• Earthquakes and Structures
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• v.18 no.2
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• pp.263-273
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• 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
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• v.13 no.3
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• pp.231-239
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• 2017

Fundamental period is one of the most critical parameters affecting the seismic design of buildings. In this paper, a very simple approach is presented for estimating the fundamental period of multiple-degree-of-freedom (MDOF) structures. The basic idea behind this approach is to replace the complicated MDOF system with an equivalent single-degree-of-freedom (SDOF) system. To realize this equivalence, a procedure for replacing a two-degree-of-freedom (2-DOF) system with an SDOF system, known as a two-to-single (TTS) procedure, is developed first; then, using the TTS procedure successively, an MDOF system is replaced with an equivalent SDOF system. The proposed approach is expressed in terms of mass, stiffness, and number of stories, without mode shape or any other parameters; thus, it is a very simple method. The accuracy of the proposed method is investigated by estimating the fundamental periods of many MDOF models; it is found that the results obtained by the proposed method agree very well with those obtained by eigenvalue analysis.

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

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

• Journal of Oriental Neuropsychiatry
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• v.14 no.1
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• pp.45-58
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• 2003

Alzheimer's disease(AD) is progressive neurodegenerative disease, which is pathologically characterized by neuritic plaques and neurofibrillary tangles associated with the acetylcholinesterase, apolipoprotein E and butylcholinesterase, and by mutations in the presenilin genes PS1 and PS2, and amyloid precursor proteins (APP) overexpression. The present research is to examine the inhibition effect of MDOF on PS-1, PS-2 and APP overexpression by detected to Western blotting. To verify the effects of MDOF on cognitive deficits further, we tested it on the scopolamine-induced amnesia model of the mice using the Morris water maze tests, and there was ameliorative effects of memory impairment as a protection to scopolamine. MDOF only partially blocked the increase in blood serum level of acetylcholinesterase and Uric acid induced by scopolamine, whereas blood glucose level was shown to attenuate the amnesia induced by scopolamine and inreased extracelluar serum level compared with only scopolamine injection. In conclusion, studies of MDOF that has been know as anti-choline and inhibition ablilities of APP overexpression, this could also be used further as a important research data for a preventive and promising symptomatic treatment for Alzheimer's disease.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.473-480
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• 1998

The substructuring pseudodynamic test is a hybrid testing method consisting of a numerical simulation of the earthquake response of an analytical model and a loading test of a specimen. The substructuring pseudodynamic testing technique has been applied to various seismic experiments since it has advantages over the shaking table test to study dynamic behaviors of relatively large scale structures. However, experimental errors are inevitable in substructuring pseudodynamic testing. Some of these errors can be monitored during the test, but, due to limitations in control system, they cannot be eliminated. For example, one cannot control exactly the displacements that are actually imposed on the structures at each time step. This paper focuses on a technique to minimize the cumulative effect of such control errors for MDOF system. For this purpose, the modified posterior adjustment of the time increment from a target value $\Delta$t$_{n}$ to an adjusted value is performed to minimize the effect of the control errors for MDOF system.for MDOF system.

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

• Structural Engineering and Mechanics
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• v.83 no.1
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• pp.31-43
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• 2022

A nonlinear gas-spring tuned mass damper is proposed to mitigate the seismic responses of the multi-degree-of-freedom (MDOF) structure, in which the nine-story benchmark model is selected as the controlled object. The nonlinear mechanical properties of the gas-spring are investigated through theoretical analysis and experiments, and the damper's control parameters are designed. The control performance and damping mechanism of the proposed damper attached to the MDOF structure are systematically studied, and its reliability is also explored by parameter sensitivity analysis. The results illustrate that the nonlinear gas-spring TMD can transfer the primary structure's vibration energy from the lower to the higher modes, and consume energy through its own relative movement. The proposed damper has excellent "Reconciling Control Performance", which not only has a comparable control effect as the linear TMD, but also has certain advantages in working stroke. Furthermore, the control parameters of the gas-spring TMD can be determined according to the external excitation amplitude and the gas-spring's initial volume.

• Computational Structural Engineering
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• v.8 no.3
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• pp.103-111
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• 1995

Evaluating nonlinear response of a MDOF system under dynamic stochastic loads such as seismic excitation usually requires excessive computational efforts. To alleviate this computational difficulty, an approximation is developed in which the MDOF inelastic system is replaced by a simple nonlinear equivalent system(ENS).Me ENS retains the most important properties of the original system such as dynamic characteristics of the first two modes and the global yielding behavior of the MDOF system. The system response is described by the maximum global(building) and local(interstory) drifts. The equivalency is achieved by two response scaling factors, a global response scaling factor R/sub G/, and a local response scaling factor R/sub L/, applied to the responses of the ENS to match those of the original MDOF system. These response scaling factors are obtained as functions of ductility and mass participation factors of the first two modes of structures by extensive regression analyses based on results of responses of the MDOF system and the ENS to actual ground accelerations recorded in past earthquakes. To develop the ENS with two response scaling factors, Special Moment Resisting Steel Frames are considered. Then, these response scaling factors are applied to the response of ENS to obtain the nonlinear response of MDOF system.

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