• Journal of Institute of Control, Robotics and Systems
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• v.8 no.4
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• pp.308-312
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• 2002

To determine the natural frequencies and damping ratios of composite laminated plates, we present an officient modal parameter estimation technique by developing residual spectrum based structural system reconstruction. The modal parameters can be estimated from poles and residues of the system transfer functions, derived from the state space system matrices. From vibration tests on cross-ply and angle-ply composite laminates, the natural frequencies and damping ratios can be estimated using the modal coordinates of the structural dynamic system reconstructed from the experimental frequency response functions. These results are compared with those of finite element analysis and single-degree-of-freedom curve fitting.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.117-124
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• 2001

A simplified method fur the eigenpair sensitivities of damped system with multiple eigenvalues is presented. This approach employs a reduced equation to determine the sensitivities of eigenpairs of the damped vibratory systems with multiple natural frequencies. In the proposed method, adjacent eigenvectors and orthonormal conditions are used to compute an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m the number of multiplicity of multiple natural frequencies. The proposed method is an improved Lee and Jung's method which was developed previously. Two equations are used to find eigenvalue derivatives and eigenvector derivatives in Lee and Jung's method. A significant advantage of this approach over Lee and Jung's method is that one algebraic equation newly developed is enough to compute such eigenvalue derivatives and eigenvector derivatives. This method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters. To demonstrate the theory of the proposed method and its possibilities in the case of multiple eigenvalues, the finite element model of the cantilever beam and 5-DOF mechanical system in the case of a non-proportionally damped system are considered as numerical examples. The design parameter of the cantilever beam is its height. and that of the 5-DOF mechanical system is a spring.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.71-78
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all variables, which are coupled by the constraints. The position velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The Perturbed constraint equations are then simultaneously solved for variations of all variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent variables variations.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.215-223
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• 2008

The differential equations governing free vibrations of the elastic arches with hollow section are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and reference are made to validate theories and numerical methods developed herein. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the rise to span length ratio.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.50-53
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• 2008

The differential equations governing free vibrations of the elastic arches with rectangular hollow section are derived in polar coordinates, in which the effect of rotatory inertia is included. Natural frequencies is computed numerically for circular arches with both clamped ends and both hinged ends. The lowest four natural frequency parameters are reported, with the rotatory inertia, as functions of three non-dimensional system parameters: the breadth ratio, the thickness ratio and the shape ratio.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2245-2250
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• 1994

The normal coordinates of a nonclassically damped systems are coupled by nonzero off-diagonal elements of modal damping matrix. The relationship between modal coupling and the frequency separation of the natural modes is presented in this paper. Contrary to widely accepted beliefs, increasing the frequency separation of the natural modes does not neccessarily diminish the effect of modal coupling. Consequently, in the pratical engineering applications, wide frequency separation of the natural modes would not be sufficient for neglecting modal coupling.

• Smart Structures and Systems
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• v.6 no.2
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• pp.115-133
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• 2010

A modal filter is a tool used to extract the modal coordinates of each individual mode from a system's output. This is achieved by mapping the response vector from the physical space to the modal space. It decomposes the system's responses into modal coordinates, and thus, on the output of the filter, the frequency response with only one peak corresponding to the natural frequency to which the filter was tuned can be obtained. As was shown in the paper (Deraemecker and Preumont 2006), structural modification (e.g. a drop in stiffness or mass due to damage) causes the appearance of spurious peaks on the output of the modal filter. A modal filter is, therefore, a great indicator of damage detection, with such advantages as low computational effort due to data reduction, ease of automation and lack of sensitivity to environmental changes. This paper presents the application of modal filters for the detection of stiffness changes. Two experiments were conducted: the first one using the simulation data obtained from the numerical 7DOF model, and the second one on the experimental data from a laboratory stand in 4 states of damage.

• Journal of Power System Engineering
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• v.4 no.2
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• pp.65-70
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• 2000

The shimmy phenomenon, or the radial vibration of steering wheel, happens frequently at a high speed, complicated with suspension system, steering system, vehicle body, engine, transmission and tire. In this study, the suspension system and steering system are modeled by the reference of vehicle body design coordinates(T.L.H), the coordinate system usually used by passenger car maker. In addition, the theoretical results from numerical method have been investigated and compared with the experimental ones by the correlating analysis between the tire and sub-system. The steering and suspension system modeled for the numerical analysis are both independent type. This study developed an analysis program which could forecast the shimmy level in advance by the variation of properties in each system and the change in design of new model.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.133-139
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• 2001

The nonlinear response statistics of an spring-pendulum system with internal resonance under narrow band random excitation is investigated analytically- The center frequency of the filtered excitation is selected to be close to natural frequency of directly excited spring mode. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The nonlinear phenomena, such as jump and multiple solutions, under narrow band random excitation were found by Gaussian closure method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.207-210
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• 2002

This paper is concerned with the experiments on the active vibration control of a plate with piezoceramic sensors and actuators. The natural frequencies of the composite plate featured by a piezo-film sensor and piezo-ceramic actuator are calculated by using the modal analysis method. Modal coordinates are introduced to obtain the state equations of the structural system. Six natural frequencies were considered in the modelling, because robust control theory which has inherent robustness to structured uncertainty is adopted to suppress the transients vibrations of a glass fiber reinforced(GFR) composite beam. A robust controller satisfying the nominal performance and robust performance is designed using robust theory based on the structured singular value. Simulations were carried out with the designed controller and effectiveness of the robust control strategy was verified by results.