• Title/Summary/Keyword: castigliano's theorem

Search Result 15, Processing Time 0.022 seconds

Ring-Shaped Inductive Sensor Design and Application to Pressure Sensing (환형 인덕티브 센서의 설계 및 압력센서로의 적용)

  • Noh, Myounggyu;Kim, Sunyoung;Baek, Seongki;Park, Young-Woo
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.39 no.10
    • /
    • pp.995-999
    • /
    • 2015
  • Inductive sensors are versatile and economical devices that are widely used to measure a wide variety of physical variables, such as displacement, force, and pressure. In this paper, we propose a simple inductive sensor consisting of a thin partial ring and a coil set. The self-inductance of the sensor was estimated using magnetic circuit analysis and validated through finite element analysis (FEA). The natural frequency of the ring was estimated using Castigliano's theorem and the method of equivalent mass. The estimation was validated through experiments and FEA. A prototype sensor with a signal processing circuit is built and applied to noninvasively sense the pressure inside a flexible tube. The obtained sensor outputs show quadratic behavior with respect to the pressure. When fitted to a quadratic equation, the least-square measurement error was less than 2%. The results confirm the feasibility of pressure sensing using the proposed inductive sensor.

Investigating the effect of edge crack on the modal properties of composite wing using dynamic stiffness matrix

  • Torabi, Ali Reza;Shams, Shahrokh;Fatehi-Narab, Mahdi
    • Steel and Composite Structures
    • /
    • v.39 no.5
    • /
    • pp.543-564
    • /
    • 2021
  • In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

Evaluation of an elastic stiffness sensitivity of leaf type HDS (판형 홀다운스프링 집합체의 탄성강성도 민감도 평가)

  • Song, Kee-Nam
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.21 no.8
    • /
    • pp.1276-1290
    • /
    • 1997
  • The previous elastic stiffness formulas of leaf type holddown spring assemblies(HDSs) have been corrected and extended to be able to consider the point of taper runout for the TT-HDS and all the strain energies for both the TT-HDS and the TW-HDS based on Euler beam theory and Castigliano'stheorem. The elastic stiffness sensitivity of the leaf type holddown spring assemblies was analyzed using the derived elastic stiffness formulas and their gradient vectors obtained from the mid-point formula. As a result of the sensitivity analysis, the elastic stiffness sensitivity at each design variable is quantified and design variables having remarkable sensitivity are identified. Among the design variables, leaf thickness is identified as that of having the most remarkable sensitivity of the elastic stiffness. In addition, it was found that the sensitivity of the leaf type HDS's elastic stiffness is exponentially correlated to the leaf thickness.

Development of Design Formulas for Pipe Loops Used in Ships Considering the Curvature of Corners (코너부 곡률을 고려한 선박용 파이프 루프 설계식 개발)

  • Park, Chi-Mo;Yang, Park-Dal-Chi
    • Journal of Ocean Engineering and Technology
    • /
    • v.23 no.4
    • /
    • pp.91-99
    • /
    • 2009
  • Many longitudinally arranged pipes in ships are subject to considerable displacement loads caused by the hull girder bending of ships and/or thermal loads in some special pipes through which fluids with highly abnormal temperatures are conveyed. As these loads may cause failure in the pipes or their supporting structures, loops have been widely adopted as a measure to prevent such failure, with the idea that they can lower the stress level in a pipe by absorbing some portion of these loads. But since such loops have some negative effects, such as causing extra manufacturing cost and occupying extra space, the number and dimensions of the loops need to be minimized. This research developed design formulas for pipe loops, modeling them as a spring element, for which the axial stiffness is calculated based on the beam theory, incorporating the effects of the curvature of loop corners and the flexibility of the straight portion of the pipe. The accuracy of the proposed design formulas was verified by comparing two results respectively obtained by the proposed formulas and MSC/NASTRAN. The paper ends with a sample application of the proposed formulas showing their efficiency.

Development of a Sample Scanner for Atomic Force Microscope (원자 현미경용 샘플 스캐너의 개발)

  • Lee, Dong-Yeon;Lee, Moo-Yeon;Gweon, Dae-Gab
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
    • /
    • 2005.11a
    • /
    • pp.879-882
    • /
    • 2005
  • This paper shows a method for design of the nano-positioning planar scanner used in the scanning probe microscope. The planar scanner is composed of flexure guides, piezoelectric actuators and feedback sensors. In the design of flexure guides, the Castigliano's theorem was used to find the stiffness of the guide. The motion amplifying mechanism was used in the piezoelectric actuator to achieve a large travel range. We found theoretically the travel range of the total system and verified using the commercial FEM(Finite element method) program. The maximum travel range of the planar scanner is above than 140 $\mu$m. The 3 axis positioning capability was verified by the mode analysis using the FEM program. Moreover, we presented the actual AFM(Atomic Force Microscope) imaging results with up to 2Hz imaging scan rate. Experimental results show that the properties of the proposed planar scanner is well enough to be used in SPM applications like AFM.

  • PDF