• 제목/요약/키워드: Vibration Equation

검색결과 1,524건 처리시간 0.031초

플로팅 링 베어링으로 지지된 터보차저 로터의 안정성 해석 (Stability Analysis of Floating Ring Bearing Supported Turbocharger)

  • 이동현;김영철;김병옥
    • Tribology and Lubricants
    • /
    • 제31권6호
    • /
    • pp.302-307
    • /
    • 2015
  • The use of turbocharger in internal combustion engines has increased as it is a key components for improving system efficiency without increasing engine size. Because of increasing demand, many studies have evaluated rotordynamic performance so as to increase rotation speed. This paper presents a linear and nonlinear analysis model for a turbocharger rotor supported by a floating ring bearing. We constructed rotor model by using the finite element method and approximated bearings as being infinitely short. In the linear model, we considered fluid film force as stiffness and damping element. In nonlinear analysis, calculation of the fluid film force involved solving the time dependent Reynolds equation. We verified the developed model by comparing the results to those of previous research. The analysis results show that there are four unstable modes, which are rigid body modes combining ring and rotor motion. As the rotating speed increases, the logarithmic decrement shows that certain unstable modes goes into the stable area or the stable mode goes into the unstable area. These unstable modes appear as sub-synchronous vibrations in nonlinear analysis. In nonlinear analysis frequency jump phenomenon demonstrated in several experimental studies appears. The analysis results also showed that frequency jump phenomenon occurs when the vibration mode changes and the sequence of unstable mode matches the linear analysis result. However, the natural frequency predicted using linear analysis differs from those obtained using nonlinear analysis.

A Study of Design of Hollow Fiber Membrane Modules for using in Artificial Lung by the PZT Actuator

  • Kim, Gi-Beum;Kim, Seong-Jong;Hong, Chul-Un;Lee, Yong-Chul;Kim, Min-Ho
    • 대한의용생체공학회:의공학회지
    • /
    • 제27권4호
    • /
    • pp.143-153
    • /
    • 2006
  • The purpose of this work was to assess and quantify the beneficial effects of gas exchange, while testingto the various frequencies of the sinusoidal wave that was excited by the PZT actuator, for patients suffering from acute respiratory distress syndrome (ARDS) or chronic respiratory problems. Also, this paper considered a simulator to design a hollow type artificial lung, and a mathematical model was used to predict a behavior of blood. This simulation was carried out according to the Montecarno's simulation method, anda fourth order Runge-Kutta method was used to solve the equation. The experimental design and procedure are then applied to the construction of a new device to assess the effectiveness of the membrane vibrations. As a result, the vibration method is very effective in the increase of gas transport. The gas exchange efficiency for the vibrating intravascular lung assist device can be increased by emphasizing the following design features: consistent and reproducible fiber geometry, and most importantly, an active means of enhancing convective mixing of water around the hollow fiber membranes. The experimental results showed the effective performance of the vibrating intravascular lung assist device. Also, we concluded that important design parameters were blood flow rates, fiber outer diameter and oxygen pressure drop. Based on the present results, it was believed that the optimal level of blood flow rates was 200$cm^3$/min.

사장교 케이블 동특성 평가를 위한 케이블 가진시스템 개발 (Development of Cable Excitation System for Evaluating Dynamic Characteristics of Stay Cables)

  • 김남식;정운;서주원;안상섭
    • 한국지진공학회논문집
    • /
    • 제7권4호
    • /
    • pp.71-79
    • /
    • 2003
  • 사장교에서 케이블은 교량 전체에 있어서 매우 중요한 요소이다. 차량, 바람 혹은 풍우에 의한 케이블의 진동은 교량의 안전성과 사용성을 감소시키는 주요 원인이 되어왔으며 이러한 문제를 해결하는 효과적인 방법중의 하나는 케이블 댐퍼를 설치하는 것이다. 이 케이블 댐퍼를 최적으로 설계하기 위해서는 케이블의 동특성을 정확하게 평가해야 하며 케이블 동특성치를 얻기 위해서는 정확한 가진이 필요하다. 따라서 본 연구에서는 케이블 가진시스템을 개발하고 성능을 평가하기 위해 케이블 가진시스템의 운동방정식을 유도하였으며, 케이블 가진기를 케이블 모형에 설치하여 정현진동실험과 공진진동실험을 수행하여 케이블의 동특성을 효과적으로 구하였다.

