• Title, Summary, Keyword: Linear Vibration Analysis

### Static equilibrium and linear vibration analysis of a high speed electric train system (고속전철 시스템의 정적평형 및 선형진동 해석)

• 김종인;유홍희;황요하
• Journal of the Korean Society for Railway
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• v.2 no.4
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• pp.1-8
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• 1999
• A formulation to perform static equilibrium and linear vibration analysis is presented in this paper. The formulation employs minimum number of equations of motion which are derived by using a partial velocity matrix. The static equilibrium analysis is performed first, then the linear vibration analysis is performed at the static equilibrium position. By using the formulation presented in this paper, static equilibrium and linear vibration analysis of a high speed electric train system are performed. A single bogie system, a power car vehicle, and a train system which consists of five vehicles are analyzed, respectively. Natural frequencies and a few lowest mode shapes of the two are identified in this paper.

### Vibration Analysis and Non-linear Equilibrium Equations of a Curved Pipe Conveying Fluid (유체가 흐르는 곡선관의 진동 해석과 비선형 평형 방정식)

• Jung, Du-Han;Chung, Jin-Tai
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.983-986
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• 2005
• Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

### Analysis of Heat and Vibration of Super-Precision Linear Motors (초정밀 선형 모터의 열$\cdot$진동 분석)

• Lee Woo Young;Rim Kyung Hwa;Seol Jin Soo;Kim Hyun Chul
• Journal of the Semiconductor & Display Technology
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• v.4 no.1
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• pp.1-8
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• 2005
• Linear motor can be directly applied to the system needed linear motions without rotary motions. To control high-speed and high-resolution, the development of the linear motors is recently required in the high-integrated and speed process industry This paper presents thermal and vibration analyses as well as measurement standards of the newly developed linear motors through analyzing the thermal behaviors and vibration characteristics of the advanced products. The thermal measurements are conducted for comparing the developed linear motor with the advanced linear motor and the Finite Volume Method(FVM) is used to identify the measurement results. And then the vibration measurement are carried out in the developed and advanced linear motors with respect to the speed. To identify the measurement results, the Finite Element Method is utilized in the developed and advanced linear motors, respectively. The FVM, FEM, and experiments make it possible to understand these characteristics. The improvement is suggested through their results conducted experiment and analyses.

### Dynamic Characteristics of Linear Motion Guide Supported by Rolling Ball Bearings (볼 베어링을 이용 Linear Motion Guide의 동적 특성에 관한 연구)

• 최재석;이용섭;김윤영;이동진;이성진;유정훈
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.326-331
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• 2004
• The linear motion (LM) guide using ball bearing has many advantages compared with conventional sliding guides. Therefore, LM guide using ball bearing has been used widely to increase the accuracy of the position of a system. This research investigates dynamic characteristics of LM guide through mainly linear analysis. Linear analysis is accomplished by Lagrange equation and finite element method. And another trial that is nonlinear analysis about one mode of LM guide(bouncing mode) from Hertzian contact theory is accomplished in the latter half of this research. Through nonlinear analysis we could observe the softening characteristic due to the Hertzian contact nonlinearity.

### Static equilibrium and linear vibration analysis of a high speed electric train system (고속 전철 시스템의 정적 평형 및 선형 진동 해석)

• 김종인;유홍희;황요하
• Proceedings of the KSR Conference
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• pp.305-312
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• 1998
• A formulation to perform static equilibrium and linear vibration analysis is presented in this paper. The formulation employs minimum number of equations of motion which are derived by using a partial velocity matrix, The static equilibrium analysis is performed first, then the linear vibration analysis is performed at the static equilibrium position. By using the formulation presented in this paper, static equilibrium and linear vibration analysis of a high speed electric train system are performed. A single bogie system, a power vehicle, and a train system which consists of five vehicles are analyzed, respectively. Natural frequencies and a few lowest mode shapes of the three are identified in this paper.

### A Study on the Stability Analysis and Non-linear Forced Torsional Vibration for the Dngine Shafting System with Viscous Damper (점성댐퍼를 갖는 엔진 축계의 안정성 해석 및 비선형 비틀림강제진동)

• 박용남;하창우;김의간;전효중
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.282-287
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• 1996
• The non-linear torsional vibrations of the propulsion shafting system with viscous damper are considered. The motion is modeled by non-linear differential equations of second order. the equivalent system is modeled by two mass softening system with Duffing's oscillator. The steady state response of a equivalent system is analyzed for primary resonance only. Harmonic balance method as a non-linear vibration analysis technique is used. Jump phenomena are explained. The primary unstable region obtained by the Mathieu equation is investigated. Both theoretical and measured results of the propulsion shafting system are compared with and evaluated. As a result of comparisons with both data, it was confirmed that Duffing's oscillator can be used as a analysis method in the modeling of the propulsion shafting system attached viscous damper with non-linear stiffness.

### Nonlinear dynamic analysis of spiral stiffened cylindrical shells rested on elastic foundation

• Steel and Composite Structures
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• v.32 no.4
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• pp.509-519
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• 2019
• In this paper, an analytical approach for the free vibration analysis of spiral stiffened functionally graded (SSFG) cylindrical shells is investigated. The SSFG shell is resting on linear and non-linear elastic foundation with damping force. The elastic foundation for the linear model is according to Winkler and Pasternak parameters and for the non-linear model, one cubic term is added. The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von $K\acute{a}rm\acute{a}n$ equations and the smeared stiffeners technique, the non-linear vibration problem has been solved. The effects of different geometrical and material parameters on the free vibration response of SSFG cylindrical shells are adopted. The results show that the angles of stiffeners and elastic foundation parameters strongly effect on the natural frequencies of the SSFG cylindrical shell.

### Vibration Analysis of Super-Precision Linear Motors (초정밀 선형 모터의 진동 분석)

• Seol, Jin-Soo;Lee, Woo-Young;Rim, Kyung-Hwa
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.840-845
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• 2004
• Development of the linear motors is recently required to control a high-speed and high-resolution in the high-integrated and speed process industry. This paper presents vibration analyses as well as measurement standards of the newly developed linear motors through analyzing the vibration characteristics of the advanced products. Vibration experiments are conducted for identifying vibration level during operation. They are also included in the modal test to analyze dynamic characteristics. Analytic data using Finite Element Method (FEM) are compared with the results of the modal. The FEM and experiments make it possible to understand these characteristics. Further, through computer simulation for the behavior of moving part to be vibration source, the best acceleration pattern of moving part movement can be verified to achieve effective moving part positioning and reduce the vibration due to moving part movement.

### Exact solution for dynamic response of size dependent torsional vibration of CNT subjected to linear and harmonic loadings

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• v.8 no.1
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• pp.25-36
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• 2020
• Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

### Dynamic Characteristics of Linear Motion Supported by Rolling Ball Bearings (볼 베어링을 사용하는 선형 운동 가이드의 동적 특성)

• Choi Jae Seok;Yi Yong-sub;Kim Yoon Young;Lee Dong Jin;Lee Sung Jin;Yoo Jeonghoon
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.9
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• pp.868-876
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• 2004
• The linear motion(LM) guide using ball bearing has many advantages compared with conventional sliding guides. Therefore, LM guide using ball bearing has been widely used to increase the accuracy of the position of a system. This research investigates dynamic characteristics of LM guide through mainly linear analyses. Linear analysis is accomplished by Lagrange equation and the finite element method. And another trial that performs nonlinear analysis about one mode(bouncing mode) of LM guide from Hertzian contact theory is accomplished in the latter half of this research. Through nonlinear analysis we could observe the softening characteristic due to the Hertzian contact nonlinearity.