• Interaction and multiscale mechanics
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• v.6 no.4
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• pp.357-375
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• 2013

In this paper, the forced vibration problem of an Euler-Bernoulli beam that is joined with a semi-infinite field of a compressible fluid is considered as a boundary value problem (BVP). This BVP includes two partial differential equations (PDE) and some boundary conditions (BC), which are introduced comprehensively. After that, the closed-form solution of this fluid-structure interaction problem is obtained in the frequency domain. Some mathematical techniques are utilized, and two unknown functions of the BVP, including the beam displacement at each section and the fluid dynamic pressure at all points, are attained. These functions are expressed as an infinite series and evaluated quantitatively for a real example in the results section. In addition, finite element analysis is carried out for comparison.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.3
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• pp.49-55
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• 2010

In this paper, the stability of cracked cantilever T-beams subjected to subtangential follower force is investigated. Also, the effect of subtangential coefficient and crack on the natural frequency of T-beams is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The values of critical follower force and the stability maps of cantilever T-beams are obtained according to the subtangential coefficient and crack severity. The results of this study will contribute to the safety testing and the stability estimation of cracked T-beams subjected to follower force.

• Coupled systems mechanics
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• v.6 no.2
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• pp.175-187
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• 2017

This paper deals with a uniform cantilever Euler-Bernoulli beam subjected to follower and transversal force at its free end as a model for a pipe conveying fluid under electromagnetic damper force. The electromagnetic damper is composed of a permanent-magnet DC motor, a ball screw and a nut. The main objective of the current work is to reduce the pipe vibration resulting from the fluid velocity and allow it to transform into electric energy. To pursue this goal, the stability and vibration of the beam model was studied using Ritz and Newmark methods. It was observed that increasing the fluid velocity results in a decrease in the motion of the free end of the pipe. The results of simulation showed that the designed semiactive electromagnetic damper controlled by on-off damping control strategy decreased the vibration amplitude of the pipe about 5.9% and regenerated energy nearly 1.9 (mJ/s). It was also revealed that the designed semi-active electromagnetic damper has better performance and more energy regeneration than the passive electromagnetic damper.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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• pp.483-491
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• 2005

In this paper a dynamic behavior of a double-cracked cantilever pipe with the tip mass and a moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, the tip mass and double cracks have been studied on the dynamic behavior of a cantilever pipe system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. Therefore, the cracks are modelled as a rotational spring. This matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. We investigated about the effect of the two cracks and a tip mass on the dynamic behavior of a cantilever pipe with a moving mass.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.553-561
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• 2011

A theoretical approach is carried out to predict the quality factors of flexible modes of a microcantilever on a squeeze-film. The frequency response function of an inertially-excited microcantilever beam is derived using an Euler-Bernoulli beam theory. The external force due to squeeze-film phenomenon is developed from the Reynolds equation. Slip boundary conditions are employed at the interfaces between the fluid and the structure to consider the gas rarefaction effect, and pressure boundary condition at both ends of fluid analysis region is enhanced to increase the exactness of predicted quality factors. To the end, an approximate equation is derived for the first bending mode of the microcantilever. Using the approximate equation, the quality factors of the second and third bending modes are calculated and compared with experimental results of previously reported work. The comparison shows the feasibility of the current approach.

• Journal of the korean Society of Automotive Engineers
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• v.8 no.4
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• pp.66-72
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• 1986

Numerical analysis has been made on the dynamic behavior of a supporting structure subjected to a force of time dependent frequency. The effect of solid viscosity is studied when the frequency of external force passes through the first critical frequency of the simple beam for four times. Within the Euler-Bernoulli beam theory, the solutions are obtained by using finite Fourier and Laplace transformation methods with respect to space and time variables. The result shows that the maximum value of the dynamic deflection is considerably affected by the value of the solid viscosity as well as the frequency difference The maximum dynamic deflection is found to occur in the frequency lower limit C of 0.85-0.985 in the presence of the solid viscosity.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.493-500
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• 2001

The purpose of this paper is to investigate the natural frequencies and mode shapes 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 three natural frequencies and the corresponding mode shapes are calculated over a wide range of section ratio, dimensionless spring constant, and mass ratio.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.225-230
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• 1999

The purpose of this paper is to investigate the natural frequencies and mode shape of columns immersed in fluid. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertial and shear deformation. The eccentricity and rotatory inerital of the tip mass are taken into account . The governing differential equations forr the free vibrations of immersed columns are solved numerically using the corresponding boundary conditoins. The lowest four natural frequencies and corresponding mode shapes are calculated over a range of non-dimensional system parameters : the ratio of fluid depth to span length, the mass ratio, the dimensionless mass moment of inertial, and the eccentricity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.689-694
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results in higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The time which produce the maximum dynamic deflection of the simply supported pipe is delayed according to the increment of the crack severity.