• Title/Summary/Keyword: Linear elastic system

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Free Vibrations of Compressive Members Resting on Linear Elastic Foundation (선형 탄성지반 위에 놓인 압축부재의 자유진동)

  • 이병구;이광범;모정만;신성철
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.42 no.6
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    • pp.122-129
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    • 2000
  • The purpose of this study is to investigate both the fundamental and some higher natural frequencies and mode shapes of compressive members resting on the linear elastic foundation. The model of compressive member is based on the classical Bernoulli-Euler beam theory. The differential equation governing free vibrations of such members subjected to an axial load is derived and solved numerically for calculating the natural frequencies and mode shapes. The Improved Euler method is used to integrate the differential equation and the Determinant Search method combined with the Regula-Falsi method to determine the natural frequencies, respectively. In numerical examples, the hinged-hinged, hinged-clamped, clamped-hinged and clamped-clamped end constraints are considered. The convergence analysis is conducted for determining the available step size in the Improved Euler method. The validation of theories developed herein is also conducted by comparing the numerical results between this study and SAP 90. The non-dimensional frequency parameters are presented as the non-dimensional system parameters: section ratio, modulus parameter and load parameter. Also typical mode shapes are presented.

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Dynamic Analysis of Constrained Mechanical System Moving on a Flexible Beam Structure(I) : General Approach (유연한 보 구조물 위를 이동하는 구속 기계계의 동력학 해석(I) : 일반적인 접근법)

  • Park, Chan-Jong;Park, Tae-Won
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.11
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    • pp.165-175
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    • 2000
  • In recent years, it becomes a very important issue to consider the mechanical systems such as high-speed vehicles and railway trains moving on elastic beam structures. In this paper, a general approach, which can predict the dynamic behavior of constrained mechanical system and elastic beam structure, is proposed. Also, various supporting conditions of a foundation support are considered for the elastic beam structures. The elastic structure is assumed to be a nonuniform and linear Bernoulli-Euler beam with proportional damping effect. Combined Differential-Algebraic Equations of motion are derived using multibody dynamics theory and Finite Element Method. The proposed equations of motion can be solved numerically using generalizd coordinate partitioning method and Predictor-Corrector algorithm, which is an implicit multi-step integration method.

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Non-linear aero-elastic response of a multi-layer TPS

  • Pasolini, P.;Dowell, E.H.;Rosa, S. De;Franco, F.;Savino, R.
    • Advances in aircraft and spacecraft science
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    • v.4 no.4
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    • pp.449-465
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    • 2017
  • The aim of the present work is to present a computational study of the non-linear aero-elastic behavior of a multi-layered Thermal Protection System (TPS). The severity of atmospheric re-entry conditions is due to the combination of high temperatures, high pressures and high velocities, and thus the aero-elastic behavior of flexible structures can be difficult to assess. In order to validate the specific computational model and the overall strategy for structural and aerodynamics analyses of flexible structures, the simplified TPS sample tested in the 8' High Temperature Tunnel (HTT) at NASA LaRC has been selected as a baseline for the validation of the present work. The von $K{\acute{a}}rm{\acute{a}}n^{\prime}s$ three dimensional large deflection theory for the structure and a hybrid Raleigh-Ritz-Galerkin approach, combined with the first order Piston Theory to describe the aerodynamic flow, have been used to derive the equations of motion. The paper shows that a good description of the physical behavior of the fabric is possible with the proposed approach. The model is further applied to investigate structural and aero-elastic influence of the number of the layers and the stitching pattern.

Development of Viscoelastic Finite Element Analysis Code for Pavement Structures (도로포장 구조해석을 위한 점탄성 유한요소 해석코드 개발)

  • Lee, Chang-Joon;Yoo, Pyeong-Jun;Choi, Ji-Young;Ohm, Byung-Sik
    • International Journal of Highway Engineering
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    • v.14 no.5
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    • pp.1-9
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    • 2012
  • PURPOSES: A viscoelastic axisymmetric finite element analysis code has been developed for stress analysis of asphalt pavement structures. METHODS: Generalized Maxwell Model (GMM) and 4-node isoparametric element were employed for finite element formulation. The code was developed using $C^{+}^{+}$ computer program language and named as KICTPAVE. For the verification of the developed code, a structural model of a pavement system was constructed. The structural model was composed of three layers: asphalt layer, crushed stone layer, and soil subgrade. Two types of analysis were considered for the verification: (1)elastic static analysis, (2)viscoelastic time-dependent analysis. For the elastic static analysis, linear elastic material model was assigned to all the layers, and a static load was applied to the structural model. For the viscoelastic time-dependent analysis, GMM and linear elastic material model were assigned to the asphalt layer and all the other layers respectively, and a cyclic loading condition was applied to the structural model. RESULTS: The stresses and deformations from KICTPAVE were compared with those from ABAQUS. The analysis results obtained from the two codes showed good agreement in time-dependent response of the element under the loading area as well as the surface deformation of asphalt layer, and horizontal and vertical stresses along the axisymmetric axis. CONCLUSIONS: The validity of KICTPAVE was confirmed by showing the agreement of the analysis results from the two codes.

A Basic Research on Estimation of Material Condition by Using Nonlinear Elastic Modulus (비선형 탄성계수를 이용한 재료변질 상태평가에대한 기초적 연구)

  • 김경조;장경영
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1995.04b
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    • pp.348-352
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    • 1995
  • In the conventional linear elasticity, ultrasonic velocity is determined by elastic modulus and density of te medium which ultrasonic wave propagates through. But, practical ultrsonic wave depends on the stress acting in the medium, and as the stress increases such dependency becomes nonlinear. This nonlinear dependencyof ultrasonic velocity on stress can be identified by using nonlinear elastic modulus up to 4th order. In thid paper, with the above background relationships between nonlinear elastic modulus and the internalstatus of materials, normal, plastic deformed or heat stressed, are discussed. For this purpose, a new type of measuring system extended from the general nondestructive UT(ultrasonic test) equipment is constructed.

