• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.703-708
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• 2006

In this paper a dynamic behavior(natural frequency) of a cracked simply supported pipe conveying fluid is presented. In addition, an analysis of the buckling instability of a cracked pipe conveying fluid subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. TI1e crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.254-257
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• 2006

In this paper a dynamic behavior(natural frequency) of a cracked cantilever and simply supported pipe conveying fluid is presented. In addition, an analysis of the flutter and buckling instability of a cracked pipe conveying fluid subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. 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.

• Smart Structures and Systems
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• v.16 no.3
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• pp.401-414
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• 2015

A developed hybrid method for crack identification of beams is presented. Based on the Euler-Bernouli beam theory and concepts of fracture mechanics, governing equation of the cracked beams is reformulated. Finite element (FE) method as a powerful numerical tool is used to discritize the equation in space domain. After transferring the equations from time domain to frequency domain, frequencies and mode shapes of the beam are obtained. Efficiency of the governed equation for free vibration analysis of the beams is shown by comparing the results with those available in literature and via ANSYS software. The used equation yields to move the influence of cracks from the stiffness matrix to the mass matrix. For crack identification measured data are produced by applying random error to the calculated frequencies and mode shapes. An objective function is prepared as root mean square error between measured and calculated data. To minimize the function, hybrid genetic algorithms (GAs) and particle swarm optimization (PSO) technique is introduced. Efficiency, Robustness, applicability and usefulness of the mixed optimization numerical tool in conjunction with the finite element method for identification of cracks locations and depths are shown via solving different examples.

• 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.

• Structural Engineering and Mechanics
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• v.54 no.5
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• pp.987-998
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• 2015

In this paper, free vibrations of a clamped-clamped double-walled carbon nanotube (DWNT) under axial force is studied. By utilizing Euler-Bernoulli beam theory, each layer of DWNT is modeled as a beam. In this analysis, nonlinear form of interlayer van der Waals (vdW) forces and nonlinearities aroused from mid-plane stretching are also considered in the equations of motion. Further, direct application of multiple scales perturbation method is utilized to solve the obtained equations and to analyze free vibrations of the DWNT. Therefore, analytical expressions are found for vibrations of each layer. Linear and nonlinear natural frequencies of the system and vibration amplitude ratios of inner to outer layers are also obtained. Finally, the results are compared with the results obtained by Galerkin method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.419-426
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• 2004

In this paper, studied about the effect of open crack and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass, 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 crack section is represented by a local flexibility matrix connecting two undamaged beam segments. Therefore, the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow is increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The position of the crack is located in the middle point of the pipe, the mid-span deflection of simply supported pipe presents maximum deflection.