Thermal Stability and Lifetime Prediction of PAG and POE Oils for a Refrigeration System

  • Park, Keun-Seo;Kang, Byung-Ha;Park, Kyoung-Kuhn;Kim, Suk-Hyun
    • International Journal of Air-Conditioning and Refrigeration
    • /
    • 제15권2호
    • /
    • pp.78-83
    • /
    • 2007
  • An experimental study has been carried out to analyze the thermal stability and to estimate the lifetime of refrigerating lubricants. PAG and POE oil are considered as test oils in this study. The viscosity of PAG and POE oil was measured by the vibration type viscometer while temperature is varied periodically in the range of $0^{\circ}C{\sim}100^{\circ}C$. In order to estimate lifetime of PAG and POE oil with temperature, the viscosity was measured while the test temperature of oils was maintained continuously at $180,\;200\;and\;220^{\circ}C$. The lifetime of oils is estimated as the decrease in viscosity change by 15%. The results indicate that the reduction rates of viscosity of PAG and POE oil are less than 5% after 510 temperature variation cycles. However, when the oils are kept at high temperature, it is found that the lifetimes of PAG oil is seen to be 244, 177 and 89 hours at the test temperature of $180,\;200\;and\;220^{\circ}C$, respectively, where as the lifetimes of POE oil are estimated to be 1,744, 1,007 and 334 hours at the temperature of $180,\;200\;and\;220^{\circ}C$, respectively. Thus, the lifetime of POE oil is found to be much longer than that of PAG oil. The lifetime correlations of PAG and POE oil are also obtained by Arrhenius's equation method in this paper.

Free vibrations of a two-cable network inter-supported by cross-links extended to ground

  • Zhou, H.J.;Wu, Y.H.;Li, L.X.;Sun, L.M.;Xing, F.
    • Smart Structures and Systems
    • /
    • 제23권6호
    • /
    • pp.653-667
    • /
    • 2019
  • Using cross-ties to connect cables together when forming a cable network is regarded as an efficient method of mitigating cable vibrations. Cross-ties have been extended and fixed on bridge decks or towers in some engineering applications. However, the dynamics of this kind of system need to be further studied, and the effects of extending cross-links to bridge decks/towers on the modal response of the system should be assessed in detail. In this paper, a system of two cables connected by an inter-supported cross-link with another lower cross-link extended to the ground is proposed and analyzed. The characteristic equation of the system is derived, and some limiting solutions in closed form of the system are derived. Roots of cable system with special configurations are also discussed, attention being given to the case when the two cables are identical. A predictable mode behavior was found when the stiffness of inter-connection cross-link and the cross-link extended to the ground were the same. The vector of mode energy distribution and the degree of mode localization index are proposed so as to distinguish global and local modes. The change of mode behaviors is further discussed in the case when the two cables are not identical. Effects of cross-link stiffness, cross-link location, mass-tension ratio, cable length ratio and frequency ratio on $1^{st}$ mode frequency and mode shape are addressed.

유한요소법을 이용한 방향성 시추의 굴진율 연구 (A study on the excavation rate of directional drilling using finite element method)

  • 정태준;신영기
    • 플랜트 저널
    • /
    • 제17권3호
    • /
    • pp.42-46
    • /
    • 2021
  • 드릴 스트링의 진동 문제는 수년간 드릴링 성능 저하의 주요 원인 중 하나로 인식되어 왔으며, 굴착 작업 시 발생하는 과도한 진동은 드릴링의 효율성, 파이프 피로, 비트의 수명 단축으로 인하여 고장을 초래할 수 있다. 이러한 진동의 원인은 드릴 스트링이 굴착 작업 중 궤적에 따라 파이프의 굽힘과 wellbore와의 접촉으로 인해 마찰이 발생하고 이러한 진동은 일반적으로 축 방향, 굴곡 및 비틀림 변형을 일으킨다. 본 연구에서는 Khulief와 Al-Naser가 제시한 모델을 바탕으로 드릴 스트링에 6자유도(DOF)의 구성요소를 갖는 모델을 적용하여 curved beam의 수치해석 값과 Analytical값을 비교하여 검증하고 드릴 스트링에 hookload와 WOB 경계조건을 주어 각 element 마다 동적 거동을 분석하였다. 실제 궤적을 적용하여 드릴 파이프의 굽힘이나 중력으로 인하여 Wellbore와 접촉되는 부분에 마찰을 적용하였고, 또한 마찰 작용 시 일정한 축 방향 속도를 유지하기 위한 PI제어 값을 설계하여 drillstring 전체의 각속도 변화와 실제 드릴 굴착 작업 중 발생하는 stick slip현상을 관찰하였다.

