• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.603-611
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• 1996

Let consider the following problem: find an element u(t) in a Banach space U from the equation $$ x'(t) = Ax(t) + f(t,x(t)) + \Phi_0 u(t), 0 \leq t \leq T $$ with initial and terminal conditions $$ x(0) = 0, x(T) = \phi $$ in a Banach space X where $\phi \in D(A)$. This problem is a kind of control engineering inverse problem and contains nonlinear term, so that it is difficult and interesting. Thee proof main result in this paper is based on the Fredholm property of [1] in section 3. Similar considerations of linear system have been dealt with in many references. Among these literatures, Suzuki[5] introduced this problem for heat equation with unknown spatially-varing conductivity. Nakagiri and Yamamoto[2] considered the identifiability problem, which A is a unknown operator to be identified, where the system is described by a linear retarded functional differential equation. We can also apply to determining the magnitude of the control set for approximate controllability if X is a reflexive space, i.e., we can consider whether a dense subset of X is covered by reachable set in section 4.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.985-1000
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• 2010

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.

• Structural Engineering and Mechanics
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• v.36 no.5
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• pp.561-573
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• 2010

The potential of the liquid column vibration absorber (LCVA) as a seismic vibration control device for structures has been explored in this paper. In this work, the structure has been modeled as a linear, viscously damped single-degree-of-freedom (SDOF) system. The governing differential equations of motion for the damper liquid and for the coupled structure-LCVA system have been derived from dynamic equilibrium. The nonlinear orifice damping in the LCVA has been linearized by a stochastic equivalent linearization technique. A transfer function formulation for the structure-LCVA system has been presented. The design parameters of the LCVA have been identified and by applying the transfer function formulation the optimum combination of these parameters has been determined to obtain the most efficient control performance of the LCVA in terms of the reduction in the root-mean-square (r.m.s.) displacement response of the structure. The study has been carried out for an example structure subjected to base input characterized by a white noise power spectral density function (PSDF). The sensitivity of the performance of the LCVA to the coefficient of head loss and to the tuning ratio have also been examined and compared with that of the liquid column damper (LCD). Finally, a simulation study has been carried out with a recorded accelerogram, to demonstrate the effectiveness of the LCVA.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.227-230
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• 1993

Recently, the development of novel control methodology enables us to improve the performance of AC-machine drives by using pulse width modulation (PWM) technique. Usually, the dynamic characteristic of induction motor (IM) has been represented by the 5-th order nonlinear differential equation. This dynamics, however, can be reduced to 3-rd order dynamics by applying direct control of IM input current. This methodology concludes that it is much easier to control IM by means of the field-oriented methods employing the current controller. Therefore a precise current control is crucial to achieve a high control performance both in dynamic and steady state operations. This paper presents an adaptive fuzzy current controller with artificial neural network (ANN) for field-oriented controlled IM. This new control structure is able to adaptively minimize a current ripple while maintaining constant switching frequency. Especially the proposed controller employs neuro-computing philosophy as well as adaptive learning pattern recognizing principles with respect to variations of the system parameters. The proposed approach is applied to the IM drive system, and its performance is tested through various simulations. Simulation results show that the proposed system, compared among several known classical methods, has a superb performance.

• Korean Journal of Computational Design and Engineering
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• v.20 no.1
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• pp.84-92
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• 2015

In this study, we describe a method to analysis dynamic behavior of an offshore wind turbine in the frequency domain and expected effects of the method. An offshore wind turbine, which is composed of platform, tower, nacelle, hubs, and blades, can be considered as multibody systems. In general, the dynamic analysis of multibody systems are carried out in the time domain, because the equations of motion derived based on the multibody dynamics are generally nonlinear differential equations. However, analyzing the dynamic behavior in time domain takes longer than in frequency domain. In this study, therefore, we describe how to analysis the system multibody systems in the frequency domain. For the frequency domain analysis, the non-linear differential equations are linearized using total derivative and Taylor series expansions, and then the linearized equations are solved in time domain. This method was applied to analysis of double pendulum system for the verification of its effectiveness, and the equations of motion for the offshore wind turbine was derived with assuming that the wind turbine is rigid multibody systems. Using this method, the dynamic behavior analysis of the offshore wind turbine can be expected to take less time.

