• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1078-1086
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• 2009

This paper presents a Fourier based algorithm for estimating the parameters of the low frequency oscillating modes. The proposed methods estimates various parameters(frequency, damping factor, mode magnitude, phase) by fitting Fourier spectrum and phase with a damped exponential cosine function. Dominant frequency is selected by taking frequency corresponding to the peak spectrum, and damping factor is estimated using the left/right spectra of Fourier spectrum. In addition, mode magnitude is calculated by the normalized peak spectrum, and phase is estimated from spectrum phase. Also, we introduce an accuracy index in order to determine the accuracy of the estimated parameters, and the index is calculated using the deviations of the peak spectrum and the left/right spectra. The parameter estimation methods proposed in this paper include very simple arithmetical processes, so the algorithms are simple and the calculation speed is very fast. The proposed methods are applied to test functions with two dominant modes. The results show that the proposed methods are highly applicable to low frequency parameter estimation.

• Smart Structures and Systems
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• v.6 no.4
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• pp.363-372
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• 2010

Accurate peak response estimation of a seismically excited structure with frictional damping system (FDS) is very difficult since the structure with FDS shows nonlinear behavior dependent on the structural period, loading characteristics, and relative magnitude between the frictional force and the excitation load. Previous studies have estimated the peak response of the structure with FDS by replacing a nonlinear system with an equivalent linear one or by employing the response spectrum obtained based on nonlinear time history and statistical analysis. In case that earthquake excitation is defined probabilistically, corresponding response of the structure with FDS becomes to have probabilistic distribution. In this study, nonlinear time history analyses were performed for the structure with FDS subjected to artificial earthquake excitation generated using Kanai-Tajimi filter. An equation for the probability density function (PDF) of the displacement response is proposed by adapting the PDF of the normal distribution. Coefficients of the proposed PDF are obtained by regression of the statistical distribution of the time history responses. Finally, the correlation between the resulting PDFs and statistical response distribution is investigated.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.11
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• pp.483-493
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• 2002

The damping ratio ${\xi}$ of the unit-step response of a second-order discrete system is a function of only the location of the closed-loop poles and is not directly related to the location of the system zero. However, the peak overshoot of the response is the function of both the damping ratio ${\xi}$ and an angle ${\alpha}$, which is the phasor angle of the damped sinusoidal response and is determined by the relative location of the zero with respect to the closed-loop poles. Therefore, if the zero and the open-loop poles are relatively adjusted, through pole-zero cancellation, to maintain the desired (or designed) closed-loop poles, the damping ratio ${\xi}$ will also be maintained, while the angle ${\alpha}$ changes. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is considered as a function of the angle ${\alpha}$ or the system zero location. In this paper the effects of the relative location of the zero on the system performance of a second-order discrete system is studied, and a design method of digital compensator which achieves a minimum peak overshoot while maintaining the desired system mode and the damping ratio of the unit step response is presented.

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1249-1260
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• 2003

This present work focuses on the influence of nonlinearities associated with impact on the rocking behavior of a rigid body block subjected to a two-dimensional excitation in the horizontal and vertical directions. The nonlinearities in rocking system are found to be strongly dependent on the impact between the block and the base that abruptly reduces the kinetic energy. In this study, the rocking systems of the two types are considered : The first is an undamped rocking system model that disregards the energy dissipation during the impact and the second is a damped rocking system, which incorporates energy dissipation during the impact. The response analysis is carried out by a numerical method using a non-dimensional rocking equation in which the variations in the excitation levels are considered. Chaos responses are observed over a wide range of parameter values, and particularly in the case of large vertical displacements, the chaotic characteristics are observed in the time histories, Poincare sections, the power spectral density and the largest Lyapunov exponents of the rocking responses. Complex behavior characteristics of rocking responses are illustrated by the Poincare sections.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.382-386
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• 2002

The damping ratio $\zeta$ of the unit-step response of a second-order discrete system is a function of only the location of the closed-loop poles and is not directly related to the location of the system zero. However, the peak overshoot of the response is the function of both the damping ratio $\zeta$ and an angle $\alpha$, which is the phasor angle of the damped sinusoidal response and is determined by the relative location of the zero with respect to the closed-loop poles. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is considered as a function of the angle $\alpha$ or the system zero location. In this paper the effects of the relative location of the zero on the system performance of a second-order discrete system is studied, and a design method of digital compensator which achieves arbitrary steady-state response with minimum peak overshoot while maintaining the desired system mode and the damping ratio of the unit step response is presented.

