• Title/Summary/Keyword: Flutter frequency

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Stability of beck's column with a rotatory spring restraining its free end (자유단이 회전스프링으로 구속된 Beck 기둥의 안정성)

  • Yun, Han-Ik;Im, Sun-Hong;Yu, Jin-Seok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.9
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    • pp.1385-1391
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    • 1997
  • An analysis is presented on the stability of an elastic cantilever column subjected to a concentrated follower force as to the influence of the elastic restraint and a tip mass at the free end. The elastic restraint is formed by the rotatory springs. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of the considered system.

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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    • 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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Influence of Elastic Restraint and Tip Mass at Free End on Stability of Leipholz's Column (Leipholz 기둥의 안정성에 미치는 자유단의 탄성구속과 말단질량의 영향)

  • 윤한익;박일주;김영수
    • Journal of KSNVE
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    • v.7 no.1
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    • pp.91-97
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    • 1997
  • An analysis is presented on the stability of an elastic cantilever column having the elastic restraints at its free end, carrying an added tip mass, and subjected to uniformly distributed follower forces. The elastic restraints are formed by both a translational spring and a rotatory spring. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of this elastic system. The added tip mass increases as a whole the critical flutter load of the elastic cantilever column, but the presence of its moment of inertia of mass has a destabilizing effect. The existence of the translational and rotatory springs at the free end increases the critical flutter load of the elastic cantilever column. Nevertheless, their effects on the critical flutter load are not uniform because of their coupling. The translational spring restraining the free end of the cantilever column decreases the critical flutter load by coupling with a large value of tip mass, while by coupling with the moment of inertia of tip pass its effect on the critical flutter load is contrary. The rotatory spring restraining the free end of the cantilever column increases the critical flutter load by coupling with the tip mass, but decreases it by coupling with the moment of inertia of the tip mass.

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Critical Loads of Tapered Beck's Columns with Clamped and Spring Supports (일단고정 타단스프링으로 지지된 변단면 Beck 기둥의 임계하중)

  • Kim Suk-Ki;Park Kwang-Kyou;Lee Byoung-Koo
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.19 no.1
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    • pp.85-92
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    • 2006
  • This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

Flutter analysis of long-span bridges using ANSYS

  • Hua, X.G.;Chen, Z.Q.;Ni, Y.Q.;Ko, J.M.
    • Wind and Structures
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    • v.10 no.1
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    • pp.61-82
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    • 2007
  • This paper presents a novel finite element (FE) model for analyzing coupled flutter of long-span bridges using the commercial FE package ANSYS. This model utilizes a specific user-defined element Matrix27 in ANSYS to model the aeroelastic forces acting on the bridge, wherein the stiffness and damping matrices are expressed in terms of the reduced wind velocity and flutter derivatives. Making use of this FE model, damped complex eigenvalue analysis is carried out to determine the complex eigenvalues, of which the real part is the logarithm decay rate and the imaginary part is the damped vibration frequency. The condition for onset of flutter instability becomes that, at a certain wind velocity, the structural system incorporating fictitious Matrix27 elements has a complex eigenvalue with zero or near-zero real part, with the imaginary part of this eigenvalue being the flutter frequency. Case studies are provided to validate the developed procedure as well as to demonstrate the flutter analysis of cable-supported bridges using ANSYS. The proposed method enables the bridge designers and engineering practitioners to analyze flutter instability by using the commercial FE package ANSYS.

Study of central buckle effects on flutter of long-span suspension bridges

  • Han, Yan;Li, Kai;Cai, C.S.
    • Wind and Structures
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    • v.31 no.5
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    • pp.403-418
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    • 2020
  • To investigate the effects of central buckles on the dynamic behavior and flutter stability of long-span suspension bridges, four different connection options between the main cable and the girder near the mid-span position of the Aizhai Bridge were studied. Based on the flutter derivatives obtained from wind tunnel tests, formulations of self-excited forces in the time domain were obtained using a nonlinear least square fitting method and a time-domain flutter analysis was realized. Subsequently, the influences of the central buckles on the critical flutter velocity, flutter frequency, and three-dimensional flutter states of the bridge were investigated. The results show that the central buckles can significantly increase the frequency of the longitudinal floating mode of the bridge and have greater influence on the frequencies of the asymmetric lateral bending mode and asymmetric torsion mode than on that of the symmetric ones. As such, the central buckles have small impact on the critical flutter velocity due to that the flutter mode of the Aizhai Bridge was essentially the symmetric torsion mode coupled with the symmetric vertical mode. However, the central buckles have certain impact on the flutter mode and the three-dimensional flutter states of the bridge. In addition, it is found that the phenomenon of complex beat vibrations (called intermittent flutter phenomenon) appeared in the flutter state of the bridge when the structural damping is 0 or very low.

