• Transactions of the Korean Society of Automotive Engineers
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• v.18 no.3
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• pp.127-132
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• 2010

Eigensolutions associated with self-excited vibration of disc brake system can be obtained by complex eigenvalue analysis. The eigenvalue sensitivity to change in contact stiffness can be used to demonstrate stability criteria and eigenvalue veering. Dynamic instability on eigenvalue loci with respect to the variation of contact stiffness is found to be related to mode interaction between two adjacent modes. This modal interaction can be effectively shown by mode shape visualization. This paper presents the methodology to construct the mode shape of disc brake system where a disc and two brake pads are coupled with contact stiffness.

• Journal of KSNVE
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• v.5 no.2
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• pp.215-224
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• 1995

In this paper, the three-dimensional finite element model is established to investigate the structural dynamic characteristics of rotor blade using a finite element analysis. Six natural frequencies and mode shapes are calculated by computer simulation. The first three flapping modal frequencies, the first two lead-lag modal frequencies, and the first feathering modal frequency are validated through comparison with the modal test results of the fixed rotor blade. The computer simulation results are found in good agreement with experimentally measured natural frequencies. The important results are obtained as follows: (1) Natural frequencies are changed due to the variation of rotational speed and fiber angle of rotor blade, (2) Weak coupling between flapping mode shape and lead-lag mode shape are detected, (3) Centrifugal force has more effect on flapping modal frequency than lead-lag modal frequency.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.194-200
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• 1999

Localized damage to a structure affects its dynamic properties, and much work has been undertaken investigating the variation of natural frequencies, damping ratios and mode shapes. This paper presents a technique based on wavelet transform to detect the existences and locations of structural damages. The procedure operates solely on the mode shape from the damaged structure, and does not require a priori knowledge of the undamaged structure. The procedure is developed using a 32-story shear building model. Applying wavelet transform to the mode shape successfully identifies the location of damage. The procedure is best suited to the mode shape obtained from the fundamental natural frequency. The wavelet coefficients from the higher mode shapes can be used to verify the location of damage, but they are not as sensitive as the wavelet coefficients of the lower mode shapes.

• Journal of KSNVE
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• v.10 no.2
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• pp.312-318
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• 2000

A modeling method for the vibration analysis of rotating cantilever plastes with stiffeners is presented. The equations of motion for the plates aer derived and trnasformed into a dimensionless form. A mass density Dirac's delta function is used to idealize the stiffener mathematically. The effects of stiffeners on the model characteristics of the plate are investigated, and mode shape variations due to some parameter variation are exhibited. It is found that veering phenomena occur between some loci and associated mode shapes change significantly during the veering phenomena.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1331-1337
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• 2003

Linearized equations of motion for the vibration analysis of rotating cantilever plates with arbitrary orientation angle are derived in the present work. Two in-plane stretch variables are introduced to be approximated. The use of the two in-plane stretch variables enables one to derive the equations of motion which include proper motion-induced stiffness variation terms. The equations of motion are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters on the modal characteristics of rotating cantilever plates are investigated through numerical study. The natural frequency loci veering along with the associated mode shape variations, which occur while the rotating speed increases, are also presented and discussed.

• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.413-421
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• 2022

Modal parameters are the main dynamic characteristics of bridge. This study aims to propose an innovative route to estimate the modal parameters for bridges by using a parked vehicle in which mode shapes with high accuracy and spatial resolution are identified by frequency measurement. Based on the theory of dynamic modification and modal identification, the mathematical formulation between the parked mass induced frequency variation and the modal parameters of a bridge is derived. Then this mathematical formulation is extended to a parked vehicle-bridge system. The arithmetic and processes for estimating the modal parameters based on the identified frequency variation of the vehicle-bridge systems when the vehicle locates at sequentially arranged positions are presented. Finally the proposed method is applied to several simulated bridges of different types. The results indicate that it can estimate the modal parameters with high accuracy and efficiency.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.1
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• pp.51-66
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• 1987

In this paper, the authors investigate theoretically the motion and longitudinal strength of ships among waves talking account of the effects of nonlinearities such as the hull shape, bottom emergence, and hydrodynamic impact. Incidentally the ship is treated as an elastic beam in heading wave condition regarding characteristics of slamming and whipping-according to the variation in the range of a quarter length of the ship forward and the increase of the elastic modes up to 4-th vibration mode were investigated by the present theory. Calculations are performed for 97m container ship and its validity is confirmed by a series of model tests. Conclusions obtained are as follows; 1) Acceleration and pressure estimated by the present theory are in good accordance with experiments. 2) The present non-linear theory may be applied for estimating longitudinal bending moment of ships in slamming and whipping conditions. 3) In investigation of the characteristic in response according to shape variation for parts under draft and vow-flare in the range of a quarter length of the ship forward, dynamic responses due to the former were much more conspicuous than those due to the later. 4) In the maximum bending moment, the considering case up to 2-the mode are larger, about $10{\sim}15%$, than that up to 4-th mode.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.6
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• pp.347-353
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• 2021

In this study, we presented a novel size optimization framework to control the linear buckling temperature and several buckling modes of plates, by optimizing thickness values of composite structures for practical engineering applications. Predicting the buckling temperature and mode shape of structures is a vital research topic in engineering to achieve structural stability. However, optimizing designs of engineering structures through engineering intuition is challenging. To address this limitation, we proposed a method that combines finite element simulation and size optimization. Based on the idea that the structural buckling temperature and mode shape of a plate are affected by the thickness of the structure, the thickness values of the nodes of the target structure were set as the design variables in this optimization method; and the buckling temperature values, and buckling mode shapes were set as the objective functions. This size optimization method enabled the determination of optimal thickness distributions, to induce the desired buckling temperature values and mode shapes. The validity of the proposed method was verified in terms of their buckling temperature values and buckling mode shapes, using several numerical examples of rectangular composite structures.

• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.719-738
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• 2010

The aim of this paper concerns with the nonlinear analysis of cable-stayed bridges including the vibration effect of cable stays. Two models for the cable stay system are built up in the study. One is the OECS (one element cable system) model in which one single element per cable stay is used and the other is MECS (multi-elements cable system) model, where multi-elements per cable stay are used. A finite element computation procedure has been set up for the nonlinear analysis of such kind of structures. For shape finding of the cable-stayed bridge with MECS model, an efficient computation procedure is presented by using the two-loop iteration method (equilibrium iteration and shape iteration) with help of the catenary function method to discretize each single cable stay. After the convergent initial shape of the bridge is found, further analysis can then be performed. The structural behaviors of cable-stayed bridges influenced by the cable lateral motion will be examined here detailedly, such as the static deflection, the natural frequencies and modes, and the dynamic responses induced by seismic loading. The results show that the MECS model offers the real shape of cable stays in the initial shape, and all the natural frequencies and modes of the bridge including global modes and local modes. The global mode of the bridge consists of coupled girder, tower and cable stays motion and is a coupled mode, while the local mode exhibits only the motion of cable stays and is uncoupled with girder and tower. The OECS model can only offers global mode of tower and girder without any motion of cable stays, because each cable stay is represented by a single straight cable (or truss) element. In the nonlinear seismic analysis, only the MECS model can offer the lateral displacement response of cable stays and the axial force variation in cable stays. The responses of towers and girders of the bridge determined by both OECS- and MECS-models have no great difference.