• Journal of the Korean Society for Aviation and Aeronautics
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• v.13 no.3
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• pp.9-21
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• 2005

The stable motion has been judged by mathematical modeling of the conditions that a rocket flies flexibly to take an active part in atmosphere. In this paper, the rocket conditions consist of the air speed, thrust and automatic attitude control. Aerodynamic force, a critical trust and a critical air speed are determined by comparing mathematical knowledges with eigenfrequencies of vibration equation. And then rocket object model is designed. Parameters and eigenfrequencies are used in dimensionless forms for in general applications by eliminating restrictions such as dimension, weight and select of materials.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.4
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• pp.363-372
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• 2016

When a system consisting of rigid and flexible bodies is optimized to improve its dynamic characteristics, its eigenfrequencies are typically maximized. While topology optimization formulations dealing with simultaneous design of a system of rigid and flexible bodies are available, studies on eigenvalue maximization of the system are rare. In particular, no work has solved for the case when the target frequency becomes one of the repeated eigenfrequencies. The problem involving repeated eigenfrequencies is solved in this study, and a topology optimization formulation and sensitivity analysis are presented. Further, several numerical case studies are considered to demonstrate the validity of the proposed formulation.

• Structural Engineering and Mechanics
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• v.25 no.3
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• pp.311-330
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• 2007

Model-based predictions of structural behavior are negatively affected by uncertainties of various type and in various stages of the structural analysis. The present paper focusses on dynamic analysis and addresses the effects of uncertainties concerning material and geometric parameters, mainly in the context of modal analysis of large-scale structures. Given the large number of uncertain parameters arising in this case, highly scalable simulation-based methods are adopted, which can deal with possibly thousands of uncertain parameters. In order to solve the reliability problem, i.e., the estimation of very small exceedance probabilities, an advanced simulation method called Line Sampling is used. In combination with an efficient algorithm for the estimation of the most important uncertain parameters, the method provides good estimates of the failure probability and enables one to quantify the error in the estimate. Another aspect here considered is the uncertainty quantification for closely-spaced eigenfrequencies. The solution here adopted represents each eigenfrequency as a weighted superposition of the full set of eigenfrequencies. In a case study performed with the FE model of a satellite it is shown that the effects of uncertain parameters can be very different in magnitude, depending on the considered response quantity. In particular, the uncertainty in the quantities of interest (eigenfrequencies) turns out to be mainly caused by very few of the uncertain parameters, which results in sharp estimates of the failure probabilities at low computational cost.

• The Journal of the Acoustical Society of Korea
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• v.35 no.1
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• pp.16-23
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• 2016

Present study shows three different methods finding the eigenfrequencies of an infinite circular cylinder under free-vibration; Elasticity theory that can be applied to general case, thin-shell theory that can be effectively applied to the cylinders with small thickness, and numerical study using Finite Element Method (FEM). The results obtained from those methods were verified through the cross check among the calculations. Changing the thickness of the cylinder for a fixed outer radius, all the eigenfrequencies below 1 kHz were found and their dependences on the modal index and the thickness were observed.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.103-113
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• 2017

Free vibration analysis of plates is necessary for the field of structural engineering because of its wide applications in practical life. Free vibration of plates is largely dependent on its thickness, aspect ratios, and boundary conditions. Here we investigate the natural frequencies of simply supported tapered isotropic rectangular plates with internal cutouts using a nine node isoparametric element. The effect of rotary inertia on Eigenfrequencies was demonstrated by calculating with- and without rotary inertia. We found that rotary inertia has a significant effect on thick plates, while rotary inertia term can be ignored in thin plates. Based on comparison with literature data, we propose that the present formulation is capable of yielding highly accurate results. Internal cutouts at various positions in tapered rectangular simply supported plates were also studied. Novel data are also reported for skew taper plates.

• Structural Engineering and Mechanics
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• v.25 no.2
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• pp.147-160
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• 2007

In this paper, a dynamic analysis based on the fuzzy set theory is presented as a possible complementary tool to the classical stochastic methods for dynamic analyses. Material parameters of a structure are influenced by uncertainties and therefore they are considered to be fuzzy quantities with given distributions, that means fuzzy numbers with given membership functions. The fuzzy dynamic analysis is conducted with help of fuzzy arithmetic defined on the so-called ${\alpha}$-cuts. The results of the analysis are also obtained in the form of fuzzy numbers, which compared to the stochastic methods is less computationaly expensive while at the same time they still provide information about the distribution of a quantity. This method is demonstrated on an analysis of a two-dimensional frame subjected to possible seismic load, where the uncertain eigenmodes and eigenfrequencies are used in the modal analysis.

• Structural Engineering and Mechanics
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• v.10 no.3
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• pp.277-288
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• 2000

The present paper, deals with the dynamic analysis of a thin-walled tower with varying cross-section and additional masses. It, especially, deals with the effect of the rotary inertia of those masses, which have been neglected up to now. Using Galerkin's method, we can find the spectrum of the eigenfrequencies and, also, the shape functions. Finally, we can solve the equations of the problem of the forced vibrations, by using Carson-Laplace's transformation. Applying this method on a tall mast with 2 concentrated masses, we can examine the effect of the rotary inertia and the diaphragmatic operation of the above masses, on the 3 first eigenfrequencies.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.349-354
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• 1992

In this paper, a modal analysis is applied for a hung Euler-Bernoulli beam with a lumped mass. We first derive the equations of motion using the Hamilton's principle. Then regarding the tension of beam as constant, we characterize the eigenfrequencies and the feature of eigenfunctions. The approximation employed here is corresponding that the lumped mass is sufficiently large than that of beam. Finally we compare the eigenfrequencies derived here with those obtained based on the Southwell's method.

• Smart Structures and Systems
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• v.8 no.2
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• pp.191-204
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• 2011

A technique for damage localization and assessment based on measurements of both eigenvectors curvatures and eigenfrequencies is proposed. The procedure is based on two successive steps: a model independent localization, based on changes of modal curvatures, and the solution of a one-dimensional minimization problem to evaluate damage intensity. The observability properties of damage parameters is discussed and, accordingly, a suitable change of coordinates is introduced. The proposed technique is illustrated with reference to a cantilever Euler beam endowed with a set of piezoelectric transducers. To assess the robustness of the algorithm, a parametric study of the identification errors with respect to the number of transducers and to the number of considered modal quantities is carried out with both clean and noise-corrupted data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.190-195
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• 2000

It has been established that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the location and depth of the crack. To identify the location and depth of a crack in a structure. Nikolakopoulos et. al. used the intersection point of the superposed contours that correspond to the eigenfrequency caused by the crack presence. However the intersecting point of the superposed contours is not only difficult to find but also incorrect to calculate. A method is presented in this paper which uses optimization technique for the location and depth of the crack. The basic idea is to find parameters which use the structural eigenfrequencies on crack depth and location and optimization algorithm. With finite element model of the structure to calculate eigenfrequencies, it is possible to formulate the inverse problem in optimization format. Method of optimization is augmented lagrange multiplier method and search direction method is BFGS variable metric method and one dimensional search method is polynomial interpolation.