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A Study on the Non-linear Forced Torsional Vibration for Propulsion Shaftings with Multi-Degree-of-Freedom System (기관축계의 비선형 다자유도 강제 비틀림진동에 관한 연구)

  • 김수철;이문식;장민오;김의간
    • Journal of Advanced Marine Engineering and Technology
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    • v.24 no.6
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    • pp.7-14
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    • 2000
  • Nowadays, the viscous damper using high viscosity oil was much to be used for engine shafting system to reduce the excessive additional stress by torsional vibration. In general, it was assumed that the viscous damper could be modelled having only damping coefficient, that is to say, whose stiffness be ignored. But it is found that there exists a jump phenomenon, as a kind of non-linear vibration, in the actual engine shafting system with a damper of high viscosity. Therefore the damper ring and the casing are modelled as two mass elastic system with a complex viscosity. Also, to analyze a non-linear phenomenon, it is assumed that the viscous damper has a linear stiffness coefficient in proportion to the angular amplitude and a non-linear stiffness coefficient in proportion to cube of the angular amplitude. For the analysis, Quasi-Newton method with BFGS(Broyden-Fletcher-Goldfarb-Shanno) formula is used. Both calculated and measured values are provided in this paper which confirm the possibility of applying non-linear theory to engine shafting system with viscous damper.

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Application of The Boundary Element Analysis Software BEASY in Engineering Pratice (공학실무에서의 경계요소해석 소프트웨어 BEASY의 적용)

  • Huh, Young;Cho, Jun-Sang
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1994.10a
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    • pp.31-37
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    • 1994
  • BEASY is a soft-ware tool which may be used to solve problems in heat transfer(linear and non-linear, steady state and transient) and linear elastic stress analysis. It is based on the boundary element method. The central part is the analysis module, called BEASY. For pre- and post-processing the BEASY Interactive Modeling System BEASY-IMS can be used. Three examples are devoted to show the capability of BEASY.

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Reference Stress Based Stress Analysis for Local Creep Rupture of a T-pipe (참조응력법에 입각한 T-배관 국부 크리프 파단 평가를 위한 응력해석 사례연구)

  • Shin Kyu-In;Yoon Kee-Bong;Kim Yun-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.8 s.251
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    • pp.873-879
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    • 2006
  • To investigate applicability of the reference stress approach as simplified inelastic stress analysis to estimate local creep rupture, detailed finite element stress analyses of a T-piece pipe with different inner pressure and system loading levels are performed. The reference stresses are obtained from the finite element (FE) limit analysis based on elastic-perfectly-plastic materials, from which the local reference stress for creep rupture is determined from R5. The resulting inelastic stresses are compared with elastic stresses resulting from linear elastic FE calculations. Furthermore they are also compared with the stresses from full elastic-creep FE analyses. It shows that the stresses estimated from the reference stress approach compare well with those from full elastic-creep FE analysis, which are significantly lower than the elastic stress results. Considering time and efforts for full inelastic creep analysis of structures, the reference stress approach is shown to be a powerful tool for creep rupture estimates and also to reduce conservatism of elastic stress analysis significantly.

Comparison of Fatigue Damage of Linear Elastic System with Respect to Vibration Input Conditions (입력가진 조건에 따른 선형 시스템의 피로손상도 비교 평가)

  • Heo, Yun Seok;Kim, Chan-Jung
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.24 no.6
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    • pp.437-443
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    • 2014
  • Vibration testing is conducted for evaluate the fatigue resistance of responsible system over excitation situations and two kinds of vibration profiles, harmonic or random, are widely used in engineering fields. Harmonic excitation profile is adequate for the rotating machinery that is primarily exposed to the orderly excited force subjected for a rotating speed; Random profile is suitable for the non-stationary vibration input, that is a ground excitation for example. Recently, the sine on random(SOR) testing method was sometimes considered to represent the real excitation conditions since the measured response signals of a target system, expecially for moving mobility, shows usually a mixture of them. So, it is important to understand the accumulated fatigue damage over different excitation patterns, harmonic and/or random, to determine the efficient vibration profile of a target system. A uniaxial vibration testing with a notched simple beam was introduced to evaluate the fatigue damage for different excitation profiles and the best choice of vibration profile was concluded from those comparison of calculated fatigue damages.

Comparison of fatigue damage of linear elastic system with respect to vibration input conditions (입력가진 조건에 따른 선형 시스템의 피로손상도 비교 평가)

  • Kim, Chan-Jung;Heo, Yun Seok
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2014.04a
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    • pp.340-345
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    • 2014
  • Vibration testing is conducted for evaluate the fatigue resistance of responsible system over excitation situations and two kinds of vibration profiles, harmonic or random, are widely used in engineering fields. Harmonic excitation profile is adequate for the rotating machinery that is primarily exposed to the orderly excited force subjected for a rotating speed; Random profile is suitable for the non-stationary vibration input, that is a ground excitation for example. Recently, the sine on random (SOR) testing method was sometimes considered to represent the real excitation conditions since the measured response signals of a target system, expecially for moving mobility, shows usually a mixture of them. So, it is important to understand the accumulated fatigue damage over different excitation patterns, harmonic and/or random, to determine the efficient vibration profile of a target system. A uniaxial vibration testing with a notched simple beam was introduced to evaluate the fatigue damage for different excitation profiles and the best choice of vibration profile was concluded from those comparison of calculated fatigue damages.

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