• Geomechanics and Engineering
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• v.14 no.1
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• pp.19-27
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• 2018

It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the Earth's inner core cannot exist in the form of a spherical structure in the assumed thermobaric conditions and calculation values of physico-mechanical parameters. Pressure level reaches a value that is significantly greater than the theoretical limit of medium strength in the model approximations at the surface of the sphere of the inner core. On the other hand, equilibrium state of the sphere is unstable on the geometric forming at much lower loads under the influence of the "dead" surface loads. In case of the action of "follower" loads, the assumed pressure value on the surface of the sphere is comparable with the value of the critical load of "internal" instability. In these cases, due to the instability of the equilibrium state, propagation of homogeneous deformations becomes uneven in the sphere. Moreover, the elastic waves with actual velocity cannot propagate in such conditions in solid medium. Violation of these fundamental conditions of mechanics required in determining the physical and mechanical properties of the medium should be taken into account in the integrated interpretations of seismic and laboratory (experimental) data. In this case, application of the linear theory of elasticity and elastic waves does not ensure the reliability of results on the structure and composition of the Earth's core despite compliance with the required integral conditions on the mass, moment of inertia and natural oscillations of the Earth.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.670-676
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• 2003

To investigate the group plugging effect the fluid-elastic instability analysis has been performed on various column and row number of the KSNP steam generator lutes. This study compares the stability ratio of the plugged tube with that of the intact one. The information on the thermal-hydraulic data of the steam generator have been obtained by using the ATHOS3-MOD1 code with and without the thermal energy transfer at the plugged region. Both of the boundary conditions of hot-leg temperature and feedwater mass flow rate are fixed for this investigation. From the results of this study the stability ratios inside the group plugging zone are decreased slightly. At the outside of group plugging zone, however, most of the stability ratios tend to be increased.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.85-92
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• 2015

This article presents the dynamic instability response of sigmoid functionally graded material plates on elastic foundation using the higher-order shear deformation theory. The higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. The results of dynamic instability analysis of sigmoid functionally graded material plate are presented using the Navier's procedure to illustrate the effect of elastic foundation parameter on dynamic response. The relations between Winkler and Pasternak elastic foundation parameter are discussed by numerical results. Also, the effects of static load factor, power-law index and side-to-thickness ratio on dynamic instability analysis are investigated and discussed. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for the dynamic instability study of S-FGM plates.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.11
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• pp.179-185
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• 2004

The effect of viscous damping on stability of beam resting on an elastic foundation subjected to a dry friction force is analytically studied. The beam resting on an elastic foundation subjected to dry friction force is modeled for simplicity into a beam resting on Kelvin-Voigt type foundation subjected to distributed follower load. In particular, the effects of four boundary conditions (clamped-free, clamped-pinned, pinned-pinned, clamped-clamped) on the system stability are considered. The critical value and instability type of columns on the elastic foundation subjected to a distributed follower load is investigated by means of finite element method for four boundary conditions. The elastic foundation modulus, viscous damping coefficient and boundary conditions affect greatly both the instability type and critical load. Also, the increase of damping coefficient raises the critical flutter load (stabilizing effect) but reduces the critical divergence load (destabilizing effect).

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.6
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• pp.216-222
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• 2001

The paper presents the dynamic stability of a flexible shoe in drum brake systems subjected to a frictional force. The frictional force between the drum and the shoe is assumed as a distributed frictional force, while the shute is modeled as an elastic beam supported by two translational springs at both ends and elastic foundations. Governing equations of motion are derived by energy expressions, and their numerical results are obtained by employing the finite element method. The critical distributed frictional force and the instability regions are demonstrated by changing the stiffness of two translational springs and elastic foundation parameters. It is also shown that the beam loses its stability by flutter and divergence depending on the stiffness of elastic supports and elastic foundation parameters. Time responses of beams corresponding to their instability types are also demonstrated.

• Structural Engineering and Mechanics
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• v.5 no.2
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• pp.193-207
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• 1997

Experimental tests are described on three ring stiffened machined circular cylinders and three ring stiffened machined circular cones, which were tested to destruction under uniform external pressure. All six vessels failed by inelastic general instability. The experiments showed that the vessels initially deformed plastically at mid-bay in the circumferential direction, and this caused the circumferential tangent modulus to become much less than the elastic Young's modulus, causing the vessels to fail through plastic general instability at pressures much less than that predicted by elastic theory. Based on a thinness ratio, two semi-empirical design charts are provided, which are intended to be used for design purposes in conjunction with the finite element method and a plastic reduction factor.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.72-77
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• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method, and study about parametrical instability of star-dome structures, which is subjected to harmonically pulsating load. When calculating stiffness matrix, we consider elastic stiffness and geometrical stiffness simultaneously. In equation of motion, we represent displacements and accelerations by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability region finally.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.1008-1015
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• 2006

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1400-1405
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• 2001

In this study, an analysis program to assess the susceptibility of steam generator tubes due to the flow-induced vibration was developed. Analysis of fluid-elastic instability and random turbulence excitation for the U-tube bundle in CE-type steam generator was accomplished. The effective mass distribution along the U-tube was obtained to calculate the natural frequency and dynamic mode shape. Finally, stability ratios and rms vibration amplitude for selected tubes are obtained.

• Steel and Composite Structures
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• v.19 no.3
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• pp.713-733
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• 2015

In this paper, viscous fluid induced nonlinear free vibration and instability analysis of a functionally graded carbon nanotube-reinforced composite (CNTRC) cylindrical shell integrated with two uniformly distributed piezoelectric layers on the top and bottom surfaces of the cylindrical shell are presented. Single-walled carbon nanotubes (SWCNTs) are selected as reinforcement and effective material properties of FG-CNTRC cylindrical shell are assumed to be graded through the thickness direction and are estimated through the rule of mixture. The elastic foundation is modeled by temperature-dependent orthotropic Pasternak medium. Considering coupling of mechanical and electrical fields, Mindlin shell theory and Hamilton's principle, the motion equations are derived. Nonlinear frequency and critical fluid velocity of sandwich structure are calculated based on differential quadrature method (DQM). The effects of different parameters such as distribution type of SWCNTs, volume fractions of SWCNTs, elastic medium and temperature gradient are discussed on the vibration and instability behavior of the sandwich structure. Results indicate that considering elastic foundation increases frequency and critical fluid velocity of system.