• Journal of KSNVE
• /
• v.8 no.1
• /
• pp.99-111
• /
• 1998

An analytical method using the substructure synthesis and assumed modes method is developed to investigate the effect of flexibility of bladed disk assembly on vibrational modes of flexible rotor system. In modeling the system, Coriolis forces, gyroscopic moments, and centrifugal stiffening effects are taken into account. Then the coupled vibrations between the shaft and bladed disk are extensively investigated using simplistic models, as the shaft rotational speed and the pretwist and stagger angles of blade are varied.

• Journal of KSNVE
• /
• v.8 no.3
• /
• pp.477-484
• /
• 1998

An analytical procedure on the base of the substructure synthesis and assumed modes method is developed to investigate the flexibility effect of bladed disk assembly on vibrational modes of flexible rotor system. In modeling the system, Coriolis forces, gyroscopic moments, and centrifugal stiffening effects are taken into account. The coupled vibrations between the shaft and bladed disk are then extensively investigated through the numerical simulation of simplified models, with varying the shaft rotational speed and the prewist and stagger angles of the blade. It is found that the Coriolis and inertia forces and the inertia torque, which are induced by the one nodal diameter modes of the bladed disk and vary depending upon the stagger and prewist angles, lead to the coupled motions of the shaft and the bladed disk.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.10a
• /
• pp.101-109
• /
• 1997

An analytical procedure on the base of the substructure synthesis and assumed modes method is developed to investigate the flexibility effect of bladed disk assembly on vibrational modes of flexible rotor system. In modeling the system, Coriolis forces, gyroscopic moments, and centrifugal stiffening effects are taken into account. The coupled vibrations between the shaft and bladed disk are then extensively investigated through the numerical simulation of simplified models, with varying the shaft rotational speed and the pretwist and stagger angles of the blade. It is found that the Coriolis and inertia forces and the inertia torque, which are induced by the one nodal diameter modes of the bladed disk and vary depending upon the stagger and pretwist angles, lead to the coupled motions of the shaft and the bladed disk.

• Journal of Educational Research in Mathematics
• /
• v.14 no.1
• /
• pp.111-127
• /
• 2004

In this note we examined some terms, parallel lines and angles in elementary school mathematics and middle school mathematics respectively. Since some terms are represented early in elementary school mathematics and not repeated after, some students are not easy to apply the terms to their lesson. Also, since the relation between parallel lines and angles are treated intuitively in 7-th grade, applying the relation for a proof in 8-th grade would be meaningless. For the variety of mathematics education, it is desirable that the relation between parallel lines and angles are treated as postulate. Also, for out standing students, it is desirable that we use deductive reasoning to prove the relation between parallel lines and angles as a theorem. In particular, the treatments of vertical angles and the relation between parallel lines and angles in 7-th grade text books must be reconsidered. Proof is very important in mathematics, and the deductive reasoning is necessary for proof. It would be efficient if some properties such as congruence of vertical angles and the relation between parallel lines and angles are dealt in 8-th grade for proof.