• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.3
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• pp.252-261
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• 2016

A spar-type floating substructure that is being widely used for offshore wind power generation is vulnerable to resonance in the heave direction because of its small water plane area. For this reason, the stable dynamic response of this floating structure should be ensured by accurately identifying the resonance characteristics. The purpose of this study is to analyze the characteristics of the combination resonance between the excitation frequency of a regular wave and natural frequencies of the floating substructure. First, the nonlinear equations of motion with two degrees of freedom are derived by assuming that the floating substructure is a rigid body, where the heaving motion and pitching motions are coupled. Moreover, to identify the characteristics of the combination resonance, the nonlinear term in the nonlinear equations is approximated up to the second order using the Taylor series expansion. Furthermore, the validity of the approximate model is confirmed through a comparison with the results of a numerical analysis which is made by applying the commercial software ANSYS AQWA to the full model. The result indicates that the combination resonance occurs at the frequencies of ${\omega}{\pm}{\omega}_5$ and $2{\omega}_{n5}$ between the excitation frequency (${\omega}$) of a regular wave and the natural frequency of the pitching motion (${\omega}_{n5}$) of the floating substructure.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.9
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• pp.849-855
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• 2010

Damping may change the response characteristics of nonlinear oscillations due to the parametric excitation of a thin cantilever beam. When the natural frequencies of the first bending and torsional modes are of the same order of magnitude, we can observe the one-to-one combination resonance in the perturbation analysis depending on the characteristic parameters. The nonlinear behavior about the combination resonance reveals a chaotic motion depending on the natural frequencies and damping ratio. We can analyze the chaotic dynamics by using the eigenvalue analysis of the perturbed components. In this paper, we derived the equations for autonomous system and solved them to obtain the characteristic equation. The stability analysis was carried out by examining the eigenvalues. Numerical integration gave the physical behavior of each mode for given parameters.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.87-100
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• 2020

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

• Investigative Magnetic Resonance Imaging
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• v.25 no.4
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• pp.218-228
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• 2021

Due to their high degree of freedom to transfer and acquire light, fiber optics can be used in the presence of strong magnetic fields. Hence, optical sensing and imaging based on fiber optics can be integrated with magnetic resonance imaging (MRI) diagnostic systems to acquire valuable information on biological tissues and organs based on a magnetic field. In this article, we explored the combination of MRI and optical sensing/imaging techniques by classifying them into the following topics: 1) functional near-infrared spectroscopy with functional MRI for brain studies and brain disease diagnoses, 2) integration of fiber-optic molecular imaging and optogenetic stimulation with MRI, and 3) optical therapeutic applications with an MRI guidance system. Through these investigations, we believe that a combination of MRI and optical sensing/imaging techniques can be employed as both research methods for multidisciplinary studies and clinical diagnostic/therapeutic devices.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.11
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• pp.2098-2110
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• 1992

An analysis is presented for the combination resonance of a clamped circular plate, which occurs when the frequency of the excitation is near the combination of the natural frequencies, that is, when ohm.=2.0mega.／sub 1／+omega.／sub 2／. The internal resonance, Omega.／sub 3／=omega.／sub 1／+2.omega.／sub 2／, is considered and its influence on the response is studied. The clamped circular plate experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is used to obtain steady-state responses of the system. Results of numerical investigations show that the increase of the excitation amplitude can reduce the amplitudes of steady-state responses. We can not find this kind of results in linear systems.

• Steel and Composite Structures
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• v.32 no.2
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• pp.253-264
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• 2019

This paper presents the combination resonances of FG porous (FGP) cylindrical shell under two-term excitation. The effect of structural damping on the system response is also considered. With regard to classical plate theory of shells, von-$K{\acute{a}}rm{\acute{a}}n$ equation and Hook law, the relations of stress-strain is derived for shell. According to the Galerkin method, the discretized motion equation is obtained. The combination resonances are obtained by using the method of multiple scales. Four types of FGP distributions consist of uniform porosity, non-symmetric porosity soft, non-symmetric porosity stiff and symmetric porosity distribution are considered. The influence of various porosity distributions, porosity coefficients of cylindrical shell and amplitude excitations on the combination resonances for FGP cylindrical shells is investigated.

• Steel and Composite Structures
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• v.51 no.4
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• pp.391-406
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• 2024

The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

• Proceedings of the Optical Society of Korea Conference
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• 1991.07a
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• pp.15-22
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• 1991

The general aspects of Laser Resonance Ionization Spectroscopy (RIS) and its application are investigated. Combination of laser selective photoionization and mass spectrometer as apromising spectroscopic as well as an analytical tool is mainly considered. The application of RIS includes mercury (Hg) atomic spectroscopy, trace analysis of lead (Pb) and resonance enhanced two photon ionization spectroscopy of Cis-hexatriene.

• Journal of the Korean Chemical Society
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• v.57 no.2
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• pp.172-175
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• 2013

We compare the relative usefulness of common basis functions and numerical integration methods in representing complex resonance state encountered in the molecular scattering problem of aluminum dimer electronic predissociation. Specifically, the basis set size and computing CPU times are monitored in order to find the minimum requirement for ensuring the modest accuracy of calculated resonance energies (0.1 $cm^{-1}$) for more than 100 resonance states. The combination of the so-called one-dimensional box eigenfunctions and energy-dependent boundary functions are found to be most efficient if integration is done using the basis set quadrature rules.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.481-500
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• 2007

The dynamic instability of doubly curved panels, subjected to non-uniform tensile in-plane harmonic edge loading $P(t)=P_s+P_d\;{\cos}{\Omega}t$ is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to simple resonances in parametrically excited doubly curved panels. Analytical expressions for the instability regions are obtained at ${\Omega}={\omega}_m+{\omega}_n$, (${\Omega}$ is the excitation frequency and ${\omega}_m$ and ${\omega}_n$ are the natural frequencies of the system) by using the method of multiple scales. It is shown that, besides the principal instability region at ${\Omega}=2{\omega}_1$, where ${\omega}_1$ is the fundamental frequency, other cases of ${\Omega}={\omega}_m+{\omega}_n$, related to other modes, can be of major importance and yield a significantly enlarged instability region. The effects of edge loading, curvature, damping and the static load factor on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which the curved panels cannot become dynamically unstable. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.