• Journal of Navigation and Port Research
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• v.40 no.6
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• pp.361-368
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• 2016

A ship's rolling motion can make crew and passengers sick and/or apply forces to the structure that cause damage.. Therefore bilge keels are equipped in most ships for anti-rolling. In special cases, anti-rolling tanks (ARTs), fin stabilizers, or gyroscopes can be installed. However, ARTs require a large area to install, and fin stabilizers and gyroscopes are costly to install and expensive to operate. This paper suggests a Anti-rolling pendulum (ARP) to reduce roll motion. ARPs acts like ARTs. However, the ARP has a circular shaped guidance arc instead of the string or wire of a simple pendulum. The device suggested has about 1/ 8 the weight and 1/ 6 the volume of a ART and is more effective. This study derives the nonlinear and linear differential equations of system motion.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.04c
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• pp.45-49
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• 2008

Polyethylene is widely used as the insulator for power cable. To investigate the conduction mechanism for power cable insulation under ac high field, it is very important to acquire the dissipation current under actual running field. Recently, we have developed the unique system, which make possible to observe the nonlinear dissipation current waveform. In this system, to observe the nonlinear properties with high accuracy, capacitive current component is canceled by using inverse capacitive current signal instead of using the bridge circuit for canceling it. We have already reported that the dissipation currents of $40\;{\mu}m$ thick LDPE film at 10 kV/mm and over 140 Hz, it starts to show nonlinearity and odd number's harmonics were getting large. To investigate the conduction mechanis ms in this region, especially space charge effect, various kinds of estimation, such as time variations of instantaneous resistivity for one cycle, FFT spectra of dissipation current waveforms and so on, has been examined. As the results of these estimations, it was found that the dissipation current will depend on not only the instantaneous value of electric field but also the time differential of applied electric field due to taking a balance between applied field and internal field. Furthermore, two large peaks of dissipation current for each half cycle were observed under certain condition. In this paper, to clarify the reason why it shows two peaks for each half cycle, the film thickness dependences of dissipation current waveforms were observed by using the three different thickness LDPE films.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.1988-1989
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• 2007

Polyethylene is widely used as the insulator for power cable. To investigate the conduction mechanism for power cable insulation under ac high field, it is very important to acquire the dissipation current under actual running field. Recently, we have developed the unique system, which make possible to observe the nonlinear dissipation current waveform. In this system, to observe the nonlinear properties with high accuracy, capacitive current component is canceled by using inverse capacitive current signal instead of using the bridge circuit for canceling it. We have already reported that the dissipation currents of $40\;{\mu}m$ thick LDPE film at 10 kV/mm and over 140 Hz, it starts to show nonlinearity and odd number's harmonics were getting large. To investigate the conduction mechanis ms in this region, especially space charge effect, various kinds of estimation, such as time variations of instantaneous resistivity for one cycle, FFT spectra of dissipation current waveforms and so on, has been examined. As the results of these estimations, it was found that the dissipation current will depend on not only the instantaneous value of electric field but also the time differential of applied electric field due to taking a balance between applied field and internal field. Furthermore, two large peaks of dissipation current for each half cycle were observed under certain condition. In this paper, to clarify the reason why it shows two peaks for each half cycle, the film thickness dependences of dissipation current waveforms were observed by using the three different thickness LDPE films.

• Steel and Composite Structures
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• v.45 no.3
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• pp.409-423
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• 2022

Nowadays, there is a high demand for great structural implementation and multifunctionality with excellent mechanical properties. The porous structures reinforced by graphene platelets (GPLs) having valuable properties, such as heat resistance, lightweight, and excellent energy absorption, have been considerably used in different engineering implementations. However, stiffness of porous structures reduces significantly, due to the internal cavities, by adding GPLs into porous medium, effective mechanical properties of the porous structure considerably enhance. This paper is relating to vibration analysis of fluidconveying cantilever porous graphene platelet reinforced (GPLR) pipe with fractional viscoelastic model resting on foundations. A dynamical model of cantilever porous GPLR pipes conveying fluid and resting on a foundation is proposed, and the vibration, natural frequencies and primary resonant of such a system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with the fractional viscoelastic model is used to govern the construction relation of nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied to the pipe and the excitation frequency is close to the first natural frequency. The governing equation for transverse motions of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.