• Title/Summary/Keyword: follower force

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Influence of Two Successively-moving Spring-mass Systems with Initial Displacement on Dynamic Behavior of a Simply-supported Beam Subjected to Uniformly Distributed Follower Forces (초기 변위를 가지고 연속 이동하는 스프링-질량계가 등분포종동력을 받는 단순지지보의 동특성에 미치는 영향)

  • 윤한익;강혁준;유진석
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.3
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    • pp.202-209
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    • 2003
  • A simply supported beam subjected to a uniformly distributed tangential follower force and the two successively moving spring-mass systems upon it constitute this vibration system. The influences of the velocities of the moving spring-mass system, the distance between two successively moving spring-mass systems and the uniformly distributed tangential follower force have been studied on the dynamic behavior of a simply supported beam by numerical method. The uniformly distributed tangential follower force is considered within its critical value of a simply supported beam without two successively moving spring-mass systems, and three kinds of constant velocities and constant initial displacement of two successively moving spring-mass systems are also chosen. Their coupling effects on the transverse vibration of the simply supported beam are inspected too. In this study the simply supported beam is deflected with small vibration proportional to natural frequency of the moving spring-mass systems. According to the increasing of initial displacement of the moving spring-mass systems the amplitude of the small vibration of the simply supported beam is increased due to the spring force. The velocity of the moving spring-mass system more affect on the transverse deflection of simply supported beam than other factors of the system and the effect is dominant at high velocity of the moving spring-mass systems.

Effect of an Intermediate Support on the Stability of a Beam resting on Elastic Foundation Subjected to Follower Force (종동력을 받는 탄성기초위에 놓인 보의 안정성에 미치는 중간 지지의 효과)

  • Kim, Jae-On;Lee, Kee-Seok
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.6
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    • pp.709-717
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    • 2007
  • This paper discussed on the effect of an intermediate support on the stability of a beam resting on elastic foundation subjected to follower force. The stability and dynamic responses of a beam resting on elastic foundation subjected to follower force are analyzed based on the finite element method. The dynamic responses of the system are studied by the mode superposition method to observe the damping rate of the motion. The beam resting on elastic foundation subjected to follower force loses its stability by flutter type or divergence type, depending on the location of the intermediate support.

Chaotic Behavior of a Double Pendulum Subjected to Follower Force (종동력을 받는 이중진자의 혼돈운동 연구)

  • 장안배;이재영
    • Journal of KSNVE
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    • v.7 no.3
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    • pp.439-447
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    • 1997
  • In this study, the dynamic instabilities of a nonlinear elastic system subjected to follower forces are investigated. The two-degree-of-freedom double pendulum model with nonlinear geometry, cubic spring, and linear viscous damping is used for the study. The constant, the initial impact forces acting at the end of the model are considered. The chaotic nature of the system is identified using the standard methods, such as time histories, power density spectrum, and Poincare maps. The responses are chaotic and unpredictable due to the sensitivity to initial conditions. The sensitivities to parameters, such as geometric initial imperfections, magnitude of follower force, direction control constant, and viscous damping, etc., are analysed. Dynamic buckling loads are computed for various parameters, where the loads are changed drastically for the small change of parameters.

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Influence of Partial Elastic Foundations on Dynamic Stability of a Cantilevered Timoshenko Beam with a Tip Mass under a follower force (끝단 질량을 갖고 종동력을 받는 외팔 Timoshenko 보의 동적안정성에 미치는 부분 탄성기초의 영향)

  • Shin, Kwang-Bok;Kim, Hyo-Jun;Ryu, Bong-Jo
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.10 s.175
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    • pp.65-71
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    • 2005
  • This paper presents the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam with a tip concentrated mass is assumed to be a Timoshenko beam taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and finite element method is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, rotary inertia of the beam and magnitude and rotary inertia of the tip mass is fully investigated.

Effect of a Partial Elastic Foundation on Dynamic Stability of a Cantilevered Timoshenko Beam under a Follower Force (종동력을 받는 외팔 Timoshenko보의 동적안정성에 미치는 부분탄성기초의 영향)

  • Ryu, Bong-Jo;Ryu, Si-Ung;Han, Hyun-Hee;Kim, Hyo-Jun
    • Proceedings of the KSME Conference
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    • 2004.04a
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    • pp.911-916
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    • 2004
  • The paper deals with the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam is assumed to be a Timoshenko beam with a concentrated mass taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and FEM is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, concentrated mass and rotary inertia of the beam is fully investigated.

