• Proceedings of the IEEK Conference
• /
• 2002.07b
• /
• pp.1216-1219
• /
• 2002

It is understood so far that the center of mass does not make any linear movement from the rotatory movement of a rigid body in the closed system. However, it has been found that the center of mass of the system could make a closed linear movement due to production of an instantaneous center of mass by the Coriolis force in the rotatory movement of a rigid body in the closed system. The nature of the closed linear movement in the non-inertial system and that of the open movement in the inertial system are different from each other. That is, the closed movement is described like the time integration of frictional forces, which is different from the open movement usually considered and described like the time integration of external forces. It is shown in this paper that the Coriolis forces, called a fictitious force in the classical mechanics, is similar to the frictional force so that it causes to move the center of mass of a closed system. In this paper, following an explanation of the closed linear movement of a non-inertial system and the open movement of an inertial system, the source of the closed linear movement phenomenon of a rotatory rigid body is presented.

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

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.17 no.5
• /
• pp.284-293
• /
• 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 of Mechanical Engineers
• /
• v.8 no.2
• /
• pp.119-126
• /
• 1984

An analysis is presented for the vibration and stability of Beck's column carring a tip mass at its free and subjected there to a follower compressive force by using variational approach. The influence of transverse shear deformation and rotatory inertial of the mass of the column upon the critical flutter load and frequency is considered, and Timoshenko's shear coefficient K' is calculated by Cowper's formulae. It is, moreover, worth noticing that the influence of inertial moment of tip mass upon the flutter load and frequency is investigated. The centroid of a tip mass is offset from the free end of the beam and located along its extended axis of the two cases, one of which has a tip mass increasing as .xi., the tip mass offset parameter, is augmented, the other has a tip mass constant but the inertial moment is variable according to a magnitude of .eta., the tip mass offset parament. This study reveals that the effects of inertial moment of a tip mass and larger value of P are specially remarkable even a tip mass is a same.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.42 no.1
• /
• pp.105-112
• /
• 2000

This paper deals with the free vibrations of columns immersed in fluid. The column model is based on the classical Bernoulli-euler theory which neblects the effects of rotatory inerital and shear deformation. The eccentricity and rotatory inertial of the concentrated mass at the top are taken into accuont. In the governing equation for the free vibration of column, thedensity of immersed part was midified to account for theadded fluid mass. The govering differential equations are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies and corresponding mode shapes are calculated over a range of non-dimensional system parameters ; the mas density ration of fluid to column, the ratio of fluid depth to span length, the ratio of tip mass to total column mass, the dimensionless mass moment of inertia, and the eccentricity.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.22 no.1
• /
• pp.9-17
• /
• 2021

Curved beams are increasingly used in buildings, vehicles, ships, and aircraft, which has resulted in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic circular arches has been the subject of a large number of investigations. One of the efficient procedures for the solution of ordinary differential equations or partial differential equations is the differential quadrature method DQM. This method has been applied to a large number of cases to overcome the difficulties of the complex computer algorithms, as well as excessive use of storage due to conditions of non-linear geometries, loadings, or material properties. This study uses DQM to analyze the in-plane vibration of the circular arches considering the effects of midsurface extension and rotatory inertia. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The solutions from DQM are compared with exact solutions or other numerical solutions for cases in which they are available and given to analyze the effects of midsurface extension and rotatory inertia on the frequency parameters of the circular arches.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.9 no.5
• /
• pp.606-612
• /
• 1985

On the stability of the Beck's column with a tip mass, the influence of the characteristics of the springs at the fixed end of the column are studied. The equations of motion and boundary conditions of this system are established by using the Hamiton's principle. On the evaluation of the stability of the column, t he effect of the shear deformation and rotatory inertial is considered in calculation. For the maintenance of the stability of the column, it is proved that the constant of the translational spring at the fixed end must be very large while th magnitude of the constant of the rotational spring at the fixed end has no effect. When the constants of the springs at the fixed end are small, it is also proved that the influence of the moment of inertial of the tip mass on the stability of the column are decreased and for the translational spring the degree of the decrease is more and more. Therefore it is found that the characteristics of the springs at the fixed end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.