• Steel and Composite Structures
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• v.15 no.1
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• pp.57-79
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• 2013

This paper studies the dynamic instability of laminated composite plates under thermal and arbitrary in-plane periodic loads using first-order shear deformation plate theory. The governing partial differential equations of motion are established by a perturbation technique. Then, the Galerkin method is applied to reduce the partial differential equations to ordinary differential equations. Based on Bolotin's method, the system equations of Mathieu-type are formulated and used to determine dynamic instability regions of laminated plates in the thermal environment. The effects of temperature, layer number, modulus ratio and load parameters on the dynamic instability of laminated plates are investigated. The results reveal that static and dynamic load, layer number, modulus ratio and uniform temperature rise have a significant influence on the thermal dynamic behavior of laminated plates.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.322-327
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• 1996

Dynamic stability of an axially oscillating cantilever beam is investigated in this paper. The equations of motion are derived and transformed into non-dimensional ones. The equations include harmonically oscillating parameters which originate from the motion-induced stiffness variation. Using the equations, the multiple scale perturbation method is employed to obtain a stability diagram. The stability diagram shows that relatively large unstable regions exist around the frequencies of the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the diagram is proved by direct numerical simulations of the dynamic system.

• Journal of KSNVE
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• v.9 no.1
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• pp.103-112
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• 1999

A new modeling and analysis technique for one-dimensional distributed parameter systems is presented. First. discretized equations of motion in Laplace domain are derived by applying discretization methods for partial differential equations of a one-dimensional structure with respect to spatial coordinate. Secondly. the z and inverse z transformations are applied to the discretized equations of motion for obtaining a dynamic matrix for a uniform element. Four different discretization methods are tested with an example. Finally, taking infinite on the number of step for a uniform element leads to an exact dynamic matrix for the uniform element. A generalized modal analysis procedure for eigenvalue analysis and modal expansion is also presented. The resulting element dynamic matrix is tested with a numerical example. Another application example is provided to demonstrate the applicability of the proposed method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.4
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• pp.247-257
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• 2003

This paper presents an analytical method to Investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic Journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill's infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.166-174
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• 2002

This paper presents an analytical method to Investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill's infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.396.2-396
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• 2002

Dynamic stability and behavior are analyzed fur Pendulum Automatic Dynamic Balancer which is a device to reduce an unbalanced mass of rotors. The nonlinear equations of motion for a system including a Pendulum Balancer are derived with respect to polar coordinate by Lagrange's equations. The perturbation method is applied to find the equilibrium positions and to obtain the linear variation equations. Based on linearized equations, the dynamic stability of the system around the equilibrium positions is investigated by the eigenvalue problem. (omitted)

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.565-573
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• 2007

This paper is concerned with the dynamic modeling, active vibration controller design and experiments for a cylindrical shell equipped with MFC actuators. The dynamic model was derived by using Rayleigh-Ritz method based on Donnel-Mushtari shell theory. The actuator and sensors for the MFC actuator equations were derived based on pin-force model. The equations of motion were then reduced to modal equations of motion by considering the modes of interest. The sensor equations were also converted to a reduced form. An aluminum shell was fabricated to demonstrate the effectiveness of modeling and control techniques. The boundary conditions at both ends of the shell were assumed to be shear diaphragm. Theoretical natural frequencies were calculated and compared to experimental result. It was observed that the theoretical result is in good agreement with experimental result for the first two modes. The multi-input and multi-output positive position feedback controller, which can cope with first two modes, was then designed based on the blockinverse theory and implemented using DSP. It was found from experiment that vibrations can be successfully suppressed.

• Advances in concrete construction
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• v.9 no.3
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• pp.327-335
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• 2020

Concrete pipes are considered important structures playing integral role in spread of cities besides transportation of gas as well as oil for far distances. Further, concrete structures under seismic load, show behaviors which require to be investigated and improved. Therefore, present research concerns dynamic stress and strain alongside deflection assessment of a concrete pipe carrying water-based nanofluid subjected to seismic loads. This pipe placed in soil is modeled through spring as well as damper. Navier-Stokes equation is utilized in order to gain force created via fluid and, moreover, mixture rule is applied to regard the influences related to nanoparticles. So as to model the structure mathematically, higher order refined shear deformation theory is exercised and with respect to energy method, the motion equations are obtained eventually. The obtained motion equations will be solved with Galerkin and Newmark procedures and consequently, the concrete pipe's dynamic stress, strain as well as deflection can be evaluated. Further, various parameters containing volume percent of nanoparticles, internal fluid, soil foundation, damping and length to diameter proportion of the pipe and their influences upon dynamic stress and strain besides displacement will be analyzed. According to conclusions, increase in volume percent of nanoparticles leads to decrease in dynamic stress, strain as well as displacement of structure.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.764-774
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• 2002

Dynamic behaviors are analyzed for an automatic ball balancer (ABB) with triple races, which is a device to reduce the unbalanced mass of optical disk drives (ODD) such as CD-ROM or DVD drives. The nonlinear equations of motion are derived by using Lagrange's equations with the polar coordinate system. It is shown that the polar coordinate system provides the complete stability analysis while the rectangular coordinate system used in other previous studies has limitations on the stability analysis. For the stability analysis, the equilibrium positions and the linearized perturbation equations are obtained by the perturbation method. Based on the linearized equations, the stability of the system is analyzed around the equilibrium positions; furthermore, to confirm the stability, the time responses for the nonlinear equations of motion are computed by using a time integration method and experimental analyses are performed. Theoretical and experimental results show a superiority of the ABB with triple races.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.619-624
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• 2007

Spectral element method (SEM) is introduced for the fully coupled structural dynamic problems, In this paper, the beam with passive constrained layered damping (PCLD) treatments is considered as a representative problems. The beam consists of a viscoelastic layer that is sandwiched between the base beam structure and an elastic layer, The fully coupled equations of motion for a PCLD beam are derived, The equations of motion are derived first by using Hamilton's principle, From this equations of motion, the spectral element is formulated for the vibration analysis by use of the SEM, As an illustrative example, a cantilevered beam is considered. It is shown that, as the thickness of VEM layer vanishes, the results become a simple layer beam's that.