• Title/Summary/Keyword: Vibration Equation

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Experimental Investigations of Relationships between Resonance Frequencies and Elastic Moduli of Composite Materials by Impulse Excitation Method (Impulse Excitation Method에 의한 복합재료의 공진 주파수와 탄성계수 관계에 대한 실험적 고찰)

  • Kim, Hyeong-Sam;Lee, Jae-Hyeok;Lee, Dong-Sik;Park, Se-Man
    • Korean Journal of Materials Research
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    • v.8 no.9
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    • pp.843-848
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    • 1998
  • The Usages of composite materials have been steadily on the rise in the industries of automobiles, air crafts, shipbuilding and other structures for transportations. Commonly required in those industries are light weight and high strength of the structures. Consequently, serious efforts in research have been focused on searching for light materials and on developments and characterizations of advanced substitutes including various kinds of composite materials. In this investigation, transversely isotropic composite materials are chosen and formed into two kinds of beams; Euler-Bernoulli beam(thin team) and Timoshenko beam(thick beam) for determinations of elastic constants. As an experimental technique Impulse Excitation Method is utilized to measure resonance frequencies of the beams of the composite materials in vibration tests. Elastic constants are evaluated from measured resonance frequencies for the two types of beams to observe and establish possible existence of effects of rotary inertia and shear deformations.

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Tearing Test for Automotive Vibroisolating Rubber and Formulation of Tearing Energy (자동차용 방진고무의 찢김시험 및 찢김에너지 정식화)

  • Moon, Hyung-Il;Kim, Heon Young;Kim, Min Gun;Kim, Ho
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.12
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    • pp.1669-1674
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    • 2012
  • A commonly analytical estimation of fatigue life on rubber components is using fatigue life equation based on various fatigue test results. However, such method has very restricted applicability in actual designing processes because performing fatigue tests requires a lot of time and money. In addition, non-standard rubber materials and their randomness make it hard to make databases. In this paper, the other fatigue life estimation method using tearing energy was suggested. We performed static and dynamic tearing test about automotive vibration rubber materials and a finite element formulation using a virtual crack to calculate the tearing energy of rubber components with complicated shapes. To using the suggested method, fatigue life of an automotive motor mount has been estimated and verified the reliability of this method by using comparison between the estimated values and the actual fatigue life.

Development of Optimization Technique of Warm Shrink Fitting Process for Automobile Transmission Part(Shaft/Gear) (자동차 변속기 단품(축/기어)용 온간압입공정 최적화 기법 개발)

  • Kim Ho-Yoon;Bae Won-Byong;Kim Chul
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.5 s.182
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    • pp.37-43
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    • 2006
  • Fitting process carried out in automobile transmission assembly line is classified into three classes; heat fitting, press fitting, and their combined fitting. Heat fitting is a method that heats gear to a suitable range under the tempering temperature and squeezes it toward the outer diameter of shaft. Its stress depends on the yield strength of gear. Press fitting is a method that generally squeezes gear toward that of shaft at room temperature by press. Another method heats warmly gear and safely squeezes it toward that of shaft. Warm shrink fitting process for automobile transmission part is now gradually increased, but the parts (shaft/gear) assembled by this process produced dimensional change in both outer diameter and profile of the gear. So that it may cause noise and vibration between gears. In order to solve these problems, we need an analysis of warm shrink fitting process, in which design parameters are involved; contact pressure according to fitting interference between outer diameter of shaft and inner diameter of gear, fitting temperature, and profile tolerance of gear. In this study, an closed form equation to predict contact pressure and fitting load was proposed in order to develop optimization technique of warm shrink fitting process and verified its reliability through the experimental results measured in the field and FEM, that is, thermal-structural coupled field analysis. Actual loads measured in the field have a good agreement with the results obtained by theoretical and finite element analysis and also the expanded amounts of the outer diameters of the gears have a good agreement with results.

The Dynamic Performance Analysis of Foil Journal Bearings Considering Coulomb Friction: Rotating Unbalance Response (마찰을 고려한 포일저널베어링의 동특성해석: 회전불균형 응답)

  • Kim, Kyung-Woong;Lee, Dong-Hyun;Kim, Young-Cheol
    • Tribology and Lubricants
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    • v.23 no.5
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    • pp.219-227
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    • 2007
  • The dynamic performance of air foil bearings relies on a coupling between a thin air film and an elastic foil structure. A number of successful analytical techniques to predict dynamic performance have been developed. However, the evaluation of its dynamic characteristic is still not enough because of the mechanical complexity of the foil structure and strong nonlinear behavior of friction force. This work presents a nonlinear transient analysis method to predict dynamic performance of foil bearings. In this method, time dependent Reynolds equation is used to calculate pressure distribution and a finite element method is used to model the bump foil structure. The analysis is treated with a direct implicit integration technique that can handle nonlinear problems and the stick-slip algorithm is used to consider friction force. Using this method the response to the mass unbalance excitation is investigated for various design parameters and operating conditions. The results of analysis show that foil bearing is very effective on the restriction of vibration at the resonance frequency compared to the rigid surface bearings and the effectiveness depends on the operating conditions, static load and a amount of mass unbalance. In addition, there exist optimum values of friction coefficient, bump foil stiffness and number of circumferential slit with regards to minimizing dynamic response at the resonance frequency. These optimum values are system dependent.

