• Proceedings of the KSME Conference
• /
• 2000.04a
• /
• pp.415-419
• /
• 2000

Multi-degree-of-freedom (MDOF) displacement measurement Is needed In many application fields: precision machine control, precision assembly, vibration analysis, and so on. This paper presents a new MDOF displacement measurement method using a laser diode (LD), two position-sensitive detectors (PSDs), and a conventional diffraction grating. It utilizes typical features of a diffraction grating to obtain the information of MDOF displacement. MDOF displacement is calculated from the independent coordinate values of the diffracted ray spots on the PSDs. Forward and inverse kinematic problems were solved to compute the MDOF displacement of a rigid body. Experimental results show maximum absolute errors of less than ${\pm}10$ micrometers in translation and ${\pm}30$ arcsecs in rotation.

• Structural Engineering and Mechanics
• /
• v.61 no.1
• /
• pp.105-116
• /
• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Journal of Industrial Technology
• /
• v.25 no.A
• /
• pp.23-30
• /
• 2005

The capacity spectrum method(CSM) can be used for the evaluation of inelastic maximum response of structures and has been recently used in the seismic design using the incorporation of pushover analysis and response spectrum method. To efficiently evaluate seismic performance of multi-degree-of freedom(MDOF) bridge structures, it is important that the equivalent response of MDOF bridge structures should be calculated. To calculate the equivalent response of MDOF system, equivalent responses are obtained by using Song method, Fajfar method and Calvi method. Also, those responses are applied to CSM method and seismic performance of bridge according to the ESDOF method are compared and evaluated straightforwardly.

• Earthquakes and Structures
• /
• v.18 no.2
• /
• pp.263-273
• /
• 2020

The use of energy concepts in seismic analysis and design of structures requires the understanding of the input energy response of multi-degree-of-freedom (MDOF) systems subjected to strong ground motions. For design purposes and non-time consuming analysis, however, it would be beneficial to associate the input energy response of MDOF systems with those of single-degree-of-freedom (SDOF) systems. In this paper, the theoretical formulation of energy input to MDOF systems is developed on the basis that only a particular portion of the total mass distributed among floor levels is effective in the nth-mode response. The input energy response histories of several reinforced concrete frames subjected to a set of eleven horizontal acceleration histories selected from actual recorded events and scaled in time domain are obtained. The contribution of the fundamental mode to the total input energy response of MDOF frames is demonstrated both graphically and numerically. The input energy of the fundamental mode is found to be a good indicator of the total energy input to two-dimensional regular MDOF structures. The numerical results computed by the proposed formulation are verified with relative input energy time histories directly computed from linear time history analysis. Finally, the elastic input energies are compared with those computed from time history analysis of nonlinear MDOF systems.

• Earthquakes and Structures
• /
• v.14 no.2
• /
• pp.155-165
• /
• 2018

Methods based on nonlinear static analysis as simple tools could be used for the seismic analysis and assessment of structures. In the present study, capability of the N2 method as a well-known nonlinear analysis procedure examines for the estimation of the damage index of multi-storey reinforced concrete frames. In the implemented framework, equivalent single-degree-of-freedom (SDOF) models are utilized for the global damage estimation of multi-degree-of-freedom (MDOF) systems. This method does not require high computational analysis and subsequently decreases the required time of seismic design and assessment process. To develop the methodology, RC frames with period range from 0.4 to 2.0 s under 40 records are studied. The effectiveness of proposed technique is evaluated through numerical study under near- and far-field earthquake ground motions. Finally, the results of developed models are compared with two other simplified schemes along with nonlinear time history analysis results of multi-storey frames. To improve the accuracy of damage estimation, a modified relation is presented based on the N2 method results for near- and far-field earthquakes.

• Earthquakes and Structures
• /
• v.7 no.1
• /
• pp.17-38
• /
• 2014

As the desire for high performance buildings increases, it is increasingly evident that engineers require reliable methods for the estimation of seismic demands on both structural and non-structural components. To this extent, improved tools for the prediction of floor spectra would assist in the assessment of acceleration sensitive non-structural and secondary components. Recently, a new procedure was successfully developed and tested for the simplified construction of floor spectra, at various levels of elastic damping, atop single-degree-of-freedom structures. This paper extends the methodology to multi-degree-of-freedom (MDOF) supporting systems responding in the elastic range, proposing a simplified modal combination approach for floor spectra over upper storeys and accounting for the limited filtering of the ground motion input that occurs over lower storeys. The procedure is tested numerically by comparing predictions with floor spectra obtained from time-history analyses of RC wall structures of 2- to 20-storeys in height. Results demonstrate that the method performs well for MDOF systems responding in the elastic range. Future research should further develop the approach to permit the prediction of floor spectra in MDOF systems that respond in the inelastic range.

