• Title/Summary/Keyword: Natural Shape Function

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Free vibration analysis of arbitrary shape plates with simplified series function (단순급수함수를 이용한 임의 형상판의 자유진동 해석)

  • 정대근
    • Journal of KSNVE
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    • v.5 no.3
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    • pp.345-352
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    • 1995
  • A very simple and computationally efficient numerical method is developed for the free vibration of arbitrary shape plates. A set of two- dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies for the arbitrary shape plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series function are constructed with adding order of polynomial. Natural frequencies are obtained for the arbitrary shape plates, with combinational boundary conditions. The obtained numerical results are presented, some cases are verified with other numerical methods in the literature.

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Vibration Analysis of Micro Speaker Diaphragm (마이크로 스피커 다이어프램의 진동해석)

  • Hong, D.K.;Woo, B.C.;Ahn, C.W.;Han, G.J.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.551-554
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    • 2005
  • This study uses a characteristic function to explain correlations between the objective function and design variables. Analysis of means and table of orthogonal array were carried out. The change of shape of diaphragm, thickness of diaphragm and voice coil weight based on the table of orthogonal array is made. Therefore this study carried to decide shape of diaphragm, voice coil weight and thickness of diaphragm for minimizing 1st natural frequency and maximizing 2nd natural frequency of diaphragm using design of experiments and characteristic function with constraints. we showed improved design factors that minimized 1st natural frequency and maximized 2nd natural frequency of diaphragm.

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A Study on the Vibration Analysis of an Automobile Steering System (승용차 스티어링 칼럼 시스템의 진동해석에 관한 연구)

  • 김찬묵;김도연
    • Journal of KSNVE
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    • v.8 no.3
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    • pp.494-503
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    • 1998
  • In this paper, in order to analyze dynamic characteristics of an automobile steering system consisting of many components, natural frequencies and transfer functions of each component and the total system are found on a FFT analyzer by experiments. Then, the data are transmitted to a commercial package program, CADA-PC. By analyzing the data, the mode shape of each natural frequency and damping values are obtained. Also, the function of a rubber coupling in column and telescoping effects on system are considered. C.A.E commercial programs are used to compare with the results of experiments. For the finite element modeling, I-DEAS is used. Data processing and post processing are operated on NASTRAN and XL, respectively. The ball-bearing and the linkage of shaft with column are modeled by spring element. Stiffness is modified from the results of experiments. The results of those show close agreement. In the mode shape of total system, wheel mode is dominant at lower frequency, while the column mode is main mode at higher. The role of rubber coupling in vibration isolation is clear on mode shape. Telescoping function makes natural frequency of column changed.

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Geometrically Nonlinear Analysis using Petrov-Galerkin Natural Element Method Natural Element Method (페트로프-갤러킨 자연요소법에 의한 기하하적 비선형 해석)

  • 이홍우;조진래
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2004.04a
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    • pp.333-340
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    • 2004
  • This paper deals with geometric nonlinear analyses using a new meshfree technique which improves the numerical integration accuracy. The new method called the Petrov-Galerkin natural element method (PGNEM) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element method (BGNEM). But, unlike BGNEM, the test shape function is differently chosen from the trial shape function. In the linear static analysis, it is ensured that the numerical integration error of the PGNEM is remarkably reduced. In this paper, the PGNEM is applied to large deformation problems, and the accuracy of the proposed numerical technique is verified through the several examples.

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A Experimental study on natural frequency measurement of passenger car tire under the load and rotation (하중을 받고 회전하는 승용차 타이어의 고유진동수 측정에 관한 실험적 연구)

  • 김병삼;홍동표;김동현
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1993.10a
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    • pp.601-606
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    • 1993
  • The natural frequency measurement of passenger car tire under the load and rotation are studied. In order to obtain theoretical natural frequency and mode shape, the plane vibration of a tire is modeled to that of circular beam. By using the Tickling method based on Hamilton's principle, theoretical results are determined by considering tension force due to tire inflation pressure, rotational velocity and tangential, radial stiffness. Modal parameters varying the inflation pressure, load, rotational velocity are determined experimentally by using frequency response function method. The results show that experimental conditions are parameter for shifting of natural frequency.