A Study on Temperature Properties Analysis for Tension Measurement of Steel Cables Using Magnetic Sensor (자기센서에 의한 강재 케이블 장력측정에서 온도특성에 대한 연구)

  • Park, Hae-won;Ahn, Bong-young;Lee, Seung-seok;Park, Jeong-hak
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.13 no.2 s.54
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    • pp.181-188
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    • 2009
  • Measuring the tensile strength of steel cables used to support bridges is a critical inspection item in terms of the safety of a bridge. Today, cable tension is measured with the vibration method and loadcell. Recently, some advanced countries have conducted studies on measuring tension with magnetic method and are suggesting prospective results. Since there were no such studies ongoing in Korea, we began a study on measuring tension with magnetic method as we are undergoing researches to improve the precision of measurements. It is necessary to consider the influence for the magnetic field and the temperature of steel cables in tension measurement of magnetic method. In this paper, we tested an output characteristic of tension sensor according to temperature and deduced temperature compensation coefficient in the given magnetic field and applied the compensation coefficient to the tension measurement system in the lab. We analyzed and evaluated testing results for the output voltages of the tension sensor according to cable tensions.

Structural Damage Assessment Using Transient Dynamic Response (동적과도응답을 사용한 구조물의 손상진단)

  • 신수봉;오성호;곽임종;고현무
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.13 no.4
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    • pp.395-404
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    • 2000
  • A damage detection and assessment algorithm is developed by measuring accelerations at limited locations of a structure under forced vibrations. The developed algorithm applies a time-domain system identification (SI) method that identifies a structure by solving a linearly constrained nonlinear optimization problem for optimal structural parameters. An equation error of the dynamic equilibrium of motion is minimized to estimate optimal parameters. An adaptive parameter grouping scheme is applied to localize damaged members with sparse measured accelerations. Damage is assessed in a statistical manner by applying a time-windowing technique to the measured time history of acceleration. Displacements and velocities at the measured degrees of freedom (DOF) are computed by integrating the measured accelerations. The displacements at the unmeasured DOF are estimated as additional unknowns to the unknown structural parameters, and the corresponding velocities and accelerations we computed by a numerical differentiation. A numerical simulation study with a truss structure is carried out to examine the efficiency of the algorithm. A data perturbation scheme is applied to determine the thresholds lot damage indices and to compute the damage possibility of each member.

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Vibration of Rectangular Plates (직사각형판(直四角形板)의 진동해석(振動解析))

  • Keuck-Chun,Kim;Tae-Young,Chung
    • Bulletin of the Society of Naval Architects of Korea
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    • v.14 no.1
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    • pp.1-10
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    • 1977
  • The major objects of this report are to supplement data of natural frequencies of thin elastic rectangular plates to the available data, and to give an experimental verification for natural frequencies obtained by Rayleigh-Ritz method, the generation set of which are eigenfunctions of Euler beams. For the first object the following five models, for which data only for the fundamental mode or data only for square plates are available, are adopted; (1) two opposed edges are clamped and the other two opposed edges simply supported (C-C, S-S), (2) one edge is simply supported and the other three edges clamped (C-C, C-S), (3) one edge is free and the other three edges clamped (C-C, C-F), (4) two adjacent edges are clamped and the other two adjacent edges free (C-F, C-F). For the (C-C, S-S) model the frequency equation obtained with the mode shapes assumed as of a single trigonometric series is solved. And for the other four models Rayleigh-Ritz method taking eigenfunctions of Euler beams as the generating set is applied. The numerical examples are obtained up to the fourth, the fifth or the sixth order depending on the range of the aspect ratio (0.1-10.0). The number of terms in the generating set for Rayleigh-Ritz method is fifteen for all models. For the experiment three models made of 3.2mm thickness mild steel plate for general structure use were prepared in following size; $300mm{\times}600mm,\;600mm{\times}600mm\;and\;900mm{\times}600mm$. Their boundary conditions are made to fit (C-C, C-F) condition. From the experiment mechanical impedance curves based on the frequency response method were obtained together with phase relation diagrams. The experimental data are resulted in good conformity to calculated values.

