the response spectrum method is used. In fact they are used in some modal combination rules in order to obtain the maximum response quantities starting from the modal maxima. Herein a method for the evaluation of the cross-correlation coefficients for non-classically damped systems is presented. It is defined in the time domain instead of the frequency domain as usually encountered in the literature. Although non-classically damped structures possess complex eigenproperties, the great advantage in using this approach lies in the fact that the evaluation of these coefficients does not require complex quantities. Moreover a further particularization of the presented method allows a simple application of the spectrum analysis requiring only one response spectrum for an assigned damping ratio. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

10.
A new response spectrum method, which is named complex multiple-support response spectrum (CMSRS) method in this article, is developed for seismic analysis of non-classically damped linear system subjected to spatially varying multiple-supported ground motion. The CMSRS method is based on fundamental principles of random vibration theory and properly accounts for the effect of correlation between the support motions as well as between the modal displacement and velocity responses of structure, and provides an reasonable and acceptable estimate of the peak response in term of peak seismic ground motions and response spectra at the support points and the coherency function. Meanwhile, three new cross-correlation coefficients or cross covariance especially for the non-classically damped linear structures with multiple-supports excitations are derived under the same assumptions of the MSRS method of classically damped system. The CMSRS method is examined and compared to the results of time history analyses in two numerical examples of non-classically damped structures in consideration of the coherences of spatially variable ground motion. The results show that for non-classically damped structure, the cross terms representing the cross covariance between the pseudo-static and dynamic component are also quite small just as same as classically damped system. In addition, it is found that the usual way of neglecting all the off-diagonal elements in transformed damping matrix in modal coordinates in order to make the concerned non-classically damped structure to become remaining proportional damping property will bring some errors in the case of subjected to spatially excited inhomogeneous ground motion.  相似文献   

11.
An analytical method, based on matrix perturbation theory, is developed whereby a simple estimate can be obtained of the maximum dynamic response of lightly damped, light equipment (modelled as a n(2)-degree-of-freedom system) attached to a structure (modelled as a n(1)-degree-of-freedom system) subjected to ground motion or impact. A natural frequency of the equipment is considered close or equal to a natural frequency of the structure. It is assumed that the information available to the designer is a time history of the ground motion or impact, or an associated design spectrum; the fixed base modal properties of the structure; and the fixed base modal properties of the equipment. The method employed avoids the direct conventional analysis of a n(2) + n(1)-degree-of-freedom system either by modal or by matrix time-marching methods; as well as errors in estimates of peak response due to the possible unreliability of numerical schemes because of the lightness of the equipment, or due to uncertainty as to the appropriate procedure for summing the contributions of the two closely spaced modes which occur in the system. The proposed procedure is demonstrated for an example equipment-structure system. Computed results based on the method are in close agreement with results obtained through a Newmark time-integration scheme.  相似文献   

12.
The stationary response of multi-degree-of-freedom non-classically damped linear systems subjected to stationary input excitation is studied. A modal decomposition procedure based on the complex eigenvectors and eigenvalues of the system is used to derive general expressions for the spectral moments of response. These expressions are in terms of cross-modal spectral moments and explicitly account for the correlation between modal responses; thus, they are applicable to structures characterized with significant non-classical damping as well as structures with closely spaced frequencies. Closed form solutions are presented for the important case of response to white-noise input. Various quantities of response of general engineering interest can be obtained in terms of these spectral moments. These include mean zero-crossing rate and mean, variance and distribution of peak response over a specified duration. Examples point out several instances where non-classical damping effects become significant and illustrate the marked improvement of the results of this study over conventional analysis based on classical damping approximations.  相似文献   

13.
After reviewing briefly a recently proposed procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady-state response, a modified procedure is presented which also appears to be highly efficient for non-classically damped systems of the type encountered in studies of soil-structure interaction. The concepts involved are developed by reference to viscously damped single-degree-of-freedom systems, and numerical solutions are included to illustrate the accuracy and efficiency of the proposed procedure and its superiority over the classical Discrete Fourier Transform approach.  相似文献   

14.
A simplified damped oscillator model is proposed to simulate unbounded soil for the vertical vibration analysis of rigid embedded foundations. Based on the dynamic responses of a foundation–soil system, an optimal equivalent model is determined as the best simplified model. Magnification responses of a foundation–soil system simulated by the optimal equivalent model are well consistent with those obtained by the half-space theory and by a widely used computer program even as embedment depth or vibrating mass increases. The optimal equivalent model utilizing only three parameters can result in responses as accurate as the existing models, which use more parameters. This proposed method uses much simpler procedure than optimization techniques used by most existing discrete models. This proposed method may also be easily and accurately applied to practical soil–structure interaction analysis.  相似文献   

