• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.47-60
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• 1997

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

• Advances in nano research
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• v.17 no.1
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• pp.61-73
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• 2024

This paper presents nonlinear vibration analysis of a composite cylindrical shell. The core of the shell is made of functionally graded (FG) porous materials and layers is fabricated of carbon nanotubes (CNTs) reinforced nanocomposites. To increase the accuracy of results, neutral surface position is considered. First-order shear deformation theory is used as displacement field to derive the basic relations of equation motions. In addition, von-Karman nonlinear strains are employed to account geometric nonlinearity and to enhance the results' precision, the exact position of the neutral surface is considered. To governing the partial equations of motion, the Hamilton's principle is used. To reduce the equation motions into a nonlinear motion equation, the Galerkin's approach is employed. After that the nonlinear motion equation is solved by multiple scales method. Effect of various parameters such as volume fraction and distribution of CNTs along the thickness directions, different patterns and efficiency coefficients of porous materials, geometric characteristics and initial conditions on nonlinear to linear ratio of frequency is investigated.

• Earthquakes and Structures
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• v.10 no.2
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• pp.389-408
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• 2016

Recently, seismic hazard analysis has become a very significant issue. New systems and available data have been also developed that could help scientists to explain the earthquakes phenomena and its physics. Scientists have begun to accept the role of uncertainty in earthquake issues and seismic hazard analysis. However, handling the existing uncertainty is still an important problem and lack of data causes difficulties in precisely quantifying uncertainty. Ground Motion Prediction Equation (GMPE) values are usually obtained in a statistical method: regression analysis. Each of these GMPEs uses the preliminary data of the selected earthquake. In this paper, a new fuzzy method was proposed to select suitable GMPE at every intensity (earthquake magnitude) and distance (site distance to fault) according to preliminary data aggregation in their area using ${\alpha}$ cut. The results showed that the use of this method as a GMPE could make a significant difference in probabilistic seismic hazard analysis (PSHA) results instead of selecting one equation or using logic tree. Also, a practical example of this new method was described in Iran as one of the world's earthquake-prone areas.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.9
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• pp.886-892
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• 2008

In this paper, a closed-loop observer to extract the center of mass (CoM) of a bipedal robot is suggested. Comparing with the simple conversion method of just using joint angle measurements, it enables to get more reliable estimates by fusing both joint angle measurements and F/T sensor outputs at ankle joints. First, a nonlinear-type observer is constructed to estimate the flexible rotational motion of the biped in the extended Kalman filter framework. It adopts the flexible inverted pendulum model which is appropriate to address the flexible motion of bipeds, specifically in the single support phase. The predicted estimates of CoM in terms of the flexible motion observer are combined with measurements (that is, output of the CoM conversion equation with joint angles). Then, we have final CoM estimates depending on the weighting values which penalize the flexible motion model and the CoM conversion equation. Simulation results show the effectiveness of the proposed algorithm.

• Structural Engineering and Mechanics
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• v.29 no.4
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• pp.433-453
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• 2008

The equation of motion of a one way (vertical) spanning strip wall, as an assembly of two rigid bodies, is presented. Only one degree of freedom is needed to completely describe the wall response as the bodies are assumed to be perfectly rectangular and are allowed to rock but not to slide horizontally. Furthermore, no arching action occurs since vertical motion of the upper body is not restrained. Consequently, the equation of motion is nonlinear, with non constant coefficients and a Coriolis acceleration term. Phenomena associated with overburden to self weight ratio, motion triggering, impulsive energy dissipation, amplitude dependency of damping and period of vibration, and scale effect are discussed, contributing to a more complete understanding of experimental observations and to an estimation of system parameters based on the wall characteristics, such as intermediate hinge height and energy damping, necessary to perform nonlinear time history analyses. A comparison to a simple standing, or parapet, wall is developed in order to better highlight the characteristics of this assembly.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1241-1261
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• 2018

We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order H which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.

• Aerospace Engineering and Technology
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• v.13 no.2
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• pp.60-65
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• 2014

In this paper, numerical integration method using operational matrix of integration is studied. Using the operational matrix of integration, modified fixed point iteration method is introduced in order to solve rapidly an initial value problem for non-linear equation of motion. As an example, an initial value problem for orbital motion is considered. Through the numerical example, it is shown that the algorithm is efficient from the computational time point of view.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.550-555
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• 2000

Nonlinear oscillation of a microbubble under ultrasound was investigated theoretically. The bubble radius-time curves calculated by the Rayleigh-Plesset equation with a polytropic index and by the Keller-Miksis equation with the analytical solution for the Navier-Stokes equations of the gases were compared with the observed results by the light scattering method. This study has revealed that the bubble behavior such as the expansion ratio and the bouncing motion after the first collapse under ultrasound depends crucially on the retarded time of the bubble motion to the applied ultrasound.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.11a
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• pp.129-135
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• 1999

A numerical analysis between the piston and cylinder in swash plate type hydraulic piston pumps under reciprocating motion is presented. A finite difference method and the Newton-Raphson method are used simultaneously to solve the Reynolds equation In the clearance and the equation of motion for the piston. The tapered piston showed stable behaviors regardless of their initial eccentric conditions in the clearance and the reciprocating speed affect highly on the piston end trajectories. Therefore, the results of present study can be used other types fluid machineries.