• 제목/요약/키워드: Mass matrix

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이중크랙을 가진 보의 동특성에 미치는 끝단질량과 이동질량의 영향 (Influence of Tip Mass and Moving Mass on Dynamic Behavior of Beam with Double-Crack)

  • 손인수;윤한익
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2004년도 추계학술대회논문집
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    • pp.713-716
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    • 2004
  • In this paper a dynamic behavior of a double-cracked cnatilver beam with a tip mass and the moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, a tip mass and double cracks have been studied on the dynamic behavior of a cantilever beam system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. ,Therefore, the cracks are modelled as a rotational spring. Totally, as a tip mass is increased, the natural frequency of cantilever beam is decreased. The position of the crack is located in front of the cantilever beam, the frequencies of a double-cracked cantilever beam presents minimum frequency.

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Free vibration analysis of cracked Timoshenko beams carrying spring-mass systems

  • Tan, Guojin;Shan, Jinghui;Wu, Chunli;Wang, Wensheng
    • Structural Engineering and Mechanics
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    • 제63권4호
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    • pp.551-565
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    • 2017
  • In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

Influence of Moving Mass on Dynamic Behavior of Simply Supported Timoshenko Beam with Crack

  • Yoon Han-Ik;Choi Chang-Soo;Son In-Soo
    • International Journal of Precision Engineering and Manufacturing
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    • 제7권1호
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    • pp.24-29
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    • 2006
  • In this paper, the effect of open crack on the dynamic behavior of simply supported Timoshenko beam with a moving mass was studied. The influences of the depth and the position of the crack on the beam were studied on the dynamic behavior of the simply supported beam system by numerical methods. The equation of motion is derived by using Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces on the crack section and is derived by applying fundamental fracture mechanics theory. As the depth of the crack increases, the mid-span deflection of the Timoshenko beam with a moving mass is increased.

Sequence Verification of Synthetic Oligonucleotides by Exonuclease Digestion and Matrix Assisted Laser Desorption Ionization Mass Spectrometry

  • Kim, Jin-Sung;Jang, Jung-Suk;Choi, Jong-Soon;Chang, Yoon-Seok
    • BMB Reports
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    • 제29권2호
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    • pp.122-126
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    • 1996
  • A series of oligonucleotides were synthesized by automatic DNA synthesizer. The purity of crude products was checked and their molecular weights determined by matrix assisted laser desorption ionization mass spectrometry (MALDI-MS) with an accuracy of better than 0.05% deviation even without using an internal standard. This mass determining technology in combination with partial digestion of oligonucleotides by 5'- and 3'-exonuclease provides a straightforward and simple method to obtain sequence information of oligonucleotides. The extension of this technology to the sequencing of modified oligonucleotides and genomic DNA and RNA might become possible.

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이동질량을 가진 단순지지 보의 동특성에 미치는 크랙의 영향 (Influence of Crack on Dynamic Behavior of Simply Supported Beam with Moving Mass)

  • 윤한익;이용운;손인수
    • 한국소음진동공학회논문집
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    • 제13권9호
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    • pp.720-729
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    • 2003
  • An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beam with the moving mass. The influences of the depth and the position of the crack in the beam have been studied on the dynamic behavior of the simply supported beam system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. As the depth of the crack is increased the frequency of the simply supported beam with the moving mass is increased.

수중에 부분 몰수된 외팔보의 고유진동 특성 (Natural Vibration Characteristics of Cantilever Plate Partially Submerged into Water)

  • 곽문규;양동호;이재하
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2012년도 추계학술대회 논문집
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    • pp.229-230
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    • 2012
  • The free flexural vibration of a cantilever plate partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates. The introduction of the elliptical coordinates naturally leads to the use of the Mathieu function. Hence, the virtual mass matrix which reflects the effect of the fluid on the natural vibration characteristics is expressed in analytical form in terms of the Mathieu functions. The virtual mass matrix is then combined with the dynamic model of a thin rectangular plate obtained by using the Rayleigh-Ritz method. This combination is used to analyze the natural vibration characteristics of a partially submerged cantilever plate qualitatively. Also, the non-dimensionalized added virtual mass incremental factors for a partially submerged cantilever plate are presented to facilitate the easy estimation of natural frequencies of a partially submerged cantilever plate. The numerical results validate the proposed approach.