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An Experimental Study on the Measurement of Radial Directional Natural Frequency in a Passenger Car Tire Roboting under the Load (하중을 받고 회전하는 승용차 타이어의 반경방향 고규진동수 측정에 관한 실험적 연구)

  • Kim, Byoung-Sam;Hong, Dong-Pyo;Chi, Chang-Heon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.1
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    • pp.1-13
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    • 1996
  • The measurement of radial directional natural frequency ina passenger car tire rotating under the load is studied. In order to obtain theoretical matural frequency and mode shape, the ploane vibration of a tire is modeled to that of circular beam. By esing the Tieking method based on Hamiltons's principle, theoretical results are determined by considering tension horce due to tire inflation pressure, retational velocity and tangential, radial stiffness. Radial directional modal parameters varying with the inflation pressure, load, rotational velocity are experimentally determined by using frequency response function method. The results show that experimental conditions canbe considered as the parameters which shift the natural frequency.

Study on the Natural Element Method using Petrov-Galerkin Concepts (페트로프-갤러킨 개념에 기초한 자연요소법에 관한 연구)

  • Lee, Hong-Woo;Cho, Jin-Rae
    • Proceedings of the KSME Conference
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    • 2003.11a
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    • pp.1274-1279
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    • 2003
  • In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called the Petrov-Galerkin natural element(PG-NE) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element(BG-NE). But, unlike BG-NE method, the test shape function is differently chosen from the trial shape function. The proposed technique ensures that the numerical integration error is remarkably reduced.

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A Study on the Shape Design of Micro Speaker Diaphragm (마이크로 스피커 다이아프램의 형상설계에 관한 연구)

  • Hong, Do-Kwa;Woo, Byung-Chul;Kim, Dong-Young;Ahn, Chan-Woo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.7 s.100
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    • pp.775-780
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    • 2005
  • This study uses a characteristic function to explain correlations between the objective function and design variables. Analysis of means and table of orthogonal array were carried out. The change of shape of diaphragm, thickness of diaphragm and voice coil weight based on the table of orthogonal array Is made. Therefore this study carried to decide design variables for minimizing 1st natural frequency and maximizing 2nd natural frequency of diaphragm using design of experiments and characteristic function with constraints. we showed improved design variables.

Shell Design Optimization Technique considering the Appearance of Close Frequencies in Optimization Process (고유진동수 접근현상을 고려한 쉘 구조물의 설계최적화기법)

  • Bae, Jung-Eun;Lee, Sang-Jin
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2006.11a
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    • pp.248-251
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    • 2006
  • This paper provides the basic theory and numerical results of shell design optimization considering the appearance of close natural frequencies in optimization process. In this study the fundamental natural frequency to be maximized is considered as the objective function and the initial volume of structures is used as the constraint function. In addition, the constraints related to natural frequency is also adopted to avoid the natural frequency closeness phenomenon during the optimization iteration. The Coon's patch is used to represent the shape and thickness distribution of shells. A degenerated shell finite element is adopted to calculate the fundamental natural frequency of the shells. The SQP available in the optimizer DoT is used to search optimum solution. From numerical results, the introduction of the frequency constraint into shell design optimization can deeply affect on the final optimum shape of shells although it is likely to be used to avoid the frequency closeness phenomenon.

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The Petrov-Galerkin Natural Element Method : II. Linear Elastostatic Analysis (페트로프-갤러킨 자연요소법 : II. 선형 정탄성 해석)

  • Cho, Jin-Rae;Lee, Hong-Woo
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.2
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    • pp.113-121
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    • 2005
  • In order to resolve a common numerical integration inaccuracy of meshfree methods, we introduce an improved natural clement method called Petrov-Galerkin natural element method(PG-NEM). While Laplace basis function is being taken for the trial shape function, the test shape function in the present method is differently defined such that its support becomes a union of Delaunay triangles. This approach eliminates the inconsistency of tile support of integrand function with the regular integration domain, and which preserves both simplicity and accuracy in the numerical integration. In this paper, the validity of the PG-NEM is verified through the representative benchmark problems in 2-d linear elasticity. For the comparison, we also analyze the problems using the conventional Bubnov-Galerkin natural element method(BG-NEM) and constant strain finite clement method(CS-FEM). From the patch test and assessment on convergence rate, we can confirm the superiority of the proposed meshfree method.