• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.1
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• pp.42-47
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• 2003

Nonlinear models for a thin ring rotating at a constant speed are developed. The geometric nonlinearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton’s principle, the coupled nonlinear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from the nonlinear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the behavior of the rotating ring.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.689-703
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• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.3 s.246
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• pp.238-245
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• 2006

This paper proposes appropriate conjugate parameters and dimensionless temperatures to analysis the conjugate problem of heat conduction in solid wall coupled with laminar film condensation flow adjacent to horizontal flat plate. An efficient methods for some fluids are proposed for its solution. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Modified Jacob number, $Ja^*/Pr$, defined by an overall temperature difference, a property ratio $\sqrt{\rho_l{\mu}_l/{\rho_v{\mu}_v}$ and the conjugate parameter $\zeta$. The obtained similarity solution reveals the effect of the conjugate parameter, and the results are compared with the simplified solution. The variations of the heat transfer rates as well as the interface temperature and frictions along the plate are shown explicitly.

• Structural Engineering and Mechanics
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• v.70 no.4
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• pp.407-420
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• 2019

In the present work, an attempt is made to explore the effects of shear in-plane preload on the wave propagation response of small-scale plates containing nanofibers. The small-scale system is assumed to be embedded in an elastic matrix. The nonlocal elasticity is utilized in order to develop a size-dependent model of plates. The proposed plate model is able to describe both nanofiber effects and the influences of being at small-scales on the wave propagation response. The size-dependent differential equations are derived for motions along all directions. The size-dependent coupled equations are solved analytically to obtain the phase and group velocities of the small-scale plate under a shear in-plane preload. The effects of this shear preload in conjunction with nanofiber and size effects as well as the influences of the elastic matrix on the wave propagation response are analyzed in detail.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.4
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• pp.127-134
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents a generalized stochastic model of dynamic system subjected to bot external and parametric nonstationary stochastic input. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method. But the second moment equation is founded to constitute an infinite coupled set of differential equations, so this equations are numerically evaluated by cumulant neglect closure method and Runge-Kutta method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Advances in nano research
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• v.15 no.5
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• pp.401-410
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• 2023

Vibration investigation of fluid-filled three layered cylindrical shells is studied here. A cylindrical shell is immersed in a fluid which is a non-viscous one. Shell motion equations are framed first order shell theory due to Love. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the wave propagation approach procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped (C-C), simply supported-simply supported (SS-SS) frequency curves are higher than that of clamped-simply (C-S) curves. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Computer software MATLAB codes are used to solve the frequency equation for extracting vibrations of fluid-filled.

• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.149-154
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• 1998

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute(KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons from spallation reactions are essentially required for operating the reactor in its steady state. furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance of the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.373-384
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• 2023

The main objective of this research work is to present analytical solutions for the thermoelastic bending analysis of sandwich plates made of functionally graded materials with an arbitrary gradient. The governing equations of equilibrium are solved for a functionally graded sandwich plates under the effect of thermal loads. The transverse shear and normal strain and stress effects on thermoelastic bending of such sandwich plates are considered. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. The results of the shear deformation theories are compared together. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated.