• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.301-308
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• 1998

This paper deals with the influence of elastic foundations on natural frequencies of curved beams. Taking into account the effects of rotatoy inertia and shear deformation, the differential equations governing free, out-of-plane vibrations of circular curved beams resting on Winkler-type foundations are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The lowest three natural frequencies are claculated over a range of non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation. The effects of rotatory inertia and shear deformation are also analyzed.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.49-58
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• 1998

On the stability of the Timoshenko cantilever column subjected of a compressive follower force, the influences of the moment of inertia of the tip mass at the free end and the characteristics of a translational spring at the free end of the column are studied. The equations of motion and boundary conditions of system are estabilished by using the d'Alembert virtual work of principle. On the evaluation of stability of the column, the effect of the shear deformation and rotatory inertia is considered in calculation. The moment of inertia of the tip mass at the free end of the column is changed by adjusting the distance c, from the free end of the column to the tip mass center. The free end of the column is supported elastically by a translational spring. For the maintenance of the good stability of the column, it is also proved that the constant of the translational spring at the free end must be very large for the case without a tip mass while it must be small for the case with a tip mass. Therefore, it is found that the shape of the tip mass and the characteristic of the spring at the free end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.185-194
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the rectangular cross section whose depth is constant but breadth is varied with the parabolic function. The fourth order ordinary differential equation with respect the vertical deflection governing free vibrations of such beam is derived based on the Timoshenko beam theory. This governing equation is solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.5
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• pp.284-293
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• 2016

One of the most efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method (DQM) has been applied to a large number of cases to overcome the difficulties of complex algorithms of computer programming, as well as the excessive use of storage due to the conditions of complex geometry and loading. The in-plane vibrations of curved beams with extensibility of the arch axis, including the effects of rotatory inertial and shear deformation, are analyzed by the DQM. The fundamental frequencies are calculated for members with various slenderness ratios, shearing flexibilities, boundary conditions, and opening angles. The results are compared with the numerical results obtained by other methods for cases in which they are available. The DQM gives good mathematical precision even when only a limited number of grid points is used, and new results according to diverse variations are also suggested.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.6
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• pp.574-580
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• 2013

At high frequencies, the statistical approach such as statistical energy analysis(SEA) and energy flow analysis(EFA) has been applied for estimation of vibroacoustic responses of various built-up structures. The energy coupling relationship between finite coupled structures is required to estimate vibrational energetics of built-up structures. Mindlin plate theory includes the rotatory inertia and shear deformation effects which are dominant as frequency increases. In this paper, the wave transmission analysis is successfully performed for EFA of co-planar coupled Mindlin plates.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.131-152
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• 2012

In-plane free vibrations of circular beams with stepped cross-sections are investigated by using the exact analytical solution. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The stepped arch is divided into a number of arches with constant cross-sections. The exact solution of the governing equations is obtained by the initial value method. Several examples of arches with different step ratios, different locations of the steps, boundary conditions, opening angles and slenderness ratios for the first few modes are presented to illustrate the validity and accuracy of the method. The effects of the geometric parameters on the natural frequencies are investigated in details. Several examples in the literature are solved and the results are given in tables. The agreement of the results is good for all examples considered. The mode transition phenomenon is also observed for the stepped arches. Some examples are solved also numerically by using the commercial finite element program ANSYS.

• Journal of Advanced Marine Engineering and Technology
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• v.10 no.4
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• pp.31-40
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• 1986

With the tendency toward high speed and high pressure in centrifugal pumps, the problem of sub-synchronous vibration has arisen, caused by the hydraulic forces of the working fluid, such as wearring, balance piston, impeller, etc.. These forces can drastically alter the rotor critical speeds and stability characteristics, and can be acted significant destabilizing forces. For preventing such self-excited vibration, the desing of the rotor system needs, which would secure the stability of the machine. In this paper, a procedure is presented for dynamic modeling of rotor-bearing-seal-impeller systems which consist of rigid disks, distributed parameter finite rotor elements and discrete bearings, seals and impellers. A finite element model including the effects of rotatory inertia and gyroscopic moments is developed using the consistent matrix approach. The technique of dynamic matrix reduction is applied to the shaft matrices to reduce them to a set of matrices of dynamic of significantly fewer degrees of freedom. The representation of bearing, seal and impeller elements is in term of linearized stiffness and damping matrices by reasonably small perturbations from equilibrium. The stability behavior of a typical double suction centrifugal pump is presented. Results show the influence of clearance and flow conditions on running speeds and stability characteristics.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.4
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• pp.118-123
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• 1997

The study suggests a method to analyze the vibration of the multi-stepped beam having the different circular cross-sections. The rotatory inertia, the shear deformation and the torque applied at both ends of the beam are considered in the governing equation. The complex displacement and the variable separation are introduced to derive the solution of the equation of each uniform beam element having constant cross-section. Then boundary conditions are applied to solve the total system. This method uses the mathematically exact solutions unlike numerical method such as the finite element method in solving the problem having the simultaneous differential equations of Timoshenko beam theory. the natural frequencies and the corresponding mode shapes are precise, especially the mode shapes are continuous.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.101-107
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• 2001

This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.965-970
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• 2002

The purpose of this paper is to investigate the free vibration characteristics 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 four natural frequencies are calculated over a wide range of section ratio, dimensionless spring constant and mass ratio.