• Smart Structures and Systems
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• v.17 no.2
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• pp.231-256
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• 2016

This study concerns the derivation of optimum tuning formulas for a passive Tuned Mass Damper (TMD) device, for the case of benchmark ideal excitations acting on a single-degree-of-freedom (SDOF) damped primary structure. The free TMD parameters are tuned first through a non-linear gradient-based optimisation algorithm, for the case of harmonic or white noise excitations, acting either as force on the SDOF primary structure or as base acceleration. The achieved optimum TMD parameters are successively interpolated according to appropriate analytical fitting proposals, by non-linear least squares, in order to produce simple and effective TMD tuning formulas. In particular, two fitting models are presented. The main proposal is composed of a simple polynomial relationship, refined within the fitting process, and constitutes the optimum choice. A second model refers to proper modifications of literature formulas for the case of an undamped primary structure. The results in terms of final (interpolated) optimum TMD parameters and of device effectiveness in reducing the structural dynamic response are finally displayed and discussed in detail, showing the wide and ready-to-use validity of the proposed optimisation procedure and achieved tuning formulas. Several post-tuning trials have been carried out as well on SDOF and MDOF shear-type frame buildings, by confirming the effective benefit provided by the proposed optimum TMD.

• Advances in aircraft and spacecraft science
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• v.3 no.2
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• pp.197-209
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• 2016

The Spacecraft (S/C) numerical sine test-predictions are usually performed through Finite Element Method (FEM) Frequency Response Analysis (FRA), that is the hypothesis of steady-state responses to harmonic excitation to the S/C base is made. In the test practice, the responses are transient and may be significantly different from those predicted through FRA. One of the most significant causes of discrepancy between prediction and test consists in the beating phenomena. After a brief overview of the topic, the typical causes of beating are described in the first part of the paper. Subsequently, focus is made on the sine sweep rate effect, which often leads to have beatings after the resonance of weakly damped modes. In this work, the approach illustrated in the literature for calculating the sine sweep rate effect in the case of Single-Degree-Of-Freedom (SDOF) oscillators is extended to Multi-Degrees-Of-Freedom (MDOF) systems, with the aim of increasing the accuracy of the numerical sine test-predictions. Assumptions and limitations of the proposed methodology are detailed along the paper. Several assessments with test results are discussed and commented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.37-43
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• 2014

The extended framework of Hamilton's principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation. Based upon such framework, a new variational numerical method of linear elasticity is provided for the classical single-degree-of-freedom dynamical systems. For the undamped system, the algorithm is symplectic with respect to the time step. For the damped system, it is shown to be accurate with good convergence characteristics.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.1
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• pp.13-19
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• 2001

This paper deals with decentralized control scheme and its application to multi-machine power systems. Decentralized control scheme has several practical advantages, because power system has geographically distributed characteristics. In this paper, decentralized observer-based optimal Power System Stabilizer(PSS) and Thyristor-Controlled Series Capacitor(TCST) controller are designed and tested in WSCC 9 bus system with one TCSC installed. Simulation results show that the proposed decentralized controller has satisfactory performances comparable to the centralized controller. In addition, using modal analysis, this paper shows that the proposed decentralized controller significantly affects only one pair of eigenvalues which have high participation with each generator, while slightly affects other eigenvalues. This result indicates that the application of the decentralized control scheme to enhance power system dynamic stability via excitation control have potential advantages because each low-damped mode occurs dominantly by each decentralized subsystem.