• Smart Structures and Systems
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• v.15 no.1
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• pp.1-13
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• 2015

This paper proposes an analytical mode decomposition (AMD) and Hilbert transform method for structural nonlinearity quantification and damage detection under earthquake loads. The measured structural response is first decomposed into several intrinsic mode functions (IMF) using the proposed AMD method. Each IMF is an amplitude modulated-frequency modulated signal with narrow frequency bandwidth. Then, the instantaneous frequencies of the decomposed IMF can be defined with Hilbert transform. However, for a nonlinear structure, the defined instantaneous frequencies from the decomposed IMF are not equal to the instantaneous frequencies of the structure itself. The theoretical derivation in this paper indicates that the instantaneous frequency of the decomposed measured response includes a slowly-varying part which represents the instantaneous frequency of the structure and rapidly-varying part for a nonlinear structure subjected to earthquake excitations. To eliminate the rapidly-varying part effects, the instantaneous frequency is integrated over time duration. Then the degree of nonlinearity index, which represents the damage severity of structure, is defined based on the integrated instantaneous frequency in this paper. A one-story hysteretic nonlinear structure with various earthquake excitations are simulated as numerical examples and the degree of nonlinearity index is obtained. Finally, the degree of nonlinearity index is estimated from the experimental data of a seven-story building under four earthquake excitations. The index values for the building subjected to a low intensity earthquake excitation, two medium intensity earthquake excitations, and a large intensity earthquake excitation are calculated as 12.8%, 23.0%, 23.2%, and 39.5%, respectively.

• Structural Engineering and Mechanics
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• v.34 no.3
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• pp.301-317
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• 2010

This paper studies the reliability of an analytical tool for predicting the lateral load-deformation response of RC columns while subjected to lateral cyclic displacements and axial load. The analytical tool in this study is based on a fiber element model implemented into the program DRAIN-2DX (fiber element). The response of RC column under cyclic displacement is defined by the behavior of concrete, and reinforcing steel under general reversed-cyclic loading. A tri-linear stress-strain relationship for the cyclic behavior of steel is proposed and the improvement in the analytical results is studied. This study only considers the behavior of columns with flexural dominant mode of failure. It is concluded that with the implementation of appropriate constitutive material models, the described analytical tools can predict the response of the columns with reasonable accuracy when compared to experimental data.

• Computers and Concrete
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• v.25 no.5
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• pp.461-470
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• 2020

This paper presents a numerical study on structural behavior of hammer head pier cap beams, extended on verges and reinforced with carbon fiber reinforced polymer (CFRP) plates. A 3-D finite element (FE) model along with a simplified analytical model are presented. Concrete damage plasticity (CDP) was adapted in the FE model and an analytical approach predicting the CFRP anchor strength was adapted in both FE and analytical model. Total five quarter-scaled pier cap beams with various CFRP reinforcing schemes were experimentally tested and analyzed with numerical approaches. Comparison between experimental results, FE results, analytical results and current ACI guideline predictions was presented. The FE results showed good agreement with experimental results in terms of failure mode, ultimate capacity, load-displacement response and strain distribution. In addition, the proposed strut-and-tie based analytical model provides the most accurate prediction of ultimate strength of extended cap beams among the three numerical approaches.

• Journal of the Korean earth science society
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• v.28 no.7
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• pp.936-946
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• 2007

Analytical geopotential field in balance with the sectoral mode (the first symmetric mode with respect to the equator) of the Rossby-Haurwitz wave on the inclined rotation axis was derived in presence of superrotation background flow. The balanced field was obtained by inverting the divergence equation with the time derivative being zero. The inversion consists of two steps, i.e., the evaluation of nonlinear forcing terms and the finding of analytical solutions based on the Poisson's equation. In the second step, the forcing terms in the from of Legendre function were readily inverted due to the fact that Legendre function is the eigenfunction of the spherical Laplacian operator, while other terms were solved either by introducing a trial function or by integrating the Legendre equation. The balanced field was found to be expressed with six zonal wavenumber components, and shown to be of asymmetric structure about the equator. In association with asymmetricity, the advantageous point of the balanced field as a validation method for the numerical model was addressed. In special cases where the strength of the background flow is a half of or exactly the same as the rotation rate of the Earth it was revealed that one of the zonal wavenumber components vanishes. The analytical balanced field was compared with the geopotential field which was obtained using a spherical harmonics spectral model. It was found that the normalized difference lied in the order of machine rounding, indicating the reliability of the analytical results. The stability of the sectoral mode of Rossby-Haurwitz wave and the associated balanced field was discussed, comparing with the flrst antisymmetric mode.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.5 no.3
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• pp.36-42
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• 2006