A simplified directly determination of natural frequencies of CNT: Via aspect ratio

  • Banoqitah, Essam Mohammed;Hussain, Muzamal;Khadimallah, Mohamed A.;Ghandourah, Emad;Yahya, Ahmad;Basha, Muhammad;Alshoaibi, Adil
    • Advances in nano research
    • /
    • 제13권3호
    • /
    • pp.207-216
    • /
    • 2022
  • In this paper, a novel model is developed for frequency behavior of single walled carbon nanotubes. The governing equation of motion is constructed method based on the Sander theory using Rayleigh-Ritz's method The frequencies enhances on increasing the power law index using simply supported, clamped and clamped free end conditions. The frequency curve for C-F is less than other conditions. It is due to the physical constraints which are applied on the edge of the CNT. It is observed that the C-F boundary condition have less frequencies from the other two conditions. The frequency phenomena for zigzag are insignificant throughout the aspect ratio. Moreover when index of power law is increased then frequencies increases for all boundary conditions. The natural frequency mechanism for the armchair (10, 10) for various values of power law index with different boundary conditions is investigated. Here frequencies decrease on increases the aspect ratio for all boundary conditions. The frequency curves of SS-SS edge condition is composed between the C-C and C-F conditions. The curves of frequency are less significant from small aspect ratio (L/d = 4.86 ~ 8.47) and decreases fast for greater ratios. It is found that the frequencies via aspect ratios, armchair (10, 10) have higher values from zigzag (10, 0). It is due to the material structure which is made by the carbon nanotubes. The power law index have momentous effect on the vibration of single walled carbon nanotubes. The present frequency result is also compared numerically experimentally with Raman Spectroscopy.

Vibrational characteristics of sandwich annular plates with damaged core and FG face sheets

  • Xi, Fei
    • Steel and Composite Structures
    • /
    • 제44권1호
    • /
    • pp.65-79
    • /
    • 2022
  • The main goal of this paper is to study the vibration of damaged core laminated annular plates with FG face sheets based on a three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. In this study the effect of microcracks on the vibrational characteristic of the sandwich plate is considered. In particular, the structures are made by an isotropic core that undergoes a progressive uniform damage, which is modeled as a decay of the mechanical properties expressed in terms of engineering constants. These defects are uniformly distributed and affect the central layer of the plates independently from the direction, this phenomenon is known as "isotropic damage" and it is fully described by a scalar parameter. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular plate is assumed to have any arbitrary boundary conditions at the circular edges including simply supported, clamped and, free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution, and boundary conditions.

A semi-analytical and numerical approach for solving 3D nonlinear cylindrical shell systems

  • Liming Dai;Kamran Foroutan
    • Structural Engineering and Mechanics
    • /
    • 제87권5호
    • /
    • pp.461-473
    • /
    • 2023
  • This study aims to solve for nonlinear cylindrical shell systems with a semi-analytical and numerical approach implementing the P-T method. The procedures and conditions for such a study are presented in practically solving and analyzing the cylindrical shell systems. An analytical model for a nonlinear thick cylindrical shell (TCS) is established on the basis of the stress function and Reddy's higher-order shear deformation theory (HSDT). According to Reddy's HSDT, Hooke's law in three dimensions, and the von-Kármán equation, the stress-strain relations are developed for the thick cylindrical shell systems, and the three coupled nonlinear governing equations are thus established and discretized as per the Galerkin method, for implementing the P-T method. The solution generated with the approach is continuous everywhere in the entire time domain considered. The approach proposed can also be used to numerically solve and analyze the nonlinear shell systems. The procedures and recurrence relations for numerical solutions of shell systems are presented. To demonstrate the application of the approach in numerically solving for nonlinear cylindrical shell systems, a specific nonlinear cylindrical shell system subjected to an external excitation is solved numerically. In numerically solving for the system, the present approach shows higher efficiency, accuracy, and reliability in comparison with that of the Runge-Kutta method. The approach with the P-T method presented is practically sound especially when continuous and high-quality numerical solutions for the shell systems are considered.

DMD기반 Kirchhoff-Love 판의 모드 분석과 수치해 예측 (DMD based modal analysis and prediction of Kirchhoff-Love plate)

  • 신성윤;조광현;배석찬
    • 한국정보통신학회논문지
    • /
    • 제26권11호
    • /
    • pp.1586-1591
    • /
    • 2022
  • Kirchhoff-Love 판 (KLP) 방정식은 특정 외력이 얇은 막에 끼치는 변형을 기술하는 잘 알려진 이론이다. 한편, frequency 도메인에서 진동하는 판을 해석하는 것은 주요 진동 주파수와 고유함수들을 구하는 것과 판의 진동을 예측하는데 중요하다. 다양한 모드 분석 방법들 중 dynamic mode decomposition (DMD)는 효율적인 data 기반 방법이다. 이 논문에서 우리는 DMD를 기반으로 sine 유형 외력의 영향력 안에 있는 KLP의 모드 분석을 수행한다. 우리는 먼저 유한차분법을 사용하여 이산적으로 표현된 시계열 형식의 KLP 해를 구한다. 720,00개의 FDM으로 생성된 해중에서, 오직 500개의 해만을 DMD의 구현을 위해 선택한다. 우리는 결과적으로 얻어진 DMD-mode를 보고한다. 또한, DMD를 통하여 KLP의 해를 예측하는 효율적인 방법을 소개한다.