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Seismic Behaviors of Concrete-Suction-Type Offshore Wind Turbine Supporting Structures Considering Soil-Structure Interaction (지반-구조물 상호작용을 고려한 콘크리트 석션식 해상풍력 지지구조물의 지진거동 특성)

  • Lee, Jin Ho;Jin, Byeong-Moo;Bae, Kyung-Tae
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.30 no.4
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    • pp.319-327
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    • 2017
  • In this study, characteristics of seismic behaviors of offshore wind turbine systems using concrete-suction-type supporting structures are investigated. Applying hydrodynamic pressure from the surrounding sea water and interaction forces from the underlying soil to the structural system which is composed of RNA, the tower, and the supporting structure, a governing equation of the system is derived and its earthquake responses are obtained. It can be observed from the analysis results that the responses are significantly influenced by soil-structure interaction because dynamic responses for higher natural vibration modes are increased due to the flexibility of soil. Therefore, the soil-structure interaction must be taken into consideration for accurate assessment of dynamic behaviors of offshore wind turbine systems using concrete-suction-type supporting structures.

A Method for the Preliminary Estimation of Vertical Natural Vibations of High Speed Boats (고속선(高速船) 선체고유상하진동(船體固有上下振動)의 초기추정(初期推定) 방법(方法))

  • K.C.,Kim;H.B.,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.17 no.1
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    • pp.25-29
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    • 1980
  • For the preliminary estimation of the vertical hull natural frequency, the Schlick's or Schlick-type formulae have been traditional ones and are still in common use today. Some investigators have made their efforts, based on statistical data of ships' system parameters, to extend the applicability of Schlick-type formulae to higher modes, or to utilize the Rayleigh method. For instance, the work done by Dinsenbacher et al.[5] belongs to the former and that of Nagamoto et al.[6] to the latter. In a part of his previous paper[7], the author, investigating the case of a cargo ship of medium size, suggested that provided statistically simplified curves such as trapezoid of system parameter distributions are available in hands, direct utlization of an ordinary computer program can be also an another convenient method by which we can obtain both natural frequencies and normal mode shapes. In this paper, to confirm the feasibility of the above suggestion, four high speed boats are investigated. The system parameters of them are originally given in [5]. The computer program used here is one confiled based on a calculation method derived from Myklestal-Prohl modeling of hull, transfer matrix formulation and an extended Gumbel's initial value method for solving frequency equation. The results of the investigation show that the direct calculation based on statistically oriented and reasonably assumed trapezoidal mean curves of system parameter distributions can give us natural frequencies within about 5% deviation up to several-noded modes and normal mode shapes serviceable at least up to 4- or 5-noded modes in comparision with those based on actual distributions of system parameters. For this simplified method the actual data required for input are only of ship length, displacement, total added mass, bending and shear rigidity at amidship. They are available at the early stage of design. By this method we can also easily trace variations of vibration characteristics in the course of ship design cycles.

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A new finite element procedure for fatigue life prediction of AL6061 plates under multiaxial loadings

  • Tarar, Wasim;Herman Shen, M.H.;George, Tommy;Cross, Charles
    • Structural Engineering and Mechanics
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    • v.35 no.5
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    • pp.571-592
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    • 2010
  • An energy-based fatigue life prediction framework was previously developed by the authors for prediction of axial, bending and shear fatigue life at various stress ratios. The framework for the prediction of fatigue life via energy analysis was based on a new constitutive law, which states the following: the amount of energy required to fracture a material is constant. In the first part of this study, energy expressions that construct the constitutive law are equated in the form of total strain energy and the distortion energy dissipated in a fatigue cycle. The resulting equation is further evaluated to acquire the equivalent stress per cycle using energy based methodologies. The equivalent stress expressions are developed both for biaxial and multiaxial fatigue loads and are used to predict the number of cycles to failure based on previously developed prediction criterion. The equivalent stress expressions developed in this study are further used in a new finite element procedure to predict the fatigue life for two and three dimensional structures. In the second part of this study, a new Quadrilateral fatigue finite element is developed through integration of constitutive law into minimum potential energy formulation. This new QUAD-4 element is capable of simulating biaxial fatigue problems. The final output of this finite element analysis both using equivalent stress approach and using the new QUAD-4 fatigue element, is in the form of number of cycles to failure for each element on a scale in ascending or descending order. Therefore, the new finite element framework can provide the number of cycles to failure at each location in gas turbine engine structural components. In order to obtain experimental data for comparison, an Al6061-T6 plate is tested using a previously developed vibration based testing framework. The finite element analysis is performed for Al6061-T6 aluminum and the results are compared with experimental results.