• Title/Summary/Keyword: free vibration mode shapes

검색결과 239건 처리시간 0.714초

Vibration Analysis of an Axially Moving Membrane with In-plane/Out-of-plane Deformations (면내/면외변형을 고려한 이송되는 박막의 진동해석)

  • Shin Changho;Chung Jintai
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • 제14권9호
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    • pp.910-918
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    • 2004
  • The vibration analysis of an axially moving membrane are investigated when the membrane has the two sets of in-plane boundary conditions, which are free and fixed constraints in the lateral direction. Since the in-plane stiffness is much higher than the out-of-plane stiffness, it is assumed during deriving the equations of motion that the in-plane motion is in a steady state. Under this assumption, the equation of out-of-plane motion is derived, which is a linear partial differential equation influenced by the in-plane stress distributions. After discretizing the equation by using the Galerkin method, the natural frequencies and mode shapes are computed. In particular, we put a focus on analyzing the effects of the in-plane boundary conditions on the natural frequencies and mode shapes of the moving membrane.

Double Fourier Sine Series Method for The Free Vibration of a Rectangular Plate (이중 사인 시리즈법에 의한 직사각형 평판의 자유 진동해석)

  • 윤종욱;이장무
    • Journal of KSNVE
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    • 제6권6호
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    • pp.771-779
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    • 1996
  • In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

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Flexural free vibration of cantilevered structures of variable stiffness and mass

  • Li, Q.S.
    • Structural Engineering and Mechanics
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    • 제8권3호
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    • pp.243-256
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    • 1999
  • Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

VIBRATION OF A CIRCULAR PLATE WITH A CONCENTRATED MASS ATTACHED ON A RADIUS

  • Lee, Jang-Moo;Hong, Jin-Sun
    • Journal of Theoretical and Applied Mechanics
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    • 제1권1호
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    • pp.89-96
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    • 1995
  • An analytical method is presented for predicting the effect of a local deviation in the form of a concentrated mass along a radial line on the free bending vibration characteristics of a nearly axisymmetric circular plate. The approach is based on the Rayleigh-Ritz method and the expression of local deviation of the concentrated radial mass as the variation of heaviside unit step function. The effects of the concentrated mass on the natural frequencies and mode shapes of the plate are predicted with a proposed nondimensional mass parameter.

Modal Analysis of Steel Box Bridge by Using the Component Mode Synthesis (CMS 방법에 의한 강교량의 동적모드해석)

  • 조병완;박종칠;김영진
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 한국전산구조공학회 1997년도 봄 학술발표회 논문집
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    • pp.177-184
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    • 1997
  • The Component Mode Synthesis Method for the -vibration analysis can be applied to the large-scaled structures, which have difficulty in modeling because of their intricate shapes and boundary conditions and need much time in computational calculations. This paper uses the Component Mode Synthesis Method to analyze the free vibration for the steel box bridge having the large number of D.O.F as an example of the large structural system. By comparing the CMS method to the other method (FEM), this paper proves the accuracy of the solution in techniques and the efficiency in time.

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In-plane free vibrations of catenary arches with unsymmetric axes

  • Wilson, James F.;Lee, Byoung Koo
    • Structural Engineering and Mechanics
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    • 제3권5호
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    • pp.511-525
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    • 1995
  • The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.

Dynamic Behavior Analysis of Stiffened Cylindrical Shell Filled with Fluid (내부가 유체로 채워진 보강원통쉘의 동적거동 해석)

  • Youm, Ki-Un;Yoon, Kyung-Ho;Lee, Young-Shin;Kim, Jong-Kiun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • 제20권9호
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    • pp.2875-2886
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    • 1996
  • This work present the experimental resutls for the free vibration of unstiffened, stiffened cylindrical shell filled with air, half water and full water. The natural frequencies and mode shapes of unstiffened, stiffened cylindrical shell are obtained experimentally also. The natural frequencies of stiffened cylindrical shell were generally highter than those of unstiffened cylindrical shell and natural requencies were decreased as cylindrical shell was filled with water. The effect of circumferential stiffener in the first mode was shown that natural frequency more increased 25% at air environment, 29% at half water environment and 37% at full water than those of unstiffened cylindrical shell, respectively. Also, the natural frequencies were decreased according to the added mass effect of fluid in the shell of unstiffened and stiffened cylindrical shell. The six mode shape results of all cases are simular and given. The natural frequencies are determined for a wide range of parameters : e.g. unstiffened shell, and filled with air, half and full water. The effects of varying the parameters on the free vibration frequencies and mode shapes are discussed.

