• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.244-251
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• 2002

The purpose of this paper is to investigate the stability of tapered columns with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The column 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 columns subjected to a subtangential follower force is solved numerically using the corresponding boundary conditions. And the bisection method is used to calculate the critical divergence/flutter load. After having verified the results of the present study, the frequency and critical divergence/flutter load are presented as functions of various nondimensional system parameters.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.1
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• pp.140-147
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• 2007

Whenever the hinge axis of aircraft wing rotates, its stiffness varies. Also, there are nonlinearities in the connection of the actuator and the hinge axis, and it is necessary to inspect the coupled effects between the actuator dynamics and the hinge nonlinearity. Nonlinear aeroelastic characteristics are investigated by using the iterative V-g method. Time domain analyses are also performed by using Karpel's minimum state approximation technique. The doublet hybrid method(DHM) is used to calculate the unsteady aerodynamic forces in subsonic regions. Structural nonlinearity located in the load links of the actuator is assumed to be friction. The friction nonlinearity of an actuator is identified by using the describing function technique. The nonlinear flutter analyses have shown that the flutter characteristics significantly depends on the structural nonlinearity as well as the dynamic stiffness of an actuator. Therefore, the dynamic stiffness of an actuator as well as the nonlinear effect of hinge axis are important factors to determine the flutter stability.

• 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.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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• pp.1355-1360
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• 2006

This paper presents the dynamic stability of a cantilevered Timoshenko beam with a concentrated mass, partially attached to elastic foundations, and subjected to a follower force. Governing equations are derived from the extended Hamilton's principle, and FEM is applied to solve the discretized equation. The influence of some parameters such as the elastic foundation parameter, the positions of partial elastic foundations, shear deformations, the rotary inertia of the beam, and the mass and the rotary inertia of the concentrated mass on the critical flutter load is investigated. Finally, the optimal attachment ratio of partial elastic foundation that maximizes the critical flutter load is presented.

• 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.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.195-217
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• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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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.

• Journal of Korean Society of Steel Construction
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• v.17 no.6 s.79
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• pp.699-705
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• 2005

This paper investigates critical loads of tapered cantilever columns with a tip mass, subjected to a follower force. The linearly tapered solid rectangular cross-sections are adopted as the column taper. The differential equation governing free vibrations of such columns, also called Beck's columns, is derived using the Bernoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters, namely, the taper type, the subtangential parameter, and the mass ratio.

• Journal of the Korea Institute of Military Science and Technology
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• v.16 no.4
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• pp.486-492
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• 2013

The pivoting composite wing is developed for the kit to be mounted on the external stores. The wing has a pivoting structure for the installation to an aircraft and high aspect ratio to increase lift drag ratio. The wing needs to be light and have sufficient strength and stiffness to satisfy structural design requirements. The wing is designed with carbon fiber composite and the structural parts are integrated to reduce cost to manufacture. In order to verify the structural performances, the design load analysis and flight load survey, the static analysis and test, the ground vibration test and flutter analysis are performed. It is shown that the wing has sufficient structural strength and stiffness to satisfy the structural design requirements.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.1-12
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• 2005

For a shear-deformable beam-column element subjected io non-conservative forces, equations of motion and a finite element formulation are presented applying extended Hamilton's principle. The influence of non-conservative force's direction parameter, internal and external damping forces, and shear deformation and rotary inertia effects on divergence and flutter loads of Beck's columns are intensively investigated based on element stiffness, damping and mass matrixes derived for the non-conservative system.