• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.189-200
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• 2001

This paper presents an experimental modal analysis of perforated rectangular plates in air or in contact with water. The penetration of holes in the plates had a triangular pattern with P/D (pitch to diameter) 2.125, 2.500, 3.000 and 3.750. The plate was clamped along the plate edges by a number of bolts and nuts. The natural frequencies of the perforated plates in air were obtained by the analytical method based on the relation between the reference kinetic and maximum potential energies and compared with the experimental results. Good agreement between the results was found for the natural frequencies of the perforated plates in air. Additionally, it was empirically found that the natural frequencies of the perforated plate in air increase with an increase of P/D, on the other hand, the natural frequencies of the perforated plate in contact with water decrease with an increase of P/D.

• Journal of Ocean Engineering and Technology
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• v.6 no.1
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• pp.69-77
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• 1992

The natural frequencies of a beam on elastic foundation are investigated in the present paper. The inhomogeneous elastic foundation can be modelled as a combination of distributed translational spring, rotational spring, intermediate supports and dampers. The natural frequencies and mode shapes of the system are obtained by using the Galerkin's method, and also compared with the results in the literature. Furthermore, the natural frequencies of the beam with elastically mounted masses, which can be used as vibration absorbers, are obtained by an efficient numerical scheme suggested in the present paper.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.95-100
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• 2006

Tolerance analysis method for natural frequencies of multi-body systems having a equilibrium position is suggested in this paper. To perform the tolerance analysis, the Monte-Carlo Method is conventionally employed. However, the Monte-Carlo Method has some weakness; spending too much time for analysis and having a low accuracy and hard to converge in the numerical unstable area. To resolve these problems, a tolerance analysis method is suggested in this paper. Sensitivity equations of natural frequencies are derived at the equilibrium position. By employing the sensitivity information of mass, damping and stiffness matrices, the sensitivity of natural frequencies can be calculated.

• Steel and Composite Structures
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• v.2 no.3
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• pp.223-236
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• 2002

An analytical procedure based on the transfer matrix method to estimate not only the natural frequencies but also vibration mode shapes of the thin-walled members composed of interconnected cylindrical shell panels is presented. The transfer matrix is derived from the differential equations for the cylindrical shell panels. The point matrix relating the state vectors between consecutive shell panels are used to allow the transfer procedures over the cross section of the members. As a result, the interactions between the shell panels of the cross sections of the members can be considered. Although the transfer matrix method is naturally a solution procedure for the one-dimensional problems, this method is well applied to thin-walled members by introducing the trigonometric series into the governing equations of the problem. The natural frequencies and vibration mode shapes of the thin-walled members composed of number of interconnected cylindrical shell panels are observed in this analysis. In addition, the effects of the number of shell panels on the natural frequencies and vibration mode shapes are also examined.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.746-751
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• 2003

When a cantilever beam rotates about the axis perpendicular to its longitudinal axis, its natural frequencies vary. This phenomenon which is caused by centrifugal inertia forces is often referred to as the stiffening effects. Since the variation of natural frequencies often creates critical problems for the rotating structures, it is necessary to control the variation of natural frequencies. As the cross section of a rotating cantilever beam varies, natural frequencies can be changed. The thickness and the width of the cantilever beam are assumed to be cubic spline functions in the present work. An optimization method is employed to find the optimal thickness and width of the rotating beam. This result can be used for the design of rotating structures such as turbine and helicopter blades.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1 s.118
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• pp.65-71
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• 2007

Tolerance analysis method for natural frequencies of multi-body systems having a equilibrium position is suggested in this paper. To perform the tolerance analysis, the Monte-Carlo Method is conventionally employed. However, the Monte-Carlo Method has some weakness; spending too much time for analysis and having a low accuracy and hard to converge in the dynamical unstable area. To resolve these problems, a tolerance analysis method is suggested in this paper. Sensitivity equations of natural frequencies are derived at the equilibrium position. By employing the sensitivity information of mass, damping and stiffness matrices, the sensitivity of natural frequencies can be calculated.

• Steel and Composite Structures
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• v.32 no.3
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• pp.305-312
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• 2019

In this study, we investigated the effect of fatigue crack propagation of the beams which have a vital importance in engineering applications, on the natural frequency of the system. Beams which have a wide range of applications, are used as fundamental structural elements in engineering structures. Therefore, early detection of any damages in these structures is of vital importance for the prevention of possible destructive damages. One of the widely used methods of early detection of damages is the vibration analysis of the structure. Hence, it is of vital importance to detect and monitor any changes in the natural frequencies of the structure. From this standpoint, in this study we experimentally investigated the effect of fatigue crack propagation on beams produced from 4140 steel, of the natural frequency of the beam. A crack was opened on the $8{\times}16{\times}500mm$ beam using a 3 mm long and 0.25 mm wide wire erosion. The beam, then, underwent 3 point bending tests at 10 Hz with a dynamic fatigue device and its natural frequencies were measured in scheduled intervals and any changes taking place on the natural frequencies of the beam were measured. This data allowed us to identify and measure the crack occurring on the beam subjected to dynamic loading, during the propagation phase. This method produced experimental data. The experimental data showed that the natural frequency of the beam decreased with the propagation of the fatigue crack on the beam.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Journal of the korean Society of Automotive Engineers
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• v.8 no.2
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• pp.51-64
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• 1986

There has been considerable interest over the last twenty years in the subject of the elastic properties of the cord-rubber laminate. This has been due to the rather intensive study of the composites materials characteristics brought about by the increased use of rigid composites materials characteristics brought about by the increased use of rigid composites in many structural applications. The object of this study is to obtain the natural frequencies and modes of the simply supported cord-rubber laminate plates prior to the study on the analysis of the dynamic properties of the pneumatic tire. To obtain these natural frequencies and modes, the 12 degrees of freedom orthotropic rectangular plate finite elements are developed. By using classical lamination theory, the stress-strain relations are represented. The governing equation for the finite element is derived by energy method. To find the natural frequencies and modes, he eigenvalues and corresponding eigenvectors are computed by the well known Jacobi power method. In order to verify the capability of this present finite element, the results of the specially orthotropic plate and the angle-ply laminate plate are compared with the analytical solution. The analytical and numberical results are in good agreement. The following problems of the simply supported plate are analyzed by the present finite element. a) the natural frequencies and mode shapes of the cord-rubber laminate plate for various aspect ratio. b) The natural frequencies and mode shapes of the orthotropic plate with the rectangular hole in its center.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.877-895
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• 2016

This paper is concerned with the analytical derivation of natural sloshing frequencies of liquid in annular cylindrical tank and its verification by experiment. The whole liquid domain is divided into three simple sub-regions, and the region-wise linearized velocity potentials are derived by the separation of variables. Two sets of matrix equations for solving the natural sloshing frequencies are derived by enforcing the boundary conditions and the continuity conditions at the interfaces between sub-regions. In addition, the natural sloshing frequencies are measured by experiment and the numerical accuracy of the proposed analytical method is verified through the comparison between the analytical and experimental results. It is confirmed that the present analytical method provides the fundamental sloshing frequencies which are in an excellent agreement with the experiment. As well, the effects of the tank radial gap, the bottom flow gap and the liquid fill height on the fundamental sloshing frequency are parametrically investigated.