• 한국철도학회논문집
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• 제9권1호
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• pp.63-68
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• 2006

This paper proposes a fast Fourier transform(FFT)-based spectral analysis method(SAM) for the dynamic responses of the linear discrete dynamic models with non-proportional damping. The SAM was developed by using discrete Fourier transform(DFT)-theory. To verify the proposed SAM, a three-DOF system with non-proportional viscous damping is considered as an illustrative example. The present SAM is evaluated by comparing the dynamic responses obtained by SAM with those obtained by Runge-Kutta method.

• 한국정밀공학회지
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• 제12권7호
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• pp.99-106
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• 1995

Frequency response functions are of great use in dynamic analysis of structural systems. The present paper proposes an efficient method for computation of the frequency rewponse functions of linear structural dynamic models with a sparse, non-proportional damping matrix. An exact condensation procedure is proposed which enables the present method to condense the matrices without resulting in any errors. Also, an iterative scheme is proposed to be able to avoid matrix inversion in computing frequency response matrix. The proposed method is illustrated through a numerical example.

• 한국소음진동공학회논문집
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• 제19권10호
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• pp.1021-1027
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• 2009

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping. In the second stage, a damping matrix is estimated with the mass and stiffness matrices fixed. Methods to estimate a damping matrix for this purpose are proposed in this paper. For a system with proportional damping, a damping matrix is estimated using the modal parameters extracted from the measured responses and the modal matrix calculated from the mass and stiffness matrices from the first stage. For a system with non-proportional damping, a damping matrix is estimated from the impedance matrix which is the inverse of the FRF matrix. Only one low or one column of the FRF matrix is measured, and the remaining FRFs are synthesized to obtain a full FRF matrix. This procedure to obtain a full FRF matrix saves time and effort to measure FRFs.

• Earthquakes and Structures
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• 제18권5호
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• pp.609-623
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• 2020

This paper presents a displacement-based seismic design procedure for new structures with fluid viscous dampers and/or for existing structures, where these devices are required as a retrofit measure and damage control. To consider the non-proportional damping produced by these devices in a conventional modal spectral analysis, the effect of the fluid viscous dampers is approximated as the sum of a proportional damping matrix and a complementary matrix which is representative of non-proportional damping matrix. To illustrate the application of this procedure and evaluate the performance of structures designed with the procedure proposed, five regular plane frames: 8, 12, 17, 20 and 25-storey, and an 8-storey building are designed. The seismic demands used for design and validation were the records obtained at the SCT site during the 1985 Michoacan earthquake, and that of the 2017 Morelos - Puebla earthquake obtained at the Culhuacan site, both stations located on soft soil sites. To validate the procedure proposed, the performances and damage distributions used as design targets were compared with the corresponding results from the nonlinear step-by-step analyses of the designed structures subjected to the same seismic demands.

• 대한기계학회논문집A
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• 제30권7호
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• pp.750-756
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• 2006

This study predicts the modified eigenvectors and eigenvalues of the non-proportional damped structure due to the change in the mass, damping and stiffness of structure by iterative method of the sensitivity coefficient using the original dynamic characteristic. The method is applied to the non-proportional damped 3 degree of freedom system by modifying the mass, damping and stiffness. The predicted dynamic characteristics are showed a good agreement with these from the structural reanalysis using the modified mass, damping and stiffness.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 춘계학술대회논문집; 부산수산대학교, 10 May 1996
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• pp.86-91
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• 1996

In this study, the modal analysis is adopted for the investigation of vibratory characteristics of a rolling stock. A governing equation for this system is deverived on a condition that the rolling stock is in proportional viscous damping and proportional hysteretic damping. By applying this method a computational modal analysis software is developed. The validity and reliability of this method is verified by comparing the results for the above case and with those of a system having proportional viscous damping and a system having general viscous damping. A system that has non-linearity, an error from the calculation may occur in the analysis. In this case, we applied the piecewise linear method to estimate the modal parameters.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.411-416
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• 2004

This paper introduces a fast Fourier transform (FFT)-based spectral analysis method for the transient responses as well as the steady-state responses of linear dynamic systems with non-proportional damping. The force vibration of a non-proportionally damped three-DOF system is considered as the illustrative numerical example. The proposed spectral analysis method is evaluated by comparing with the numerical solution obtained by the Runge-Kutta method

• 한국소음진동공학회논문집
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• 제20권10호
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• pp.923-930
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• 2010

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping, and in the second stage, damping matrices are estimated with the mass and stiffness matrices fixed. Three methods to estimate damping matrices for this purpose are proposed in this paper. The methods include one for proportional damping systems and two for non-proportional damping systems. Method 1 utilizes orthogonality of normal modes and estimates damping matrices using the modal parameters extracted from the measured responses. Method 2 estimates damping matrices from impedance matrices which are the inverse of FRF matrices. Method 3 estimates damping using the equation which relates a damping matrix to the difference between the analytical and measured FRFs. The characteristics of the three methods are investigated by applying them to simulated discrete system data and experimental cantilever beam data.

• Structural Engineering and Mechanics
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• 제55권6호
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• pp.1241-1260
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• 2015

Any rational approach to define the configuration and size of viscous fluid dampers in a structure should be based on the dynamic properties of the system with the dampers. In this paper we propose an alternative representation of the complex eigenvalues of multi degree of freedom systems with dampers to calculate new equivalent natural frequencies. Analytical expressions for the dynamic properties of a two-story building model with a linear viscous damper in the first floor (i.e. with a non-proportional damping matrix) are derived. The formulas permit to obtain the equivalent damping ratios and equivalent natural frequencies for all the modes as a function of the mass, stiffness and damping coefficient for underdamped and overdamped systems. It is shown that the commonly used formula to define the equivalent natural frequency is not applicable for this type of system and for others where the damping matrix is not proportional to the mass matrix, stiffness matrix or both. Moreover, the new expressions for the equivalent natural frequencies expose a novel phenomenon; the use of viscous fluid dampers can modify the vibration frequencies of the structure. The significance of the new equivalent natural frequencies is expounded by means of a simulated free vibration test. The proposed approach may offer a new perspective to study the effect of viscous dampers on the dynamic properties of a structure.

• International Journal of Aeronautical and Space Sciences
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• 제9권1호
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• pp.85-99
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• 2008

The dynamic response analysis for large structures using finite element method requires a large amount of computational resources. This paper presents an efficient vibration analysis procedure by combining node-based substructuring reduction method with a response analysis scheme for structures with undamped, proportional or nonproportional damping. The iterative form of substructuring reduction scheme is derived to reduce the full eigenproblem and to calculate the dynamic responses. In calculating the time response, direct integration scheme is used because it can be applied directly to the reduced model. Especially for the non proportional damping matrix, the transformation matrices defined in the displacement space are used to reduce the system. The efficiency and the effectiveness of the present method are demonstrated through the numerical examples.