Damped frequencies of precast modular steel-concrete composite railway track slabs

  • Kaewunruen, Sakdirat;Kimani, Stephen Kimindiri
    • Steel and Composite Structures
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    • 제25권4호
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    • pp.427-442
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    • 2017
  • This paper presents unprecedented damped oscillation behaviours of a precast steel-concrete composite slab panel for track support. The steel-concrete composite slab track is an innovative slab track, a form of ballastless track which is becoming increasingly attractive to asset owners as they seek to reduce lifecycle costs and deal with increasing rail traffic speeds. The slender nature of the slab panel due to its reduced depth of construction makes it susceptible to vibration problems. The aim of the study is driven by the need to address the limited research available to date on the dynamic behaviour of steel-concrete composite slab panels for track support. Free vibration analysis of the track slab has been carried out using ABAQUS. Both undamped and damped eigenfrequencies and eigenmodes have been extracted using the Lancsoz method. The fundamental natural frequencies of the slab panel have been identified together with corresponding mode shapes. To investigate the sensitivity of the natural frequencies and mode shapes, parametric studies have been established, considering concrete strength and mass and steel's modulus of elasticity. This study is the world first to observe crossover phenomena that result in the inversion of the natural orders without interaction. It also reveals that replacement of the steel with aluminium or carbon fibre sheeting can only marginally reduce the natural frequencies of the slab panel.

Free vibration analysis of tall buildings with outrigger-belt truss system

  • Malekinejad, Mohsen;Rahgozar, Reza
    • Earthquakes and Structures
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    • 제2권1호
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    • pp.89-107
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    • 2011
  • In this paper a simple mathematical model is presented for estimating the natural frequencies and corresponding mode shapes of a tall building with outrigger-belt truss system. For this purposes an equivalent continuum system is analyzed in which a tall building structure is replaced by an idealized cantilever continuum beam representing the structural characteristics. The equivalent system is comprised of a cantilever shear beam in parallel to a cantilever flexural beam that is constrained by a rotational spring at outrigger-belt truss location. The mathematical modeling and the derivation of the equation of motion are given for the cantilevers with identically paralleled and rotational spring. The equation of motion and the associated boundary conditions are analytically obtained by using Hamilton's variational principle. After obtaining non-trivial solution of the eigensystem, the resulting is used to determine the natural frequencies and associated mode shapes of free vibration analysis. A numerical example for a 40 story tall building has been solved with proposed method and finite element method. The results of the proposed mathematical model have good adaptation with those obtained from finite element analysis. Proposed model is practically suitable for quick evaluations during the preliminary design stages.

Theory and Experiments of Free Vibration Characteristics for the Composite Beam with Transverse Open Cracks (크랙이 있는 복합재료 보 자유진동특성의 이론과 실험적 입증)

  • 하태완
    • Journal of the Korea Institute of Military Science and Technology
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    • 제5권2호
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    • pp.217-227
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    • 2002
  • Theoretical and experimental free vibration characteristics of cantilevered laminated composite beams with single or multiple transverse non-propagating open cracks are investigated. The presence of intrinsic cracks in beams modifies the flexibility and in turn free vibration characteristics of the structures, and the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack. Also the experimental results are well coincide with the numerical results in the decrease of natural frequencies and the transformation of mode shapes because of intrinsic cracks in the composite or aluminum beams. It is revealed that non-destructive crack detection(NDT) or vibration based inspection(VBI) is possible by analyzing the free vibration responses of cracked composite beams.