• Structural Engineering and Mechanics
• /
• v.13 no.4
• /
• pp.369-385
• /
• 2002

Ductility capacity is comprehensively studied for steel moment-resisting frames. Local, story and global ductility are being considered. An appropriate measure of global ductility is suggested. A time domain nonlinear seismic response algorithm is used to evaluate several definitions of ductility. It is observed that for one-story structures, resembling a single degree of freedom (SDOF) system, all definitions of global ductility seem to give reasonable values. However, for complex structures it may give unreasonable values. It indicates that using SDOF systems to estimate the ductility capacity may be a very crude approximation. For multi degree of freedom (MDOF) systems some definitions may not be appropriate, even though they are used in the profession. Results also indicate that the structural global ductility of 4, commonly used for moment-resisting steel frames, cannot be justified based on this study. The ductility of MDOF structural systems and the corresponding equivalent SDOF systems is studied. The global ductility values are very different for the two representations. The ductility reduction factor $F_{\mu}$ is also estimated. For a given frame, the values of the $F_{\mu}$ parameter significantly vary from one earthquake to another, even though the maximum deformation in terms of the interstory displacement is roughly the same for all earthquakes. This is because the $F_{\mu}$ values depend on the amount of dissipated energy, which in turn depends on the plastic mechanism, formed in the frames as well as on the loading, unloading and reloading process at plastic hinges. Based on the results of this study, the Newmark and Hall procedure to relate the ductility reduction factor and the ductility parameter cannot be justified. The reason for this is that SDOF systems were used to model real frames in these studies. Higher mode effects were neglected and energy dissipation was not explicitly considered. In addition, it is not possible to observe the formation of a collapse mechanism in the equivalent SDOF systems. Therefore, the ductility parameter and the force reduction factor should be estimated by using the MDOF representation.

• Smart Structures and Systems
• /
• v.31 no.5
• /
• pp.531-543
• /
• 2023

Base isolation is one of the most widely implemented and well-known technique to reduce structural vibration and damages during an earthquake. However, while the base-isolated structure reduces storey drift significantly, it also increases the base drifts causing many practical problems. This study proposes the use of Shape Memory Alloys (SMA) wires for the reduction in base drift while controlling the overall structure vibrations. A multi-degree-of-freedom (MDOF) structure along with base isolators and Shape-Memory-Alloys (SMA) wires in diagonal is tested experimentally and analytically. The isolation bearing considered in this study consists of laminates of steel and silicon rubber. The performance of the proposed structure is evaluated and studied under different loadings including harmonic loading and seismic excitation. To assess the seismic performance of the proposed structure, shake table tests are conducted on base-isolated MDOF frame structure incorporating SMA wires, which is subjected to incremental harmonic and historic seismic loadings. Root mean square acceleration, displacement and drift are analyzed and discussed in detail for each story. To better understand the structure response, the percentage reduction of displacement is also determined for each story. The result shows that the reduction in the response of the proposed structure is much better than conventional base-isolated structure.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2003.09a
• /
• pp.419-426
• /
• 2003

An efficient procedure using LQR method for determining optimal sliding surfaces appropriate for different controller types is provided. The parametric evaluation of the dynamic characteristics of sliding surfaces is peformed in terms of SMC controller performance of single-degree-of-freedom(SDOF) systems. The control force limit is considered in this procedure. Numerical simulations for multi-degree-of-freedom(MDOF) systems verify the effectiveness of proposed method.

• Wind and Structures
• /
• v.32 no.3
• /
• pp.219-225
• /
• 2021

Wind tunnel test models for super tall buildings mainly include synchronized pressure models, high-frequency force balance models, forced vibration models and aeroelastic models. Aeroelastic models, especially MDOF aeroelastic models, are relatively accurate, and designing MDOF model is an important step in aero-model wind tunnel tests. In this paper, the authors propose a simple and accurate design method for MDOF model. The purpose of this paper is to make it easier to design MDOF models without unnecessary experimentation, which is of great significance for the use of the aero-model for tall buildings.