• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.73-80
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• 2006

In order to examine the validity of an asymptotic solution for nonlinear interaction in asymmetric vibration modes of a perfect circular plate, we obtain the numerical solution. The motion of the plate is governed by nonlinear partial differential equation. The initial and boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution. It is found that traveling waves relating clockwise and counterclockwise as well as standing wave are depicted by the numerical solution.

• Earthquakes and Structures
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• v.25 no.6
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• pp.455-467
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• 2023

This study focuses on demonstrating the effectiveness of vibration control of tuned rotary mass damper (TRMD) for reducing the bidirectional and torsional response of the irregular asymmetric structure with voided slabs under earthquake excitations. The TRMD arranged in plane of one-story eccentric structure is proposed as a distributed tuned rotary mass damper (DTRMD) system. Lagrange's equation is used to derive the equations of motion of the controlled system. The optimum position and number of TRMD are numerically investigated under harmonic excitation and the control effects of different distributions are discussed. Furthermore, a shaking table test is conducted under different excitation cases, including free vibration, forced vibration and seismic wave to investigate the absorption performance of the device. The numerical simulations of different distributions of the TRMDs show that the DTRMDs are more effective in reduction of the displacement response of the asymmetric structure under the same mass ratio, even when the degree of eccentricity becomes large. However, with small degree of eccentricity, the unreasonable asymmetrical arrangement may cause the increase of the peak value of the rotational angular displacement. Finally, the experimental investigations exhibit similar results of translational displacement of the structure. It is concluded that the vibration of the irregular asymmetric structure can be controlled more economically and effectively by reducing the mass ratio through reducing the quantity of TRMDs at the high stiffness end.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.498-504
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• 2002

Vibration beat phenomenon is theoretically investigated on a slightly asymmetric cylindrical shell, which is a simplified model of Korean bell. Mode pairs of the slightly asymmetric shell are obtained by receptance analysis and impulse response of the shell is derived using modal expansion and Laplace transform. Based on the impulse response model, beat mapping method is proposed to explain the reason that the beat of a bell vibration shows periodic distribution on the circumference. Beat characteristics of King Song-Dok Bell are explained in detail using the beat map and the measured modal data.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.9
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• pp.685-693
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• 2002

Analytical model of beat response is derived on a slightly asymmetric ring and the model is veryfied by experiment. The asymmetric ring is a simplified model used to explain the beat property of a Korean bell. The asymmetric ring has mode pairs having slight frequency difference in each radial mode. Each mode pair produces beat phenomenon by the interaction of the two close frequency components. Based on the analytical model, beat maps are first proposed and characteristics of beat on the circumference are detaily explained.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.530-533
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• 2004

It is well known that many real systems have asymmetric mass, damping and stiffness matrices. In this case, the method for calculating eigenpair sensitivity is different from that of symmetric system. To determine the derivatives of the eigenpairs in asymmetric damped case, a modal method was recently developed by Adhikari. When a dynamic system has many degrees of freedom, only a few lower modes are available, and because the higher modes should be truncated to use the modal method, the errors may become significant. In this paper a procedure for determining the sensitivities of the eigenpairs of asymmetric damped system using a few lowest set of modes is proposed. Numerical examples show that proposed method achieves better calculating efficiency and highly accurate results when a few modes are used.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.4
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• pp.308-313
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• 2012

Robust tuning rules of the motion profile are proposed to minimize the residual vibration. For asymmetric S-curve profile, tuning rules are analytically formulated using Laplace-domain approach. When the system modeling is known exactly, by placing a single zero of the motion profile on the pole of the system, the residual vibration can be perfectly eliminated under undamped system. However, if there are some amounts of the modeling errors, the residual vibration significantly increases. To track this issue, the robust tuning rules against modeling error are discussed. One of the proposed robust tuning rules is placing the multiple zeros of the motion profile on the pole of the system, and the other is placing the zeros of the motion profile around the pole of the system. Thanks to the proposed robust tuning rules, motion profile becomes more robust to modeling errors while minimizing the residual vibration. By simulation, the effectiveness of the proposed robust tuning rules is verified.

• Structural Engineering and Mechanics
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• v.33 no.1
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• pp.95-107
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• 2009

A method for vibration analysis of asymmetric shear wall and Thin walled open section structures is presented in this paper. The whole structure is idealized as an equivalent bending-warping torsion beam in this method. The governing differential equations of equivalent bending-warping torsion beam are formulated using continuum approach and posed in the form of simple storey transfer matrix. By using the storey transfer matrices and point transfer matrices which consider the inertial forces, system transfer matrix is obtained. Natural frequencies can be calculated by applying the boundary conditions. The structural properties of building may change in the proposed method. A numerical example has been solved at the end of study by a program written in MATLAB to verify the presented method. The results of this example display the agreement between the proposed method and the other valid method given in literature.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.1-17
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• 2013

In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of $6{\times}6$ by transforming the obtained stiffness matrix. Thus, the dimension, which is $12n{\times}12n$ in classical finite elements, is reduced to the dimension of $6{\times}6$. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.304-309
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• 2003

A new modal analysis method for rotor systems with periodically time-varying parameters is proposed. The essence of method is to introduce modulated coordinates to derive the equivalent time-invariant equation. This paper presents a modal analysis method using modulated coordinates fur general rotors, of which rotating and stationary parts both possess asymmetric properties. The equation of motion with time-varying parameters is transformed to an infinite order matrix equation with the time-invariant parameters. A theory of modal analysis for the system is presented with the infinite order equation and a couple of reduced order equations. A numerical example with simple asymmetric rotor is provided to demonstrate the effectiveness of the proposed method

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.27 no.2
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• pp.234-242
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• 2017

This study investigates vibro-acoustic characteristics of a short, thick cylinder containing a slot given a pined-free boundaries. Using the finite element analysis results, structural modes of the asymmetric cylinder (with a slot) are expressed as the linear combinations of modes of the symmetric cylinder made of same material with identical geometry except the slot. Based on synthesized modal vibrations, acoustic modes of the asymmetric cylinder are obtained with two approaches, i.e., Rayleigh integral calculation and modal expansion of the acoustic modes of the symmetric cylinder. Also, acoustic powers, max. sound pressure and directivity pattern are obtained from acoustic modes and verified with the boundary element analyses. Based on these results, the accuracy of proposed approaches in calculating the vibro-acoustic properties of a short, thick, asymmetric cylinder has been confirmed. The procedure can be applied to the similar cylinders with other boundaries or asymmetric properties. Also, attenuation of vibration and/or sound radiation of the cylinder type practical components can be studied using these approaches.