• Journal of Yeungnam Medical Science
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• 제39권3호
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• pp.266-267
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• 2022

• Journal of Yeungnam Medical Science
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• 제40권1호
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• pp.106-108
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• 2023

• Journal of Yeungnam Medical Science
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• 제40권2호
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• pp.223-224
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• 2023

• Journal of Yeungnam Medical Science
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• 제40권4호
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• pp.457-460
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• 2023

• Structural Engineering and Mechanics
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• 제73권6호
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• pp.685-698
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• 2020

The dynamic stability of a functionally graded polymer microbeam reinforced by graphene oxides subjected to a periodic axial force is investigated. The microbeam is assumed to rest on an elastic substrate and is subjected to various immovable boundary restraints. The weight fraction of graphene oxides nanofillers is graded across the beam thickness. The effective Young's modulus of the functionally graded graphene oxides reinforced composite (FG-GORC) was determined using modified Halpin-Tsai model, with the mixture rule used to evaluate the effective Poisson's ratio and the mass density. An improved third order shear deformation theory (TSDT) is used in conjunction with the Chebyshev polynomial-based Ritz method to derive the Mathieu-Hill equations for dynamic stability of the FG-GORC microbeam, in which the scale effect is taken into account based on modified couple stress theory. Then, the Mathieu-Hill equation was solved using Bolotin's method to predict the principle unstable regions of the FG-GORC microbeams. The numerical results show the effects of the small scale, the graphene oxides nanofillers as well as the elastic substrate on the dynamic stability behaviors of the FG-GORC microbeams.

• 한국정밀공학회지
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• 제22권11호
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• pp.111-117
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• 2005

The vibration problems associated with gear coupled rotors have been the focus of much engineering work. These systems are complex and difficult to analyze in that they have the problems associated with conventional rotors plus those additional problems associated with the gear couplings. This paper examines the problems peculiar to the gear mesh. Because of the meshing action of gears, the elasticity of the gear teeth introduces time-varying stiffness coefficients into the governing equations of motion. This means that system response must be thought of in terms of Mathieu-type equations, where multiple-frequency response occur due to the periodic coefficients. The meshing action of the gears also couples the lateral and torsional gear motions. Gear errors, such as tooth profile and spacing errors, produce forces and torque that excite the system at multiple frequencies, some of which are much higher than shaft rotational speed. To investigate how to the time-varying stiffness in the gear teeth and the gear errors act one the dynamic response of the gear coupled rotors, a three-dimensional dynamic model with lateral-tortional oscillation is developed. The harmonic balance technique is employed to solve this mathieu-type problem.

• 한국소음진동공학회논문집
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• 제18권2호
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• pp.160-168
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• 2008

This paper presents the study on the stability of nonlinear oscillations of a thin cantilever beam subject to harmonic base excitation in vertical direction. Two partial differential governing equations under combined parametric and external excitations were derived and converted into two-degree-of-freedom ordinary differential Mathieu equations by using the Galerkin method. We used the method of multiple scales in order to analyze one-to-one combination resonance. From these, we could obtain the eigenvalue problem and analyze the stability of the system. From the thin cantilever experiment using foamax, we could observe the nonlinear modes of bending, twisting, sway, and snap-through buckling. In addition to qualitative information, the experiment using aluminum gave also the quantitative information for the stability of combination resonance of a thin cantilever beam under parametric excitation.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.87-97
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• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• 전기의세계
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• 제16권1호
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• pp.14-18
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• 1967

To analyze th frequency modulation system the characteristic equation of the F-M system, i.e., Mathieu's equation, is derived from the equivalent circuits of direct modulation system. The analysis of F-M equation is undertaken by the Yonsei 101 Analog Computer. And the computer solution is compared with the theoretical solution. It is concluded that not only the frequency but also the amplitude of the carrier wave are changed by varying the modulation index and the system becomes unstable if the modulation index is increased near to unity.

• Structural Engineering and Mechanics
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• 제8권2호
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• pp.193-205
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• 1999

A formulation for the dynamic stability analysis of cylindrical shells resting on elastic foundations is presented. In this previously not studied problem, a normal-mode expansion of the partial differential equations of motion, which includes the effects of the foundation as well as a harmonic axial loading, yields a system of Mathieu-Hill equations the stability of which is analyzed using Bolotin's method. The present study examines the effects of the elastic foundation on the instability regions of the cylindrical shell for the transverse, longitudinal and circumferential modes.