• Journal of Mechanical Science and Technology
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• v.18 no.12
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• pp.2148-2157
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• 2004

The paper deals with the vibration and dynamic stability of cantilevered pipes conveying fluid on elastic foundations. The relationship between the eigenvalue branches and corresponding unstable modes associated with the flutter of the pipe is thoroughly investigated. Governing equations of motion are derived from the extended Hamilton's principle, and a numerical scheme using finite element methods is applied to obtain the discretized equations. The critical flow velocity and stability maps of the pipe are obtained for various elastic foundation parameters, mass ratios of the pipe, and structural damping coefficients. Especially critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place, are precisely determined. Finally, the flutter configuration of the pipe at the critical flow velocities is drawn graphically at every twelfth period to define the order of the quasi-mode of flutter configuration.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.5
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• pp.541-549
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• 2007

In the case of control for mechanical systems, it is highly useful to be able to provide a compact model of the mechanical system to control engineers using the smallest number of state variables, while still providing an accurate model. The reduced mechanical model can then be inserted into the complete system models and used for extended system-level dynamic simulation. In this paper, moment-matching based model order reductions (MOR) using Krylov subspaces, which reduce the number of degrees of freedom of an original finite element model via the Arnoldi process, are presented to study the eigenvalue and frequency response problems of a HDD actuator and suspension system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.486-491
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• 2003

The paper presents the relationship between the eigenvalue branches and the corresponding flutter modes of cantilevered pipes conveying fluid. The pipes are located on elastic foundations which can be regarded as a soil model. In this paper, elastic foundations are assumed as linear distributed translational springs. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. The critical How velocity and stability maps of the pipe are investigated according to the variation of elastic foundation parameters, mass ratios of the pipe and internal damping Parameter. Also, the vibrational modes associated with flutter are shown.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.665-669
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• 2003

The paper deals with the relationship between the eigenvalue branches and the corresponding flutter modes of cantilevered pipes with a tip mass conveying fluid. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. The order of branches and unstable modes associated with flutter are defined in the stability maps of mass ratios of the pipe and the critical flow velocity. As a result, the relationship between the flutter related to the eigenvalue branches and the flutter modes are investigated thoroughly.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.362-367
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• 1996

In this paper, the eigenstructure of a class of linear time varying systems, termed as linear quasi-time invariant(LQTI) systems, is investigated. A system composed of dynamic devices such as linear time varying capacitors and resistors can be an example of the class. To effectively describe and analyze the LQTI systems, a generalized differential operator G is introduced. Then the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characteristics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. Also the corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency domain analysis of the systems under consideration. As an application example, a LQTI circuit is examined by using the concept of eigenstructure of LQTI system. The LQTI filter processes the sinusoidal signals modulated by some functions.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.398-401
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• 2001

There are two methods to calculate design sensitivity such as direct differentiation method and adjoint method. A sort of direct differentiation method for design sensitivity analysis costs too much when number of design variables is much larger than the number of response functions whose design sensitivity analyses are required. Therefore, an adjoint method is suggested for the case that the dimension of design variables is lager than the number of response function. An adjoint method is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation, requiring only the eigenvalue and its associated eigenvectors for mode being differentiated. This method has been extended to the repeated eigenvalue problem. In this paper, we propose an adjoint method for deign sensitivity analysis of damped vibratory systems with distinct eigenvalues.

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.69-93
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• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.11
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• pp.1115-1122
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• 2004

The paper discussed the effect of a tip mass on the stability of pipes on elastic foundations. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. With or without internal damping, the critical flow velocities of the pipes are investigated according to the variation of elastic foundation parameters and tip mass ratios. Also. the relationship between the eigenvalue branches and the corresponding flutter modes of the cantilevered pipes with a tip mass on the elastic foundations is fully investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.10
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• pp.1041-1047
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• 2004

This paper deals with the dynamic stability and vibration of a discontinuous cantilevered Pipe conveying fluid. The present model consists of two segments with different cross-sections. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. The critical flow velocities and stability maps of the pipe are obtained by changing ratios of second area moment of inertia and mass ratios. Finally, the vibrational modes associated with flutter are shown graphically.