15.
Rolling isolation systems (RISs) protect mission‐critical equipment and valuable property from earthquake hazards by decoupling the dynamic responses of vibration‐sensitive objects from horizontal floor motions. These responses involve the constrained rolling of steel balls between bowl‐shaped surfaces. The light damping of steel balls rolling between steel plates can be augmented by adhering thin rubber sheets to the plates, thereby increasing the rolling resistance and decreasing the displacement demand on the RIS. An assessment of the ability of lightly‐ and heavily‐damped RISs to mitigate the hazard of seismically induced failures requires high‐fidelity models that can adequately capture the systems' intrinsic nonlinear behavior. The simplified model presented in this paper is applicable to RISs with any potential energy function, is amenable to both lightly‐ and heavily‐damped RISs, and is validated through the successful prediction of peak responses for a wide range of disturbance frequencies and intensities. The validated model can therefore be used to compute the spectra of peak floor motions for which displacement demands equal capacity. These spectra are compared with representative floor motion spectra provided by the American Society of Civil Engineers 7–10. The damping provided by rolling between thin viscoelastic sheets increases the allowable floor motion intensity by a factor of 2–3, depending on the period of motion. Acceleration responses of isolation systems with damping supplied in this fashion do not grow with increased damping, even for short‐period excitations. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

16.
Response parameters used to estimate nonstructural damage differ depending on whether deformation‐sensitive or acceleration‐sensitive components are considered. In the latter case, seismic demand is usually represented through floor spectra, that is response spectra in terms of pseudo‐acceleration, which are calculated at the floor levels of the structure where the nonstructural components are attached to. Objective of this paper is to present a new spectrum‐to‐spectrum method for calculating floor acceleration spectra, which is able to explicitly account for epistemic uncertainties in the modal properties of the supporting structure. By using this method, effects on the spectra of possible variations from nominal values of the periods of vibration of the structure can be estimated. The method derives from the extension of closed‐form equations recently proposed by the authors to predict uniform hazard floor acceleration spectra. These equations are built to rigorously account for the input ground motion uncertainty, that is the record‐to‐record variability of the nonstructural response. In order to evaluate the proposed method, comparisons with exact spectra obtained from a standard probabilistic seismic demand analysis, as well as spectra calculated using the Eurocode 8 equation, are finally shown. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

17.
为了研究设备所在楼层位置对设备-结构相互作用的影响,以某高层钢框架为例,将设备分别放置于结构顶层和底层设计了2种设备-结构体系模型,然后利用ANSYS有限元分析软件对整体模型进行地震响应时程分析。分析结果表明:在El Centro波、Taft波和人工波作用下,当设备频率与结构基频调谐时,设备-结构相互作用会令结构动力响应减小而设备动力响应显著增大;设备-结构相互作用的大小与设备所在楼层密切相关:顶层设备与结构间的相互作用比底层更加剧烈,这与位于不同楼层的设备间等效质量以及底端输入激励频谱的差异有关。  相似文献   

18.
The evaluation of the dynamic response of non-classically damped linear structures requires the solution of an eigenproblem with complex eigenvalues and modal shapes. Since in practice only a small number of complex modes are needed, the complex eigenvalue problem is solved in the modal subspace in which the generalized damping matrix is not uncoupled by classical real modes. It follows that the evaluation of the structural response requires in both cases the determination of complex modes by numerical techniques, which are not as robust as techniques currently used for the solution of the real eigenvalue problem, and the use of complex algebra. In the present paper an unconditionally stable step-by-step procedure is presented for the response of non-classically damped structures in the modal subspace without using complex quantities. The method is based on the evaluation of the fundamental operator in approximated form of the numerical procedure. In addition, the method can be easily modified to incorporate the modal superposition pseudo-static correction terms.  相似文献   

19.
The feasibility of using viscoelastic (VE) dampers to mitigate earthquake-induced structural response is studied in this paper. The properties of VE dampers are briefly described. A procedure for evaluating the VE damping effect when added to a structure is proposed in which the damping effect of VE dampers is incorporated into modal damping ratios through an energy approach. Computer simulation of the damped response of a multi-storey steel frame structure shows significant reduction in floor displacement levels.  相似文献   

20.
A displacement-based design (DBD) procedure aiming to proportion hysteretic damped braces (HYDBs) in order to attain, for a specific level of seismic intensity, a designated performance level of a structure is proposed for the retrofitting of framed buildings. A key step for the reliability of the DBD procedure is the selection of the equivalent viscous damping in order to account for the energy dissipated by the damped braced frame. In this paper, expressions of the equivalent damping are obtained considering the energy dissipated by the HYDBs and the framed structure. To this end, dynamic analyses of an equivalent single degree of freedom system, whose response is idealized by a trilinear model, are carried out considering real accelerograms matching, on the average, Eurocode 8 (EC8) response spectrum for a medium subsoil class. Then, a three-storey reinforced concrete (r.c.) framed structure of a school building, designed in a medium-risk seismic region according to the Italian code in force in 1975, is supposed as retrofitted as if in a high-risk seismic region of the current seismic code (NTC08) by the insertion of HYDBs. Nonlinear static analyses are carried out to evaluate the vulnerability of the primary structure, characterized by the lack of interior girders along the floor slab direction, and to select optimal properties of the HYDBs. The effectiveness of the retrofitting solutions is checked referring to nonlinear dynamic analyses, considering artificially generated accelerograms whose response spectra match those adopted by NTC08 for the earthquake design levels corresponding to the serviceability and ultimate limit states.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号