• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.619-631
• /
• 2000

We study a class of catalytic super Brownian motion X in 1-dimension. We show under some conditions of catalyst, the process X is absolutely continuous and we get a stochastic partial differential equation for X.

• Structural Engineering and Mechanics
• /
• v.64 no.5
• /
• pp.611-620
• /
• 2017

A new theory of weightless sagging planer elasto-flexible cables under point loads is developed earlier by the authors and used for predicting the nonlinear dynamic response of cable-suspended linear elastic beams. However, this theory is not valid for nonlinear elastic cracked concrete beams possessing different positive and negative flexural rigidity. In the present paper, the flexural response of simply supported cracked concrete beams suspended from cables by two hangers is presented. Following a procedure established earlier, rate-type constitutive equations and third order nonlinear differential equations of motion for the structures undergoing small elastic displacements are derived. Upon general quasi-static loading, negative nodal forces, moments and support reactions may be introduced in the cable-suspended concrete beams and linear modal frequencies may abruptly change. Subharmonic resonances are predicted under harmonic loading. Uncoupling of the nodal response is proposed as a more general criterion of crossover phenomenon. Significance of the bilinearity ratio of the concrete beam and elasto-configurational displacements of the cable for the structural response is brought out. The relevance of the proposed theory for the analysis and the design of the cable-suspended bridges is critically evaluated.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.12
• /
• pp.2647-2655
• /
• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.181-189
• /
• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).

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

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.401-416
• /
• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.11
• /
• pp.2776-2788
• /
• 1996

A new feature-based motion parameter estimation for arbitrary-shaped regions is proposed. Existing motion parameter estimation algorithms such as gradient-based algorithm require iterations that are very sensitive to initial values and which often converge to a local minimum. In this paper, the motion parameters of an object are obtained by solving a set of linear equations derived by the motion of salient feature points of the object. In order to estimate the displacement of the feature points, a new process called the "bi-directional correspondence scheme" is proposed to ensure the robjstness of correspondence. The proposed correspondence scheme iteratively selects the feature points and their corresponding points until unique one-to-one correspondence is established. Furthermore, initially obtained motion paramerters are refined using an iterative method to give a better performance. The proposed algorithm can be used for motion estimationin object-based image coder, and the experimental resuls show that the proposed method outperforms existing schemes schemes in estimating motion parameters of objects in image sequences.sequences.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.8 no.3
• /
• pp.252-261
• /
• 2016

A spar-type floating substructure that is being widely used for offshore wind power generation is vulnerable to resonance in the heave direction because of its small water plane area. For this reason, the stable dynamic response of this floating structure should be ensured by accurately identifying the resonance characteristics. The purpose of this study is to analyze the characteristics of the combination resonance between the excitation frequency of a regular wave and natural frequencies of the floating substructure. First, the nonlinear equations of motion with two degrees of freedom are derived by assuming that the floating substructure is a rigid body, where the heaving motion and pitching motions are coupled. Moreover, to identify the characteristics of the combination resonance, the nonlinear term in the nonlinear equations is approximated up to the second order using the Taylor series expansion. Furthermore, the validity of the approximate model is confirmed through a comparison with the results of a numerical analysis which is made by applying the commercial software ANSYS AQWA to the full model. The result indicates that the combination resonance occurs at the frequencies of ${\omega}{\pm}{\omega}_5$ and $2{\omega}_{n5}$ between the excitation frequency (${\omega}$) of a regular wave and the natural frequency of the pitching motion (${\omega}_{n5}$) of the floating substructure.

• Earthquakes and Structures
• /
• v.8 no.5
• /
• pp.957-976
• /
• 2015

Recently, two energy-based response parameters, i.e., the absolute and the relative elastic input energy equivalent velocity, have been receiving a lot of research attention. Several studies, in fact, have demonstrated the potential of these intensity measures in the prediction of the seismic structural response. Although some ground motion prediction equations have been developed for these parameters, they only provide marginal distributions without information about the joint occurrence of the spectral values at different periods. In order to build new prediction models for the two equivalent velocities, a large set of ground motion records is used to calculate the correlation coefficients between the response spectral values corresponding to different periods and components of the ground motion. Then, functional forms adopted in models from the literature are calibrated to fit the obtained data. A new functional form is proposed to improve the predictions of the considered models from the literature. The components of the ground motion considered in this study are the two horizontal ones only. Potential uses of the proposed equations in addition to the prediction of the correlation coefficients of the equivalent velocity spectral values are shown, such as the prediction of derived intensity measures and the development of conditional mean spectra.

• Structural Engineering and Mechanics
• /
• v.64 no.4
• /
• pp.515-526
• /
• 2017

Dynamic response of functionally graded Carbon nanotubes (FG-CNT) reinforced pipes conveying viscous fluid under accelerated moving load is presented. The mixture rule is used for obtaining the material properties of nano-composite pipe. The radial force induced by viscous fluid is calculated by Navier-Stokes equation. The material properties of pipe are considered temperature-dependent. The structure is simulated by Reddy higher-order shear deformation shell theory and the corresponding motion equations are derived by Hamilton's principal. Differential quadrature (DQ) method and the Integral Quadrature (IQ) are applied for analogizing the motion equations and then the Newmark time integration scheme is used for obtaining the dynamic response of structure. The effects of different parameters such as boundary conditions, geometrical parameters, velocity and acceleration of moving load, CNT volume percent and distribution type are shown on the dynamic response of pipe. Results indicate that increasing CNTs leads to decrease in transient deflection of structure. In accelerated motion of the moving load, the maximum displacement is occurred later with respect to decelerated motion of moving load.