• Steel and Composite Structures
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• v.25 no.4
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• pp.497-503
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• 2017

In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.19-26
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• 2003

In energy-based design, the structures are generally transformed into equivalent SDOF systems to obtain the input and the dissipated energy. In this study the energy demands in multi-story structures were compared with that of equivalent single degree of freedom systems to validate the transformation method. Three-, eight-, and twenty-story steel moment-resisting frames and buckling restrained braced frames are compared with those of equivalent single degree of freedom systems. Sixty earthquake ground motions recorded in different soil conditions were used to compute the input and hysteretic energy demands in model structures. According to the analysis results, in 3 and 8-story structures the hysteretic energy demands computed in the equivalent SDOF structures are compatible with those computed in the original MDOF structures, while in the 20-story structures the transformed equivalent structures underestimated the hysteretic energy demands.

• Wind and Structures
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• v.21 no.5
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• pp.523-536
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• 2015

To study the vibration frequency of super high-rise buildings in the process of vortex induced vibration (VIV), wind tunnel tests of multi-degree-of-freedom (MDOF) aero-elastic models were carried out to measure the vibration frequency of the system directly. The effects of structural damping, wind field category, mass density, reduced wind velocity ($V_r$), as well as VIV displacement on the VIV frequency were investigated systematically. It was found that the frequency drift phenomenon cannot be ignored when the building is very high and flexible. When $V_r$ is less than 8, the drift magnitude of the frequency is typically positive. When $V_r$ is close to the critical wind velocity of resonance, the frequency drift magnitude becomes negative and reaches a minimum at the critical wind velocity. When $V_r$ is larger than12, the frequency drift magnitude almost maintains a stable value that is slightly smaller than the fundamental frequency of the aero-elastic model. Furthermore, the vibration frequency does not lock in the vortex shedding frequency completely, and it can even be significantly modified by the vortex shedding frequency when the reduced wind velocity is close to 10.5.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2006.03a
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• pp.519-526
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• 2006

This paper compares the seismic response control performance of linear and non-linear models fer tuned liquid damper (TLD). The existing linear and nonlinear TLD models were used for the numerical analysis of single degree of freedom (SDOF) and multi degree of freedom (MDOF) systems with TLD. The nonlinear model considers the variation of the frequency and damping of the TLD with varying excitation amplitude while the linear one has the invariant parameters. Numerical analysis results from SDOF systems indicate that the nonlinear model shows about 5% better control performance than linear one when the mass ratio is 2% and the optimal parameters for reducing peak responses are dependent on the characteristics of the excitation earthquake loads.

• Smart Structures and Systems
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• v.15 no.3
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• pp.897-911
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• 2015

This study presents a novel approach based on advancements in Evolutionary Computation for data-driven modeling of complex multi-dimensional memory-dependent systems. The investigated example is a benchmark coupled three-dimensional system that incorporates 6 Bouc-Wen elements, and is subjected to external excitations at three points. The proposed technique of this research adapts Genetic Programming for discovering the optimum structure of the differential equation of an auxiliary variable associated with every specific degree-of-freedom of this system that integrates the imposed effect of vibrations at all other degrees-of-freedom. After the termination of the first phase of the optimization process, a system of differential equations is formed that represent the multi-dimensional hysteretic system. Then, the parameters of this system of differential equations are optimized in the second phase using Genetic Algorithms to yield accurate response estimates globally, because the separately obtained differential equations are coupled essentially, and their true performance can be assessed only when the entire system of coupled differential equations is solved. The resultant model after the second phase of optimization is a low-order low-complexity surrogate computational model that represents the investigated three-dimensional memory-dependent system. Hence, this research presents a promising data-driven modeling technique for obtaining optimized representative models for multi-dimensional hysteretic systems that yield reasonably accurate results, and can be generalized to many problems, in various fields, ranging from engineering to economics as well as biology.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1990.10a
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• pp.79-84
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• 1990

The modal parameter estimations of linear multi-degree-of-freedom structural dynamic systems are carried out in time domain. For this purpose, the equation of motion is transformed into the autoregressive and moving average model with auxiliary stochastic input (ARMAX) model. The parameters of the ARMAX model are estimated by using the sequential prediction error method. Then, the modal parameters of the system are obtained thereafter. Experimental results are given for a 3-story building model subject to ground exitations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.229-234
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• 2001

A practical and effective semi-active on-off control law is developed for vibration attenuation of a natural, multi-degree-of-freedom suspension system, when its operational response mode is available. It does not need the accurate system parameters and dynamics of semi-active actuator. It reduces the total vibratory energy of the system including the work done by external disturbances and the maximum energy dissipation direction of the semi-active control device is tuned to the operational response mode of the structure. The effectiveness of the control law is illustrated with a three degree-of-freedom excavator cabin model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1989.10a
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• pp.46-50
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• 1989

Methods for the estimation of the coefficient matrices in the equation of motion for a linear multi-degree-of-freedom structure arc studied. For this purpose, the equation of motion is transformed into an auto-regressive and moving average with auxiliary input (ARMAX) model. The ARMAX parameters are evaluated using several methods of parameter estimation; such as toe least squares, the instrumental variable, the maximum likelihood and the limited Information maximum likelihood methods. Then the parameters of the equation of motion are recovered therefrom. Numerical example is given for a 3-story building model subjected to an earthquake exitation.

• Structural Engineering and Mechanics
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• v.13 no.4
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• pp.369-385
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• 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
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• v.3 no.4
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• pp.423-437
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• 2007

The empirical mode decomposition (EMD) method is well-known for its ability to decompose a multi-component signal into a set of intrinsic mode functions (IMFs). The method uses a sifting process in which local extrema of a signal are identified and followed by a spline fitting approximation for decomposition. This method provides an effective and robust approach for decomposing nonlinear and non-stationary signals. On the other hand, the IMF components do not automatically guarantee a well-defined physical meaning hence it is necessary to validate the IMF components carefully prior to any further processing and interpretation. In this paper, an attempt to use the EMD method to identify properties of nonlinear elastic multi-degree-of-freedom structures is explored. It is first shown that the IMF components of the displacement and velocity responses of a nonlinear elastic structure are numerically close to the nonlinear normal mode (NNM) responses obtained from two-dimensional invariant manifolds. The IMF components can then be used in the context of the NNM method to estimate the properties of the nonlinear elastic structure. A two-degree-of-freedom shear-beam building model is used as an example to illustrate the proposed technique. Numerical results show that combining the EMD and the NNM method provides a possible means for obtaining nonlinear properties in a structure.