• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.185-197
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• 2001

This paper presents the effect of axial stretching on large amplitude free vibration of an extensible suspended cable supported at the same level. The model formulation developed in this study is based on the virtual work-energy functional of cables which involves strain energy due to axial stretching and work done by external forces. The difference in the Euler equations between equilibrium and motion states is considered. The resulting equations govern the horizontal and vertical motion of the cables, and are coupled and highly nonlinear. The solution for the nonlinear static equilibrium configuration is determined by the shooting method while the solution for the large amplitude free vibration is obtained by using the second-order central finite difference scheme with time integration. Numerical examples are given to demonstrate the vibration behaviour of extensible suspended cables.

• The Journal of Korean Physical Therapy
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• v.32 no.4
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• pp.245-249
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• 2020

Purpose: This study examined the effects of local vibration using a massage gun on the triceps surae flexibility by measuring the ankle dorsiflexion range of motion (ROM) compared to static stretching in healthy adults. Methods: Twenty healthy subjects were instructed in this study. They were allocated randomly to two groups: local vibration (LV) and static stretching (SS). The ankle dorsiflexion ROM was measured before and after the intervention in supine (open kinetic chain, OKC) and standing (closed kinetic chain, CKC). The LV group received local vibration using a massage gun for five minutes on their triceps surae, and the SS group stood on the Q board with a dorsiflexed ankle for five minutes. The ROM between pre- and post-intervention and the change in ROM between two groups were analyzed. A paired t-test was used to compare the ROM between pre- and post-intervention, while an independent t-test was used to compare the change in ROM between the two groups. Results: Both groups showed a significant difference between pre- and post-intervention in the position of both the OKC and CKC. The change in ROM, however, was not significantly different between the two groups. Conclusion: The application of local vibration using a massage gun for five minutes on the triceps surae could improve its flexibility as much as the application of static stretching. A massage gun for the application of a local vibration stimulus may be effective, simple, portable, and comfortable.

• Bulletin of the Korean Chemical Society
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• v.34 no.2
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• pp.553-557
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• 2013

The stretching vibration of OH of ice Ih is studied by Car-Parrinello molecular dynamics in regarding the effect of mixed H/D contamination while the vibrational spectrum is considered by velocity-velocity autocorrelations of the sampled ensemble. When hydrogen atoms are immersed randomly into the deuterated ice, a typical vibrational frequency of OH stretching mode is observed to be similar to that from the pure $H_2O$ ice. When focusing on the correlation of isolated neighboring OH stretching, a narrower and blue shifted peak is observed at the high frequency range as a result of the screening from the complex many body correlations by $D_2O$ environment. It is also specifically related to the symmetric intermolecular correlations between neighboring OH stretching modes. More enhanced high frequency range can be explained by the expansion of such two body correlations to collective many body correlations among all possible OH stretching modes. This contribution becomes important when it involves in chemical interactions via excitation of such vibrational states.

• Journal of the Korean Society of Physical Medicine
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• v.12 no.4
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• pp.39-46
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• 2017

PURPOSE: The effectiveness of the stretching to increase the range of motion of the joint, reduce the risk of injury, enhance athletic performance or decrease post exercise muscle soreness. This study was to compare the effect of the stretching method applied on the shortened hamstring muscle for flexibility, strength, pressure pain threshold value and muscle tone. METHODS: This study is a two-group pretest- posttest design. Fifty-four healthy young adults were randomly assigned to a vibration-assisted stretching group (VASG, n=27) or a static stretching group (SSG, n=27). Participants performed each stretch in 4 sets of 30 seconds each. A 30-second break time was provided between the sets. The range of motion, strength, pressure pain threshold values and muscle tone of the hamstring muscle were measured to compare the effects of the stretching methods. RESULTS: Both the VASG and the SSG participants showed significant improvement in the range of motion and strength (p<.05); however, the increase in the VASG was significantly higher than that in the SSG (p<.05). The pressure pain threshold values and muscle tone were significantly decreased only in the VASG (p<.05). CONCLUSION: These findings indicate that vibration-supported stretching is an effective intervention for people with hamstring shortening, with high pain level and muscle tone decrease.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.771-781
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• 2018

This study deals with free vibrations analysis with stretching effect of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation. Four different carbon nanotubes (CNTs) distributions including uniform and three types of functionally graded distributions of CNTs through the thickness are considered. The rule of mixture is used to describe the effective material properties of the nanocomposite beams. The significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The governing equations are derived through using Hamilton's principle. Natural frequencies are obtained for nanocomposite beams. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of free vibration analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. The effects of different parameters of the beam on the vibration responses of CNTRC beam are discussed.

• Structural Engineering and Mechanics
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• v.56 no.2
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• pp.223-240
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• 2015

In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen's nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (${\varepsilon}_z{\neq}0$), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.

• Bulletin of the Korean Chemical Society
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• v.22 no.12
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• pp.1297-1298
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• 2001

• Journal of the Korean Chemical Society
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• v.64 no.6
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• pp.350-353
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• 2020

The validity of the calculation method based on the local mode in hydrogen-bonded water molecules was investigated by comparing the frequencies of the local and normal modes of OH stretching vibration in water molecules. By calculating a monomer, dimer, and trimer of water molecules using a quantum chemical ab initio theory, we examined how the frequencies of the local and normal modes and the anharmonicity of local modes vary with molecular cluster size. It was shown that, as the number of molecules increases from monomer to trimer, the anharmonicity of OH bonds increases and the difference between local and normal mode frequencies decreases. This confirms that local-mode-based calculations that can easily handle the anharmonicity can be appropriate for the calculation of the OH stretching frequency of water molecules in the condensed phase.

• Earthquakes and Structures
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• v.16 no.5
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• pp.547-561
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• 2019

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

• Coupled systems mechanics
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• v.4 no.1
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• pp.99-114
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• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.