• The Journal of the Acoustical Society of Korea
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• 제18권4E호
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• pp.20-25
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• 1999

To get accurate natural frequencies of an engine crankshafts, finite element equations of motion are developed, taking real geometries of the shaft into account. For the crankshaft with wide crank webs, a specialized rotating web element is developed. This includes the effects of rotary inertia, gyroscopic moment, and shear. After the finite element equations are constructed, eigenvalues are extracted from the system equations to get natural frequencies, based on the Sturm sequence method which exploits the banded forms of the system matrices to reduce computations. The scheme developed can be used for the free vibration analysis of any type of spinning structures which include skew symmetric gyroscopic moment matrix in the system matrices. The results are compared with experimental data in order to confirm the study.

• Advances in nano research
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• 제8권3호
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• pp.245-254
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• 2020

This work examines the fundamental vibrational characteristics of a spinning CNT-based nano-rotor assuming a nonlocal elasticity Euler-Bernoulli beam theory. The rotary inertia, gyroscopic, and rotor mass unbalance effects are all taken into consideration in the beam model. Assuming a nonlocal theory, two coupled 6th-order partial differential equations governing the vibration of the rotating SWCNT are first derived. In order to acquire the natural frequencies and dynamic response of the nano-rotor system, the nonlinear equations of motion are numerically solved. The nano-rotor system frequency spectrum is shown to exhibit two distinct frequencies: one positive and one negative. The positive frequency is known as to represent the forward whirling mode, whereas the negative characterizes the backward mode. First, the results obtained within the framework of this numerical study are compared with few existing data (i.e., molecular dynamics) and showed an overall acceptable agreement. Then, a thorough and detailed parametric study is carried out to study the effect of several parameters on the nano-rotor frequencies such as: the nanotube radius, the input angular velocity and the small scale parameters. It is shown that the vibration characteristics of a spinning SWCNT are significantly influenced when these parameters are changed.

• The Journal of the Acoustical Society of Korea
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• 제15권4E호
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• pp.37-44
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• 1996

To get accurate vibration analysis of rotor-bearing systems, finite element models of high speed rotating shaft, unbalance disk, and fluid film journal bearing are developed. The study includes the effects of rotary inertia, gyroscopic moment, damping, shear deformation, and axial torque in the same model. It does not include the axial force effect, but the extension is straighforward. The finite elements developed can be used in the analysis design of any type of multiple rotor bearing system. To show the accuracy of the models, numerical examples are demonstrated.

• 소음진동
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• 제8권1호
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• pp.99-111
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• 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.

• 한국정밀공학회지
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• 제14권12호
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• pp.166-173
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• 1997

Influence coefficients on two-plane flexible rotor balancing model are derived by using the transfer matrix method. The model has a rigid uniform cylinder at mid-span of flexible shafts. Both faces of the rigid cylinder are used as the balancing planes. Calculated influence coefficients show that there exist the rotating speed ranges which are useless or insensitive for the balancing. Gyroscopic effect and damping are considered in the study and their effects are discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.842-848
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• 2013

Developments of Solid-State Gyroscopy during last decades are impressive and were based on thin-walled shell resonators like HRG or CRG made from fused quartz or leuko-sapphire. However, a number of design choices for inertial-grade gyroscopes, which can be used for high-g applications and for mass- or middle-scale production, is still very limited. So, considerations of fundamental physical effects in solids that can be used for development of a miniature, completely solid-state, and lower-cost sensor look urgent. There is a variety of different types of bulk acoustic (elastic) waves (BAW) in anisotropic solids. Shear waves with different variants of their polarization have to be studied especially carefully, because shear sounds in glasses and crystals are sensitive to a turn of the solid as a whole, and, so, they can be used for development of gyroscopic sensors. For an isotropic medium (for a glass or a fine polycrystalline body), classic Lame's theorem (so-called, a general solution of Elasticity Theory or Green-Lame's representation) has been modified for enough general case: an elastic medium rotated about an arbitrary set of axes. Travelling, standing, and mixed shear waves propagating in an infinite isotopic medium (or between a pair of parallel reflecting surfaces) have been considered too. An analogy with classic Foucault's pendulum has been underlined for the effect of a turn of a polarizational plane (i.e., an integration effect for an input angular rate) due to a medium's turn about the axis of the wave propagation. These cases demonstrate a whole-angle regime of gyroscopic operation. Single-crystals are anisotropic media, and, therefore, to reflect influence of the crystal's rotation, classic Christoffel-Green's tensors have been modified. Cases of acoustic axes corresponding to equal velocities for a pair of the pure-transverse (shear) waves have of an evident applied interest. For such a special direction in a crystal, different polarizations of waves are possible, and the gyroscopic effect of "polarizational precession" can be observed like for a glass. Naturally, formation of a wave pattern in a massive elastic body is much more complex due to reflections from its boundaries. Some of these complexities can be eliminated. However, a non-homogeneity has a fundamental nature for any amorphous medium due to its thermodynamically-unstable micro-structure, having fluctuations of the rapidly-frozen liquid. For single-crystalline structures, blockness (walls of dislocations) plays a similar role. Physical nature and kinematic particularities of several typical "drifts" in polarizational BAW gyros (P-BAW) have been considered briefly too. They include irregular precessions ("polarizational beats") due to: non-homogeneity of mass density and elastic moduli, dissymmetry of intrinsic losses, and an angular mismatch between propagation and acoustic axes.

• 소음진동
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• 제8권3호
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• pp.477-484
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• 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.

• 한국정밀공학회지
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• 제19권10호
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• pp.37-44
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• 2002

The dynamic behavior of rotor-bearing system has been investigated using finite element method. A procedure is presented for dynamic modeling of rotor-bearing system which consists of shaft elements, rigid disk, flexible bearing and support structure. A finite element model including the effects of rotary inertia, shear deformation, gyroscopic moments is developed. Linear stiffness and damping coefficients are calculated for 2 lobe sleeve bearing. The whirl frequency, mode shape, stability and unbalance response of rotor system including effects of bearing coefficient and support structures are calculated.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.902-909
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• 2006

In this study, three-dimensional rotordynamic analyses have been conducted using equivalent beam, hybrid and fun three-dimensional models. The Present computational method is based on the general finite element method with rotating gyroscopic effects of a rotor system. General purpose commercial finite element code, SAMCEF which includes practical rotordynamics module with various types of rotor analysis methods and bearing elements is applied. For the purpose of numerical verification, comparison study for a benchmark rotor model with support bearings is performed first. Detailed finite element models based on three different modeling concepts are constructed and then computational analyses are conducted for the realistic and complex three-dimensional rotor system. The results for rotor stability and mass unbalance response are presented and compared with the experimental vibration test conducted in this study.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1997년도 추계학술대회논문집; 한국과학기술회관; 6 Nov. 1997
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• pp.101-109
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• 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.