• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1217-1225
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• 2001

The governing equations are derived for the analysis of a stepped labyrinth gas seal generally used in high performance compressors, gas turbines, and steam turbines. The bulk-flow is assumed for a single cavity control volume set up in a stepped labyrinth cavity and the flow is assumed to be completely turbulent in the circumferential direction. The Moodys wall-friction-factor model is used for the calculation of wall shear stresses in the single cavity control volume. For the reaction force developed by the stepped labyrinth gas seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about a centered position. Integration of the resultant first-order pressure distribution along and around the seal defines the rotordynamic coefficients of the stepped labyrinth gas seal. The resulting leakage and rotordynamic characteristics of the stepped labyrinth gas seal are presented and compared with Scharrers theoretical analysis using Blasius wall-friction-factor model. The present analysis shows a good qualitative agreement of leakage characteristics with Scharrers analysis, but underpredicts by about 20%. For the rotordynamic coefficients, the present analysis generally yields smaller predictied values compared with Scharrers analysis.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.706-712
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• 1986

The unsteay heat transfer from an isothermal circular cylinder in fluctuating cross flow is simulated numerically, for the case where the amplitude of the oscillating velocity is small compared with the mean velocity. By solving the linear perturbation equations derived from the unsteady full Navier-Stokes and the energy equations, the amplitude and the phase of heat transfer response are obtained in the range of Reynolds number R$_{3}$ < 40. The effects of the velocity, the cylinder radius and the frequency on the response are expressed graphically in terms of the normalized velocity and the cylinder radius.

• Structural Engineering and Mechanics
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• v.54 no.5
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• pp.987-998
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• 2015

In this paper, free vibrations of a clamped-clamped double-walled carbon nanotube (DWNT) under axial force is studied. By utilizing Euler-Bernoulli beam theory, each layer of DWNT is modeled as a beam. In this analysis, nonlinear form of interlayer van der Waals (vdW) forces and nonlinearities aroused from mid-plane stretching are also considered in the equations of motion. Further, direct application of multiple scales perturbation method is utilized to solve the obtained equations and to analyze free vibrations of the DWNT. Therefore, analytical expressions are found for vibrations of each layer. Linear and nonlinear natural frequencies of the system and vibration amplitude ratios of inner to outer layers are also obtained. Finally, the results are compared with the results obtained by Galerkin method.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.705-718
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• 2011

The aim of the investigation described in this paper is to study the nonlinear parametric vibrations and stability of a simply-supported viscoelastic beam with an intra-span spring. Taking into account a time-dependent tension inside the beam as the main source of parametric excitations, as well as employing a two-parameter rheological model, the equations of motion are derived using Newton's second law of motion. These equations are then solved via a perturbation technique which yields approximate analytical expressions for the frequency-response curves. Regarding the main parametric resonance case, the local stability of limit cycles is analyzed. Moreover, some numerical examples are provided in the last section.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.191-203
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• 2010

To investigate the critical buckling load and post-buckling behavior of an axially loaded pile entirely embedded in soil, the non-linear large deflection differential equation for a pinned pile, based on the Winkler-model and the discretionary distribution function of the foundation coefficient along pile shaft, was established by energy method. Assuming that the deflection function was a power series of some perturbation parameter according to the boundary condition and load in the pile, the non-linear large deflection differential equation was transformed to a series of linear differential equations by using perturbation approach. By taking the perturbation parameter at middle deflection, the higher-order asymptotic solution of load-deflection was then found. Effect of ratios of soil depth to pile length, and ratios of pile stiffness to soil stiffness on the critical buckling load and performance of piles (entirely embedded and partially embedded) after flexural buckling were analyzed. Results show that the buckling load capacity increases as the ratios of pile stiffness to soil stiffness increasing. The pile performance will be more stable when ratios of soil depth to pile length, and soil stiffness to pile stiffness decrease.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2010.10a
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• pp.391-392
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• 2010

• Journal of Energy Engineering
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• v.23 no.4
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• pp.41-48
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• 2014

Leak of liquid has been categorized conventionally into instantaneous release and continuous release. In this study, the spread of cryogenic liquid due to limited period of release is investigated for the first time to establish a new classification method with recognizing the irrationality of the conventional one. Such physical phenomena are governed by simultaneous equations concerning volume, radius and height of pool of the cryogenic liquid, and major parameters are evaporation rate per unit area, time of release, and spill quantity. The simultaneous governing equations is decoupled to get efficiently perturbation solutions. As the results, for the same spill quantity, in view of release model, combined release model that consists of continuous and consecutive instantaneous model is necessary with small time of release, while continuous model is solely required with large time of release. Also, the combined model is necessary for small spill quantity with the same time of release. These two regimes of release are clearly distinguished using the perturbation solution to provide a clear basis for the new classification of release models.

• Journal of KSNVE
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• v.6 no.5
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• pp.567-574
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• 1996

This paper concerns an articulated space robot with flexible links. The equations of its motion are derived by means of the Lagrangian mechanics. Assuming that magnitude of elastic motions are relatively small, the perturbation approach is taken to separate the original equations of motion into linear and nonlinear equations. Th effect the desired payload motion, open loop control inputs are first determined based on the nonlinear equations. One the other hand, in order to reduce the positional errors during the maneuver, vibration suppression is actively done with a feedforward control for disturbance cancellation to some extent. Additionally, for performance robustness against residual disturbance, an LQ control modified to have a prescribed degree of stability is applied based on the linear equations. Measurement equations are formulated to be used for the maximum likelihood estimator to reconstruct states from the original robot equations of motion. Finally, numerical simulations show effectiveness of the proposed control design scheme.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Earthquakes and Structures
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• v.9 no.1
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• pp.221-232
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• 2015

In this study, Homotopy Perturbation Method (HPM) is used to solve the nonlinear oscillators with damping. We have considered two strong nonlinear equations to show the application of the method. The Runge-Kutta's algorithm is used to obtain the numerical solution for the problems. The method works very well for the whole range of initial amplitudes and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear physics and engineering problems. Finally to show the accuracy of the HPM, the results have been shown graphically and compared with the numerical solution.