• Title/Summary/Keyword: Euler-beam theory

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Free Vibration Characteristics of Partially Embedded Piles (부분근입된 말뚝의 자유진동 특성)

  • 신성철;진태기;오상진;박광규
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.05a
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    • pp.435-440
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    • 2002
  • The free vibration of partially embedded piles is investigated. The pile model is based on the Bernoulli-Euler beam theory and the soil is idealized as a Winkler model for mathematical simplicity. The governing differential equation for the free vibrations of such members is solved numerically The piles with one typical end constraint (clamped/hinged/free) and the other hinged end with rotational spring are applied in numerical examples. The lowest three natural frequencies are calculated over a range of non-dimensional system parameters: the rotational spring parameter, the relative stiffness and the embedded ratio.

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In-Plane and Out-of-Plane Vibration Analysis of Uniformly Curved Pipes Conveying Fluid (내부 유동이 있는 곡선 파이프의 면내 및 면외 진동 해석)

  • Lee, Soo-Il;Chung, Jin-Tai
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.11a
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    • pp.649-654
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    • 2000
  • The non-linear differential equations of motion of a fluid conveying curved pipe are derived by making use of Hamiltonian approach. The extensible dynamics of the pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the basic analysis results are discussed. Using eigenfrequency analysis, it can be shown that the natural frequencies are changed with flow velocity.

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Damage detection in structural beam elements using hybrid neuro fuzzy systems

  • Aydin, Kamil;Kisi, Ozgur
    • Smart Structures and Systems
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    • v.16 no.6
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    • pp.1107-1132
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    • 2015
  • A damage detection algorithm based on neuro fuzzy hybrid system is presented in this study for location and severity predictions of cracks in beam-like structures. A combination of eigenfrequencies and rotation deviation curves are utilized as input to the soft computing technique. Both single and multiple damage cases are considered. Theoretical expressions leading to modal properties of damaged beam elements are provided. The beam formulation is based on Euler-Bernoulli theory. The cracked section of beam is simulated employing discrete spring model whose compliance is computed from stress intensity factors of fracture mechanics. A hybrid neuro fuzzy technique is utilized to solve the inverse problem of crack identification. Two different neuro fuzzy systems including grid partitioning (GP) and subtractive clustering (SC) are investigated for the highlighted problem. Several error metrics are utilized for evaluating the accuracy of the hybrid algorithms. The study is the first in terms of 1) using the two models of neuro fuzzy systems in crack detection and 2) considering multiple damages in beam elements employing the fused neuro fuzzy procedures. At the end of the study, the developed hybrid models are tested by utilizing the noise-contaminated data. Considering the robustness of the models, they can be employed as damage identification algorithms in health monitoring of beam-like structures.

Stability Analysis of Cracked Cantilever Beam with Tip Mass and Follower Force (끝단질량과 종동력을 가진 크랙 외팔 보의 안정성 해석)

  • Son, In-Soo;Yoon, Han-Ik;Ahn, Tae-Su
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.7 s.124
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    • pp.605-610
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    • 2007
  • In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam subjected to follower force is presented. In addition, an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Besides, the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

Free Vibrations of Tapered Cantilever-Type Beams with Tip Mass at the Free End (자유단에 집중질량을 갖는 캔틸레버형 변단면 보의 자유진동)

  • Oh, Sang-Jin;Lee, Jae-Young;Park, Kwang-Kyou;Mo, Jeong-Man
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.965-970
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    • 2002
  • The purpose of this paper is to investigate the free vibration characteristics of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass with translational elastic support at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a wide range of section ratio, dimensionless spring constant and mass ratio.

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MEMS Accelerometer Modeling and Performance Analysis by Considering Signal Distortion (신호왜곡 현상을 고려한 MEMS 가속도 센서 모델링 및 성능특성 분석)

  • Kim, Yong-Il;Yoo, Hong-Hee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.2
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    • pp.106-111
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    • 2011
  • In this paper, assumed mode method on Euler beam theory is employed and signal distortion is considered to obtain the performances of a MEMS accelerometer which are a sensitivity and measurable frequency range(MFR). Not only the sensitivities and MFR but also the variations of dynamic responses and natural frequencies of the MEMS accelerometer are investigated for several sets of beam properties such as length, width, thickness and Young's modulus. It is stated that the variations of beam properties significantly influence the performances of the MEMS accelerometer and the relationship between sensitivities and MFR is inversely proportional to each other.

Free Vibrations of Tapered Beams with General Boundary Conditions and Tip Masses (끝단 질량과 일반적인 단부조건을 갖는 변단면 보의 자유진동)

  • 오상진;이병구;박광규;이종국
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.802-807
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    • 2003
  • The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

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Non-Linear Behavior of Shear Deformable Variable-Arc-Length Beams (전단변형을 고려한 변화곡선길이보의 비선형 거동)

  • 이병구;이태은;김종웅;김영일
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2001.04a
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    • pp.146-153
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    • 2001
  • In this paper, the governing differential equations for the non-linear behavior of shear deformable variable-arc-length beams subjected to an end moment are derived. The beam model is based on the Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to integrate the governing differential equations and to compute the beam's rotation at the left end of the beams. Numerical results are compared with existing closed-form and numerical solutions by other methods for cases in which they are available. The characteristic values of deflection curves for various load parameters are calculated and discussed.

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Free Vibrations of Generally Restrained Beams (일반적인 단부조건을 갖는 보의 자유진동)

  • 신성철;김봉규;안대순;김선기
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.05a
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    • pp.864-869
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    • 2003
  • The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and point masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a range of non-dimensional system parameters.

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Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section

  • Atmane, Hassen Ait;Tounsi, Abdelouahed;Ziane, Noureddine;Mechab, Ismail
    • Steel and Composite Structures
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    • v.11 no.6
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    • pp.489-504
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    • 2011
  • This paper presents a theoretical investigation in free vibration of sigmoid functionally graded beams with variable cross-section by using Bernoulli-Euler beam theory. The mechanical properties are assumed to vary continuously through the thickness of the beam, and obey a two power law of the volume fraction of the constituents. Governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the vibration of the S-FGM beam are obtained for three different types of boundary conditions associated with simply supported, clamped and free ends. Results show that, all other parameters remaining the same, the natural frequencies of S-FGM beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of S-FGM beams knowing that of similar homogeneous beams.