An improved complex multiple-support response spectrum method for the nonclassically damped linear system with coupled damping作者： Liu-Guohuan , Jj L, C L, G L, Jj H |
 |
|||||
 下载次数：
次 更多论文下载...
PDF格式（左键浏览，右键另存）：
DOI 10.1007/s10518-015-9818-y
Abstract：An improved complex multiple-support response spectrum (CMSRS) method considering the coupled damping, which is ignored in conventional CMSRS method, is proposed in this article. Due to the nonorthogonality of the damping matrix, the complex mode analysis method is adopted for equation decoupling. Nine new cross-correlation coefficients are introduced into theCMSRS formulae, thus the correlations between the modal responses under different excitations (velocity or acceleration) are comprehensively considered. A typical structure equipped with concentrated or coupled damper is taken as example to illustrate the differences between the conventional and improved CMSRS methods. Numerical results indicate that, for the structure equipped with the concentrated damper, the coupled damping has a minor effect on the dynamic response. However, for the structure equipped with the coupled damper, the relative deviation between the responses calculated by the two methods increases with increasindamping.Themaximumrelative deviation of displacement even exceeds 20 %.Therefore, it is significant to consider the coupled damping in seismic engineering.
Keywords：Non-classical damping system Multiple-support excitations Response spectrum method Complex mode superposition method Coupled damping
Introduction
In structural seismic design, response spectrum method is widely adopted in many existing building codes and specifications. However, the traditional response spectrum method is developed on the basis of uniform earthquake excitation and is inapplicable for the long-span structures subjected to multiple-support excitations. Several investigators extended the response spectrum method for the case of multiple-support excitations. Rutenberg and Heidebrecht (1987) proposed a simple and approximate response spectrum technique for the multiplesupport excitations problem. Yamamura and Tanaka (1990) studied the response of flexible multi-degree-of-freedom systems under multiple-support excitations by dividing the ground motion of the supports into independent subgroups. The coherency effect is included in the response spectrum analysis by Berrah and Kausel (1992) for the structures subjected to spatially varying motion. Kiureghian and Neumnhofer (1992) developed a responses spectrum method for multiple-support excitations using the principles of random vibration for classically damped linear system. Lou and Ku (1995) proposed a response spectrummethod for the seismic analysis of a multiple-support structure subjected to spatially varying ground motions. The large-span structure seismic response has been analyzed in Kato’s papers (Kato and Su 2002; Kato et al. 2003) considering the input difference, wave passage effect and local site effect. Song et al.(2007) presented a transformation approach for relatively accurate and rapid determination of the maximum peak responses of a linear structure subjected to three-dimensional excitations within all possible seismic incident angles. Alexander (2008) used real multi-station data from
SMART-1 to generate amore detailed picture of the spatial heterogeneity. Liang and Lee (2013) suggested a methodology to estimate the structural dynamic response considering regular time invariant loads as well as extreme loads, which are time variable.Based on the theoretical investigation, different kinds of structures, e.g., rigid plate (Hao
1991), symmetric and asymmetric structures (Hao and Xiao 1995, 1996), cable-stayed bridge (Allam and Datta 2000), multilayer architecture (Heredia-Zavoni and Leyva 2003),
two-line-support large space structure (Su et al. 2006) and train-bridge system (Zhang et al. 2010), and so on, are taken as examples to calculate their dynamic responses under
multiple-support seismic excitations.Recently, the dynamic analysis of non-classically damped linear systems attracts much attention, because many non-uniform damping problems are involved in practical structure analysis, e.g., soil-structure interaction system, structures equipped with supplemental dampers and structures composed of materials with different damping. For a non-classically damped linear system, the traditional mode superposition method fails due to the nonorthogonality of the damping matrix. A modal decomposition procedure based on the complex eigenvectors and eigenvalues of the system is used by Igusa et al. (1984) to derive general expressions for spectral moments of response. Maldonado and Singh (1991) presented a response spectrum method which combines the analytical advantage of the mode acceleration formulation and the practical advantage of the mode displacement formulation for seismic response calculation of non-classically damped structures. Constantinou and Symans (1992) studied earthquake dynamic responses of the one-story and three-story steel structures both with and without fluid viscous dampers. Results show that the addition of supplemental dampers significantly reduces the response of the structure in terms of both interstory drifts and shear forces. Moreover, the comparison between the experimental
responses and the analytical results show very good agreement. In order to get practical conditions of structural controllability, two necessary conditions of controllability of a
repeated eigenvalues system (regular and defective system) and their proofs are given by Yao and Gao (2011). Zhou et al. (2004, 2008; Yu et al. 2012) developed the CMSRS method for seismic analysis of non-classically damped linear system subjected to spatially varying multiple-support ground motions. It is debatable whether the coupled damping of non-classically damped linear system can be ignored in conventional CMSRS method. An improved CMSRS method for considering the coupled damping, which is ignored in conventional CMSRS method, is proposed in this paper. Furthermore, a typical structure equipped with concentrated or coupled damper is taken as example to investigate the difference between the conventional and improved CMSRS methods.
Conclusions It is debatable whether the coupled damping of non-classically damped linear system can be ignored in conventional CMSRS method. Therefore, the conventional CMSRS method is reconsidered and reanalyzed in detail in this paper and the main conclusions are summarized as follows: 1. An improved CMSRS method accounting for the coupled damping is deduced and proposed on the basis of conventional CMSRS method and random vibration theory. The complex mode analysis method is adopted to decouple the dynamic equation due to the nonorthogonality of the damping matrix, and the equations for structure
response estimations under multiple-support seismic excitations are deduced. Nine new cross-correlation coefficients are introduced into the CMSRS formulae, thus the
correlations between the modal responses under different input excitations (velocity or acceleration) are comprehensively considered.2. A typical structure equipped with concentrated or coupled damper is taken as example to investigate the differences between the conventional and improved CMSRS methods. The El Centro and Tianjin ground motions recorded at firm- and soft-soil conditions are selected as the dynamic excitations respectively. Results indicate that the coupled damping has a slight effect on the dynamic response of the structure equipped with a concentrated damper, but for the structure equipped with a coupled damper, e.g., the viscoelastic damper or the laminated rubber bearing, unnegligible errors will be introduced if the coupled damping is ignored. Moreover, the comparison between the displacement results from the proposed frequency method and the time history method for the structure equipped with coupled damper shows good agreement. Numerical results indicate that the improved CMSRS method is more reasonable and accurate for the dynamic analysis of structures equipped with coupled damper. |
||||||
| welcome to www.liuguohuan.net |
| 天津大学 建筑工程学院 ； 天津大学 前沿技术研究院； 国家重点实验室-水利工程仿真与安全 |
