• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.517-526
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• 2001

In this paper, we study the continuous wavelet transform on the Heisenberg group H$^n$, and describe the related continuous multiscale analysis. By using the wavelet packet transform we obtain a reconstruction formula on L$^2$(H$^n$).

• Interaction and multiscale mechanics
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• v.1 no.4
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• pp.467-476
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• 2008

In this work, a nano-size rocksalt crystal (magnesium oxide) is considered as a continuous collection of unit cells, while each unit cell consists of discrete atoms; and modeled by a multiscale concurrent atomic/continuum field theory. The response of the crystal to an electromagnetic (EM) wave is studied. Finite element analysis is performed by solving the governing equations of the multiscale theory. Due to the applied EM field, the inhomogeneous motions of discrete atoms in the polarizable crystal give rise to the change of microstructure and the polarization wave. The relation between the natural frequency of this system and the driving frequency of the applied EM field is found and discussed.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2147-2158
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• 2006

The continuous wavelet transform (CWT) has a frequency-adaptive time-frequency tiling property, which makes it popular for the analysis of dispersive elastic wave signals. However, because the time-frequency tiling of CWT is not signal-dependent, it still has some limitations in the analysis of elastic waves with spectral components that are dispersed rapidly in time. The objective of this paper is to introduce an advanced time-frequency analysis method, called the dispersion-based continuous wavelet transform (D-CWT) whose time-frequency tiling is adaptively varied according to the dispersion relation of the waves to be analyzed. In the D-CWT method, time-frequency tiling can have frequency-adaptive characteristics like CWT and adaptively rotate in the time-frequency plane depending on the local wave dispersion. Therefore, D-CWT provides higher time-frequency localization than the conventional CWT. In this work, D-CWT method is applied to the analysis of dispersive elastic waves measured in waveguide experiments and an efficient procedure to extract information on the dispersion relation hidden in a wave signal is presented. In addition, the ridge property of the present transform is investigated theoretically to show its effectiveness in analyzing highly time-varying signals. Numerical simulations and experimental results are presented to show the effectiveness of the present method.

• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.1-12
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• 2012

Considerable longitudinal rail forces and displacements may develop in continuous welded rail (CWR) track on long-span bridges due to temperature variations. The track stability may be disturbed due to excessive relative displacements between the sleepers and ballast bed and the accompanied reduction in frictional resistance. For high-speed tracks, however, solving these problems by installing rail expansion devices in the track is not an attractive solution as these devices may cause a local disturbance of the vertical track stiffness and track geometry which will require intensive maintenance. With reference to temperature, two actions are considered by the bridge loading standards, the uniform variation in the rail and deck temperature and the temperature gradient in deck. Generally, the effect of temperature gradient has been disregarded in the interaction analysis. This paper mainly deals with the effect of temperature gradient on the track-bridge interaction with respect to the support reaction, rail stresses and stability. The study presented in this paper was not mentioned in the related codes so far.

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.321-331
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• 2010

A new technique is proposed for bridge structural damage detection based on spatial wavelet analysis of the time history obtained from vehicle body moving over the bridge, which is different from traditional detection techniques based on the bridge response. A simply-supported Bernoulli-Euler beam subjected to a moving spring-mass unit is established, with the crack in the beam simulated by modeling the cracked section as a rotational spring connecting two undamaged beam segments, and the equations of motion for the system is derived. By using the transfer matrix method, the natural frequencies and mode shapes of the cracked beam are determined. The responses of the beam and the moving spring-mass unit are obtained by modal decomposition theory. The continuous wavelet transform is calculated on the displacement time histories of the sprung-mass. The case study result shows that the damage location can be accurately determined and the method is effective.

• Composites Research
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• v.33 no.6
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• pp.415-420
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• 2020

The interfacial properties in carbon fiber composites, which control the overall mechanical properties of the composites, are very important. Effective interface enhancement work is conducted on the modification of the carbon fiber surface with carbon nanotubes (CNTs). Nonetheless, most surface modifications methods do have their own drawbacks such as high temperatures with a range of 600~1000℃, which should be implemented for CNT growth on carbon fibers that can cause carbon fiber damages affecting deterioration of composites properties. This study includes the use of in-situ interfacial polymerization of polyamide 610/CNT to fabricate the carbon fiber composites. The process is very fast and continuous and can disperse CNTs with random orientation in the interface resulting in enhanced interfacial properties. Scanning electron microscopy was conducted to investigate the CNT dispersion and composites morphology, and the thermal stability of the composites was analyzed via thermogravimetric analysis. In addition, fiber pull-out tests were used to assess interfacial strength between fiber and matrix.

• The Journal of Korean Institute of Information Technology
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• v.17 no.6
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• pp.103-114
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• 2019

Moving-target detection using frequency-modulated continuous-wave (FMCW) radar systems has recently attracted attention. Detection tasks are more challenging with noise resulting from signals reflected from strong static objects or small moving objects(clutter) within radar range. Robust Principal Component Analysis (RPCA) approach for FMCW radar to detect moving objects in noisy environments is employed in this paper. In detail, compensation and calibration are first applied to raw input signals. Then, RPCA via Gradient Descents (RPCA-GD) is adopted to model the low-rank noisy background. A novel update algorithm for RPCA is proposed to reduce the computation cost. Finally, moving-targets are localized using an Automatic Multiscale-based Peak Detection (AMPD) method. All processing steps are based on a sliding window approach. The proposed scheme shows impressive results in both processing time and accuracy in comparison to other RPCA-based approaches on various experimental scenarios.