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Effects of Slenderness Ratio on Dynamic Behavior of Cracked Beams Subjected to Subtangential Follower Force (경사종동력과 크랙을 가진 보의 진동특성에 미치는 세장비의 영향)

  • Son, In-Soo;Yoon, Han-Ik
    • Journal of the Korean Society for Precision Engineering
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    • v.26 no.9
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    • pp.112-120
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    • 2009
  • In this paper the purpose is to investigate the stability and variation of natural frequency of a cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the stability of a cantilever beam as the crack effect and slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. By using the results of this paper, we can obtain the judgment base that the choice of beam models for the effect of slenderness ratio and crack.

Stability Analysis of Beck's Column (Beck 기둥의 안정성 해석)

  • Lee, Byoung-Koo;Lee, Tae-Eun;Kang, Hee-Jong;Kim, Gwon-Sik
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11a
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    • pp.903-906
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    • 2005
  • The purpose of this paper is to investigate free vibrations and critical loads of the uniform Beck's columns with a tip spring, carrying a tip mass. The ordinary differential equation governing free vibrations of such Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the mass moment of inertia and spring parameter.

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Effect of an Intermediate Support on the Stability of Elastic Material Subjected to Dry Friction Force (건성마찰력을 받는 탄성재료의 안정성에 미치는 중간 지지의 효과)

  • 류시웅;장탁순
    • Journal of the Korean Society for Precision Engineering
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    • v.21 no.8
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    • pp.129-135
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    • 2004
  • This paper discussed on the effect of an intermediate support on the stability of elastic material subjected to dry friction force. It is assumed in this paper that the dry frictional force between a tool stand and an elastic material can be modeled as a distributed follower force. The elastic material on the friction material is modeled for simplicity into an elastic beam on Winkler-type elastic foundation. The stability of beams on the elastic foundation subjected to distributed follower force is formulated by using finite element method to have a standard eigenvalue problem. The first two eigen-frequencies are obtained to investigate the dynamics of the beam. The eigen-frequencies yield the stability bound and the corresponding unstable mode. The considered beams lose its stability by flutter or divergence, depending on the location of intermediate support.

Study on the Stability of Elastic Material Subjected to Dry Friction Force (건성마찰력을 받는 탄성재료의 안정성에 관한 연구)

  • Ko, Jun-Bin;Jang, Tag-Soon;Ryu, Si-Ung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.28 no.2
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    • pp.143-148
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    • 2004
  • This paper discussed on the stability of elastic material subjected to dry friction force for low boundary conditions: clamped free, clamped-simply supported, simply supported-simply supported, clamped-clamped. It is assumed in this paper that the dry frictional force between a tool stand and an elastic material can be modeled as a distributed follower force. The friction material is modeled for simplicity into a Winkler-type elastic foundation. The stability of beams on the elastic foundation subjected to distribute follower force is formulated by using finite element method to have a standard eigenvalue problem. It is found that the clamped-free beam loses its stability in the flutter type instability, the simply supported-simply supported beam loses its stability in the divergence type instability and the other two boundary conditions the beams lose their stability in the divergence-flutter type instability.

Structural Damping Effects on Stability of a Cantilever Column under Sub-tangentially Follower Force (종동력을 받는 외팔기둥의 동적 안정성에 미치는 구조감쇠 효과)

  • Min, Dong-Ju;Park, Jae-gyun;Kim, Moon-Young
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.26 no.6_spc
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    • pp.635-643
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    • 2016
  • A stability theory of a damped cantilever column under sub-tangential follower forces is first summarized based on the stability map. It is then demonstrated that internal and external damping can be exactly transformed to Rayleigh damping so that the damping coefficients can be effectively determined using proportional damping. Particularly a parametric study with variation of damping coefficients is performed in association with flutter loads of Beck's column and it is shown that two damping coefficients can be correctly estimated for real systems under the assumption of Rayleigh damping. Finally a frequency equation of a cantilever beam subjected to both a sub-tangentially follower force and two kinds of damping forces is presented in the closed-form and its stability maps are constructed and compared with FE solutions in the practical range of damping coefficients.