• Tribology and Lubricants
• /
• v.22 no.2
• /
• pp.93-98
• /
• 2006

The numerical analysis of the negative pressure porous gas bearings is presented. The pressure distribution is calculated using the finite difference method. The Reynolds equation and Darcy's equation are solved simultaneously. The air bearing stiffness and damping are evaluated using the perturbation method. Rectangular uniform grid is employed to model the bearing. The vacuum preloading is considered. The pressure in the vacuum pocket is assumed to be a constant negative pressure. The total load, stiffness, damping and flow rate are calculated fur several geometrical configurations and several values of negative pressure. It is found that too large vacuum pocket can result in negative total force.

• Structural Engineering and Mechanics
• /
• v.83 no.6
• /
• pp.729-744
• /
• 2022

In this paper, an analytical formulation is proposed to predict the vertical vibration response due to the pedestrian walking on a footbridge considering the human-structure interaction, where the footbridge and pedestrian are represented by the Euler beam and linear oscillator model, respectively. The derived coupled equation of motion is a nonlinear fourth-order partial differential equation. An uncoupled solution strategy based on the combined weighted residual and perturbation method) is proposed to reduce the tedious computation, which allows the separate integration between the bridge and pedestrian subsystems. The theoretical study demonstrates that the pedestrian subsystem can be treated as a structural system with added mass, damping, and stiffness. The analysis procedure is then applied to a case study under the conditions of single pedestrian and multi pedestrians, and the results are validated and compared numerically. For convenient vibration design of a footbridge, the simplified peak acceleration formula and the idea of decoupling problem are thus proposed.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1495-1510
• /
• 2022

This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.

• Structural Engineering and Mechanics
• /
• v.48 no.6
• /
• pp.823-831
• /
• 2013

In this paper, it has been attempted to present a powerful analytical approach called Homotopy Perturbation Method (HPM). Free vibration of an electrostatically actuated microbeam is considered to study analytically. The effect of important parameters on the response of the system is considered. Some comparisons are presented to verify the results with other researcher's results and numerical solutions. It has been indicated that HPM could be easily extend to any nonlinear equation. We try to provide an easy method to achieve high accurate solution which valid for whole domain.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2003.10a
• /
• pp.65-70
• /
• 2003

In this work variations of orbital parameters are first derived from the perturbation equations using difference equation method under Earth oblateness and atmospheric drag. A simple and effective scheme is proposed to compute the required delta v and fuel consumption to compensate for atmospheric drag. The scheme is applied to KOMPSAT example. And by means of numerical simulations we quantitatively analyze influences due to each perturbation source, i.e., nonspherical Earth, atmospheric drag, third body gravities (Sun, Moon), and solar radiation.

• Journal of Institute of Control, Robotics and Systems
• /
• v.3 no.1
• /
• pp.17-22
• /
• 1997

The stability robustness problem of linear discrete-time systems with time-varying perturbations is considered. By using Lyapunov direct method, the perturbation bounds for guaranteeing the quadratic stability of the uncertain systems are derived. In the previous results, the perturbation bounds are derived by the quadratic equation stemmed from Lyapunov method. In this paper, the bounds are obtained by a numerical optimization technique. Linear matrix inequalities are proposed to compute the perturbation bounds. It is demonstrated that the suggested bound is less conservative for the uncertain systems with unstructured perturbations and seems to be maximal in many examples. Furthermore, the suggested bound is shown to be maximal for the special classes of structured perturbations.

• KSTLE International Journal
• /
• v.10 no.1_2
• /
• pp.6-12
• /
• 2009

In this study, the effect of oil supply conditions on the dynamic performance of a hydrodynamic journal bearing is analyzed numerically. Axial length, circumferential length and location of oil grooves are considered as oil supply conditions. The perturbation equations of the perturbed film contents are obtained by applying Elrod's universal equation implementing JFO film rupture / reformation boundary conditions to Lund's infinitesimal perturbation method. The dynamic coefficients of a hydrodynamic journal bearing are calculated by solving the perturbation equations, and the linear stability analysis is carried out by using those for a variety of oil supply conditions.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.845-862
• /
• 2010

In a recent paper, M.A. Noor et al. (Hindawi publishing corporation, Mathematical Problems in Engineering, Volume 2008, Article ID 696734, 11 pages, doi:10.1155/2008/696734) proposed the variational homotopy perturbation method (VHPM) for solving higher dimentional initial boundary value problems. In this paper, we consider the proposed method for analytic treatment of the linear and nonlinear ordinary differential equations, homogeneous or inhomogeneous. The results reveal that the proposed method is very effective and simple and can be applied for other linear and nonlinear problems in mathematical.

• Nuclear Engineering and Technology
• /
• v.27 no.3
• /
• pp.374-384
• /
• 1995

The mathematical adjoint solution of the Analytic Function Expansion (AFEN) method is found by solving the transposed matrix equation of AFEN nodal equation with only minor modification to the forward solution code AFEN. The perturbation calculations are then performed to estimate the change of reactivity by using the mathematical adjoint The adjoint calculational scheme in this study does not require the knowledge of the physical adjoint or the eigenvalue of the forward equation. Using the adjoint solutions, the exact and first-order perturbation calculations are peformed for the well-known benchmark problems (i.e., IAEA-2D benchmark problem and EPRI-9R benchmark problem). The results show that the mathematical adjoint flux calculated in the code is the correct adjoint solution of the AFEN method.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.11
• /
• pp.989-996
• /
• 2012

The purpose of this paper is to analyze GPS (Global Positioning System) satellite orbital mechanics, and then to propose a novel long-term GPS satellite orbit prediction scheme including virtual planet perturbation. The GPS orbital information is a necessary prerequisite to pinpointing the location of a GPS receiver. When a GPS receiver has been shut down for a long time, however, the time needed to fix it before its reuse is too long due to the long-standing GPS orbital information. To overcome this problem, the GPS orbital mechanics was studied, such as Newton's equation of motion for the GPS satellite, including the non-spherical Earth effect, the luni-solar attraction, and residual perturbations. The residual perturbations are modeled as a virtual planet using the least-square algorithm for a moment. Through the modeling of the virtual planet with the aforementioned orbital mechanics, a novel GPS orbit prediction scheme is proposed. The numerical results showed that the prediction error was dramatically reduced after the inclusion of virtual planet perturbation.