• Structural Engineering and Mechanics
• /
• v.73 no.3
• /
• pp.271-286
• /
• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.

• Earthquakes and Structures
• /
• v.4 no.4
• /
• pp.341-363
• /
• 2013

Earthquake response calculation, parametric analysis and seismic parameter optimization of base-isolated structures are some critical issues for seismic design of base-isolated structures. To calculate the earthquake responses for such non-symmetric and non-classical damping linear systems and to implement the earthquake resistant design codes, a modified complex mode superposition design response spectrum method is put forward. Furthermore, to do parameter optimization for base-isolation structures, a graphical approach is proposed by analyzing the relationship between the base shear ratio of a seismic base-isolation floor to non-seismic base-isolation one and frequency ratio-damping ratio, as well as the relationship between the seismic base-isolation floor displacement and frequency ratio-damping ratio. In addition, the influences of mode number and site classification on the seismic base-isolation structure and corresponding optimum parameters are investigated. It is demonstrated that the modified complex mode superposition design response spectrum method is more precise and more convenient to engineering applications for utilizing the damping reduction factors and the design response spectrum, and the proposed graphical approach for parameter optimization of seismic base-isolation structures is compendious and feasible.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1993.04a
• /
• pp.37-44
• /
• 1993

There are a lot of linear dynamic analysis methods for complex structures. Each method has advantages and shortcomings. Method of dynamic analysis for complex structure is selected considering characteristics of dynamic loading, computer facility available number of degree of freedem and accuracy of results. It is a main point of view to get economical results rather then accurate ones for analysis of general complex structures, Mode superposition method and direct integration method are generally used. However, the characteristics of load is not considered in mode superpositon method, the personal computer cannot be used in direct integration methods. To over-come these shortcomings, the component mode method incorporating Ritz algorithm updated is proposed to solve economically dynamic behavior of the structures. The purpose of study is a formulation of algorithm, and computer programing suitable for dynamic analysis of the complex structure in personal computer environment.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.14 no.1
• /
• pp.13-20
• /
• 1994

Determination of the number of modes to be included in the mode superposition method(MSM) is very important and difficult. Mode acceleration method(MAM) is recommended recently with the intention to overcome the problem. But the solution of the MAM is complex and complicate in frequency domain analysis. In this paper, advanced mode acceleration method(AMAM) is formulated and examined. The results from example analyses show that AMAM is a simple, accurate and reliable method compared with the MSM and the MAM.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.12 no.4
• /
• pp.671-679
• /
• 1999

건물의 진동에너지 소산능력을 향상하기 위하여 점탄성감쇠를 설치하게 되면 이른바 비비례 감쇠시스템이 되어 구조물은 복소수형태의 고유모드와 고유치를 가진다. 복소모드중첩법은 이러한 복소모드를 이용하여 중첩함으로써 비비례 감쇠시스템 구조물의 정확한 동적 거동을 얻을 수 있는 방법이다. 그러나 건물이 고층화되면 많은 자유도로 인하여 고유치해석 및 모드중첩과정에서 많은 시간과 노력이 필요하게 된다. 본 논문에서는 효율적인 구조물의 모형화를 위하여 강막가정과 행렬응축기법을 적용하였다. 또한 몇 개의 주요 모드만을 선택하여 중첩하는 방법에 대하여 연구하였으며 구조물의 진동에 영향을 주는 모드의 선택을 위한 복소모드 응답참여계수를 제안하였다. 제안된 해석방법의 정확성과 효율성을 검토하기 위하여 예제 구조물을 대상으로 해석한 결과, 응답의 정확성을 유지하면서 해석에 필요한 시간을 대폭 절감할 수 있었다.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.18 no.4 s.70
• /
• pp.373-383
• /
• 2005

The cask is used to transfer the radioactive material in various fields required to withstand hypothetical accident condition such as 9m drop impact in accordance with the requirement of the domestic requlations and IAEA. So far the impact force has been obtained by the finite element method with complex computational procedure. In this study, the dynamic impact response of the cask body is analyzed using the mode superposition method, and the analysis method is proposed. The results we also validated by comparing with previous experimental results and finite element analysis results. The present method Is simpler than finite element method and can be used to predict the global impact response of cask

• Structural Engineering and Mechanics
• /
• v.64 no.4
• /
• pp.473-485
• /
• 2017

An isolated building, composed of superstructure and isolation system which have very different damping properties, is typically non-classical damping system. This results in inapplicability of traditional response spectrum method for isolated buildings. A multidimensional response spectrum method based on complex mode superposition is herein introduced, which properly takes into account the non-classical damping feature in the structure and a new method is developed to estimate velocity spectra from the commonly used displacement or pseudo-acceleration spectra based on random vibration theory. The error of forced decoupling method, an approximated approach, is discussed in the viewpoint of energy transfer. From the base-isolated benchmark model, as a numerical example, application of the procedure is illustrated companying with comparison study of time-history method, forced decoupling method and the proposed method. The results show that the proposed method is valid, while forced decoupling approach can't reflect the characteristics of isolated buildings and may lead to insecurity of structures.

• Journal of KSNVE
• /
• v.10 no.1
• /
• pp.64-73
• /
• 2000

We present finite element equations in the Laplace-domain for linear viscoelastic and viscoelstically damped structures governed by a constitutive equation involving factional order derivative opeartors. These equations yield a nonstandard eigenproblem consisted of frequency dependent stiffness matrix. To solve this nonstandard eigenproblem we suggest an eigenvalue iteration procedure in the Laplace-domain. Improved Zenor and GHM material function type constitutive equations in the Laplace-domain are also available for this procedure. From above equations, complex eigenvalues and complex eigenvectors are obtained. Using obtained eigenvalues and eigenvectors, time domain analysis is performed by means of mode superposition. Finally, finite element solutions of viscoelastic and viscoeleastically damped sandwich beam are presented as an example.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.14 no.2
• /
• pp.75-84
• /
• 2010

An in-cabinet response spectrum should be generated to perform the seismic qualification of devices and instruments mounted inside safety-related electrical equipment installed in nuclear power plants. The response spectrum is available by obtaining accurate seismic responses at the device mounting location of the cabinet. The dynamic behavior of most of electrical equipment may not be easily analyzed due to their complex mass and stiffness distributions. Considering these facts, this study proposes a procedure to estimate the seismic responses of a structure by a combination of a test and subsequent analysis. This technique firstly constructs the modal equations of the structure by using the experiment modal parameters obtained from the impact test. Then the seismic responses of the structure may be calculated by a mode superposition method. A simple steel frame structure was fabricated as a specimen for the validation of the proposed method. The seismic responses of the specimen were estimated by using the proposed technique and compared with the measurements obtained from the shaking table tests. The study results show that it is possible to accurately estimate the seismic response of the structure by using the experimental modal parameters obtained from the impact test.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.5 no.4
• /
• pp.197-203
• /
• 2001

This study presents the results of shaking table test of scaled model structures with added viscoelastic dampers, which are considered to be one of the most efficient means of upgrading existing structures against seismic loads. The experimental results were compared with those from analysis based on the linear modeling of viscoelastic dampers. The parameters obtained from free vibration test were utilized in the analysis. According to the results the added viscoelastic dampers turned out to be effective in reducing the responses of the model structures. It was also found that the analysis with linear modeling of viscoelastic dampers could simulate the test results accurately.