The analytical realization of uncoupled system was introduced in this study using times series and its spectrum analysis. The ARMAX spectra of time series methods were compared with the conventional FFT spectrum. Also, the response of second order system uncoupled was solved using the Runge-Kutta Gill method. In this numerical analysis, the displacement, velocity and acceleration were calculated. The displacement response among them was used for the power spectrum analysis. The ARMAX algorithm in time series was proved to be appropriate for the mode estimation and spectrum analysis. Using the separate response of first and second mode, each modes were calculated separately and the response of mixed modes was also analyzed for the mode estimation using several time series methods.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.11
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• pp.6406-6411
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• 2014

This paper presents the analytical-FE (finite element) squeal model, which can provide the efficient simulation time and accuracy. The system geometry and the extraction of the vibration modes were constructed using the finite element method. Instead, the friction contact model was derived from theoretical contact kinematics of the rotating disc and the stationary pads. This modeling procedure was incorporated into the perturbed equations of motion based on the finite elements of the system. Throughout the analytical-FE squeal model, the accuracy of linear stability analysis and the simulation time of FE squeal analysis were improved. In addition, the sensitivity of contact stiffness on brake squeal and the mode-coupling mechanism were provided by the system parameter study.

• Computers and Concrete
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• v.22 no.6
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• pp.573-592
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• 2018

An analytical methodology for the calculation of the flexural and the shear capacity of concrete members with Fibre-Reinforced-Polymer (FRP) bars as tensional reinforcement is proposed. The flexural analysis is initially based on the design provisions of ACI 440.1R-15 which have properly been modified to develop general charts that simplify computations and provide hand calculations. The specially developed charts include non-dimensional variables and can easily be applied in sections with various geometrical properties, concrete grade and FRP properties. The proposed shear model combines three theoretical considerations to facilitate calculations. A unified flexural/shear approach is developed in flow chart which can be used to estimate the ultimate strength and the expected failure mode of a concrete beam reinforced with longitudinal FRP bars, with or without transverse reinforcement. The proposed methodology is verified using existing experimental data of 138 beams from the literature, and it predicts the load-bearing capacity and the failure mode with satisfactory accuracy.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.155-172
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• 2000

Mode interactions at Unstable fluid interfaces induced by a shock wave (Richtmyer-Meshkov Instability) are studied both analytically and numerically. The analytical approach is based on a potential flow model with source singularities in incompressible fluids of infinite density ratio. The potential flow model shows that a single bubble has a decaying growth rates at late time and an asymptotic constant radius. Bubble interactions, bubbles of different radii propagates with different velocities and the leading bubbles grow in size at the expense of their neighboring bubbles, are predicted by the potential flow model. This phenomenon is validated by full numerical simulations of the Richtmyer-Meshkov instability in compressible fluids for initial multi-frequency perturbations on the unstable interface.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.335-348
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• 2015

The influence of the interface imperfect bonding on the flexural wave dispersion in the bilayered hollow circular cylinder is studied with utilizing three-dimensional linear theory of elastodynamics. The shear-spring type model is used for describing the imperfect bonding on the interface between the layers and the degree of the imperfectness is estimated through the dimensionless shear-spring parameters which enter the mentioned model. The method for finding the analytical expressions for the sought values and dispersion equation are discussed and detailed. Numerical results on the lowest first and second modes are presented and analyzed. These results are obtained for various values of the shear-spring parameters. According to these results, in particular, it is established that as a results of the imperfection of the bonding between the layers the new branches of the dispersion related the first fundamental mode arise and the character of the dispersion curve related to the second mode becomes more complicated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.2
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• pp.150-160
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• 2002

The free vibration characteristics of the triple cylindrical shells filled with fluid are investigated. The triple cylindrical shells are filled with compressible fluid. The boundary condition is clamped at both ends. Analytical method is developed to evaluate natural frequencies of triple cylindrical shells using Sanders' shell theory and courier series expansion by Stokes' transformation. Their results are compared with those of finite element method to verify the validation of the method developed. The modal characteristics of shells filled with fluid at region 1, 2 and 3 are evaluated.