Flutter Characteristics of a Morphing Flight Vehicle with Varying Inboard and Outboard Folding Angles

  • Shrestha, Pratik;Jeong, Min-Soo;Lee, In;Bae, Jae-Sung;Koo, Kyo-Nam
    • International Journal of Aeronautical and Space Sciences
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    • v.14 no.2
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    • pp.133-139
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    • 2013
  • Morphing aircraft capable of varying their wing form can operate efficiently at various flight conditions. However, radical morphing of the aircraft leads to increased structural complexities, resulting in occurrence of dynamic instabilities such as flutter, which can lead to catastrophic events. Therefore, it is of utmost importance to investigate and understand the changes in flutter characteristics of morphing wings, to ensure uncompromised safety and maximum reliability. In this paper, a study on the flutter characteristics of the folding wing type morphing concept is conducted, to examine the effect of changes in folding angles on the flutter speed and flutter frequency. The subsonic aerodynamic theory Doublet Lattice Method (DLM) and p-k method are used, to perform the flutter analysis in MSC.NASTRAN. The present baseline flutter characteristics correspond well with the results from previous study. Furthermore, enhancement of the flutter characteristics of an aluminum folding wing is proposed, by varying the outboard wing folding angle independently of the inboard wing folding angle. It is clearly found that the flutter characteristics are strongly influenced by changes in the inboard/outboard folding angles, and significant improvement in the flutter characteristics of a folding wing can be achieved, by varying its outboard wing folding angle.

Stability Analysis of Beck's Column with a Tip Mass Restrained by a Spring (스프링으로 지지된 자유단에 집중질량을 갖는 Beck 기둥의 안정성 해석)

  • Li, Guangfan;Oh, Sang-Jin;Kim, Gwon-Sik;Lee, Byoung-Koo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.11
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    • pp.1287-1294
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    • 2005
  • The purpose of this paper is to investigate free vibrations and critical loads of the Beck's columns with a tip spring, which carry a tip mass. The ordinary differential equation governing free vibrations of 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 corves 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 subtangential parameter, mass ratio and spring parameter.

Aerodynamic flutter analysis of a new suspension bridge with double main spans

  • Zhang, W.M.;Ge, Y.J.;Levitan, M.L.
    • Wind and Structures
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    • v.14 no.3
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    • pp.187-208
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    • 2011
  • Based on the ANSYS, an approach of full-mode aerodynamic flutter analysis for long-span suspension bridges has been presented in this paper, in which the nonlinearities of structure, aerostatic and aerodynamic force due to the deformation under the static wind loading are fully considered. Aerostatic analysis is conducted to predict the equilibrium position of a bridge structure in the beginning, and then flutter analysis of such a deformed bridge structure is performed. A corresponding computer program is developed and used to predict the critical flutter wind velocity and the corresponding flutter frequency of a long-span suspension bridge with double main span. A time-domain analysis of the bridge is also carried out to verify the frequency-domain computational results and the effectiveness of the approach proposed in this paper. Then, the nonlinear effects on aerodynamic behaviors due to aerostatic action are discussed in detail. Finally, the results are compared with those of traditional suspension bridges with single main span. The results show that the aerostatic action has an important influence on the flutter stability of long-span suspension bridges. As for a suspension bridge with double main spans, the flutter mode is the first anti-symmetrical torsional vibration mode, which is also the first torsional vibration mode in natural mode list. Furthermore, a double main-span suspension bridge is better in structural dynamic and aerodynamic performances than a corresponding single main-span structure with the same bridging capacity.

Approximation of Distributed Aerodynamic Force to a Few Concentrated Forces for Studying Supersonic Panel Flutter (초고속 패널 플러터 연구를 위한 분포 공기력의 집중하중 근사화)

  • Dhital, Kailash;Han, Jae-Hung;Lee, Yoon-Kyu
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.26 no.5
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    • pp.518-527
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    • 2016
  • The present study considers the usage of concentrated forces to simulate real panel flutter. The concept of using concentrated forces have been validated for studying the flutter of wing structure in subsonic flow, yet its application in the supersonic region remained to be explored. Hence, a simply supported panel subjected to forces, equivalent to aerodynamic force is considered for studying supersonic panel flutter. The distributed aerodynamic forces are approximated to few concentrated forces by taking numerical integration. The aeroelastic equation is formulated using the classical small-deflection theory and the piston theory for linear panel flutter whereas for emulated panel flutter the flutter equation is derived by replacing the pressure due to aerodynamic loading with pressure from concentrated loading. Finally, flutter frequency, flutter dynamic pressure, and corresponding mode shape are found for emulated panel flutter and compared with linear panel flutter. Two important parameters, the number of concentrated forces and their location are discussed through numerical examples and optimization process respectively. So far, the flutter results acquired in this study are reasonable to suggest the feasibility of reproducing panel flutter using concentrated forces.