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다합금계 백주철의 탄화물 및 기지조직이 내마모성에 미치는 영향 (Effects of Carbide and Matrix Structures on Abrasion Wear Resistance of Multi-Component White Cast Iron)

  • 류성곤
    • 한국재료학회지
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    • 제7권4호
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    • pp.310-316
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    • 1997
  • The effects of carbide and matrix structures on the abrasion wear resistance of multi-component white cast irons with 3.0 mass%C have been studied in this paper. Four different heats were poured in order to obtain the specimens with different combinations of the carbide structures: a basic iron(3.0 mass%C-5.0 mass%Cr-5.0 mass%V-5.0 mass% Mo-12.5mass%W)for M$_{6}$C and M$_{7}$C$_{3}$ carbides, and a Cr free iron(3.0 mass%C-5.0 mass%V-2.5mass%Mo-12.5 mass%W) for MC and M6C carbides. A conventional high Cr free free iron(3.0 mass%C-5.0 mass%V-2.5 mass%Mo-12.5 mass%W) for MC and M6C carbides. A conventional high Cr white cast iron was also poured to compare its wear resistance with those of the multi-component white cast irons. In the as-cast condition, the range of abrasive wear rate(Rw=mg/min) was from 4.15 to 5.98 . The lowest Rw, which means the highest wear resistance, was obtained in the basic iron with nodular MC, lamellar M$_{2}$C and cellular M$_{7}$C$_{3}$ carbides. On the other hand, the Rw of the high Cr white cast iron ranked between the basic iron and the Mo and W free iron. In each alloy, the Rw of air hardened or tempered specimen was lower than that of the as-cast one because of the change of matrix structures by the heat treatments. The Rw of the hear treated speci-mens increased in the order Mo and W free iron, basic iron, Cr free iron, high Cr iron, and V free iron.n.n.n.

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Improved Calibration for the Analysis of Emerging Contaminants in Wastewater Using Ultra High Performance Liquid Chromatography and Time-of-Flight Mass Spectrometry

  • Pellinen, Jukka;Lepisto, Riikka-Juulia;Savolainen, Santeri
    • Mass Spectrometry Letters
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    • 제9권3호
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    • pp.77-80
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    • 2018
  • The focus of this paper is to present techniques to overcome certain difficulties in quantitative analysis with a time-of-flight mass spectrometer (TOF-MS). The method is based on conventional solid-phase extraction, followed by reversed-phase ultra high performance liquid chromatography of the extract, and mass spectrometric analysis. The target compounds included atenolol, atrazine, caffeine, carbamazepine, diclofenac, estrone, ibuprofen, naproxen, simazine, sucralose, sulfamethoxazole, and triclosan. The matrix effects caused by high concentrations of organic compounds in wastewater are especially significant in electrospray ionization mass spectroscopy. Internal-standard calibration with isotopically labeled standards corrects the results for many matrix effects, but some peculiarities were observed. The problems encountered in quantitation of carbamazepine and triclosan, due to nonlinear calibration were solved by changing the internal standard and using a narrower mass window. With simazine, the use of a quadratic calibration curve was the best solution.

Influence of Tip mass on Dynamic Behavior of Cracked Cantilever Pipe Conveying Fluid with Moving Mass

  • Yoon Han-Ik;Son In-Soo
    • Journal of Mechanical Science and Technology
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    • 제19권9호
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    • pp.1731-1741
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    • 2005
  • In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.

Estimation of Beam Mode Frequencies of Co-axial Cylinders Immersed in Fluid by Equivalent Mass Approach

  • Kim, Tae-Wan;Park, Suhn;Park, Keun-Bae
    • Nuclear Engineering and Technology
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    • 제35권1호
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    • pp.1-13
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    • 2003
  • In this study, an effective method to estimate the fundamental frequencies of co-axial cylinders immersed in fluid is proposed. The proposed method makes use of the equivalent mass or density that is derived from the added mass matrix caused by the fluid-structure interaction (FSI) phenomenon. The equivalent mass is defined from the added mass matrix based on a 2-D potential flow theory. The theory on two co-axial cylinders extended to the case of three cylinders. To prove the validity of the proposed method, the eigenvalue analyses upon coaxial cylinders coupled with fluid gaps are peformed using the equivalent mass. The analyses results upon various fluid gap is conditions reveal that the present method could provide accurate frequencies and be suitable for expecting the fundamental frequencies of fluid coupled cylinders in beam mode vibration.