• Title, Summary, Keyword: Free vibration

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Free vibration analysis of composite conical shells using the discrete singular convolution algorithm

  • Civalek, Omer
    • Steel and Composite Structures
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    • v.6 no.4
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    • pp.353-366
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    • 2006
  • The discrete singular convolution (DSC) algorithm for determining the frequencies of the free vibration of single isotropic and orthotropic laminated conical shells is developed by using a numerical solution of the governing differential equations of motion based on Love's first approximation thin shell theory. By applying the discrete singular convolution method, the free vibration equations of motion of the composite laminated conical shell are transformed to a set of algebraic equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. The obtained results are in excellent agreement with those in the literature.

Eight-node field-consistent hexahedron element in dynamic problems

  • Rajendran, S.;Prathap, G.
    • Structural Engineering and Mechanics
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    • v.8 no.1
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    • pp.19-26
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    • 1999
  • Superior performance of field consistent eight-node hexahedron element in static bending problems has already been demonstrated in literature. In this paper, its performance in free vibration is investigated. Free vibration frequencies of typical test problems have been computed using this element. The results establish its superior performance in free vibration, particularly in thin plate application and near incompressibility regimes, demonstrating that shear locking, Poisson's stiffening and volumetric locking have been eliminated.

Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories

  • Rahmani, Omid;Asemani, S. Samane
    • Structural Engineering and Mechanics
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    • v.74 no.2
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    • pp.175-187
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    • 2020
  • The theories having been developed thus far account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In this paper, the effect of surface on the axial buckling and free vibration of nanobeams is studied using various refined higher-order shear deformation beam theories. Furthermore, these theories have strong similarities with Euler-Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and expressions of the resultant stress. The equations of motion and boundary conditions were derived from Hamilton's principle. The resultant system of ordinary differential equations was solved analytically. The effects of the nanobeam length-to-thickness ratio, thickness, and modes on the buckling and free vibration of the nanobeams were also investigated. Finally, it was found that the buckling and free vibration behavior of a nanobeam is size-dependent and that surface effects and surface energy produce significant effects by increasing the ratio of surface area to bulk at nano-scale. The results indicated that surface effects influence the buckling and free vibration performance of nanobeams and that increasing the length-to-thickness increases the buckling and free vibration in various higher-order shear deformation beam theories. This study can assist in measuring the mechanical properties of nanobeams accurately and designing nanobeam-based devices and systems.

A Study on the Ground Vibration of the Front and the Back Direction of the Free Face in the Bench Blasting (계단식 발파에 있어서 자유면 전.후방의 지반진동에 관한 연구)

  • 기경철;김일중
    • Explosives and Blasting
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    • v.20 no.2
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    • pp.21-31
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    • 2002
  • We did bench blasting upon the natural rock which it's uniaxial compressive strength was about $1,420~1,476kgf/\textrm{cm}^2$. This is the results we inferred after measuring, analyzing the ground vibration velocity of the front and back direction from the free face of the bench blasting. We have to induce the square and cube root scaled equation and the general equation to guarantee confidence upon the data when analyzing the measurement data of the test blasting. The variable distance is in reverse proportion to the permitted ground vibration velocity. The shorter is the exploding point to a protection structure, the bigger is the reflection that the direction of the free face experts the ground vibration velocity, The ground vibration velocity front of the free face tends become reduced about 38~46% compare with back of the free face in the range that the permitted ground vibration velocity is 2.0~5.0mm/sec. In case of 2.0mm/sec, when a protection structure is within about 95m, the max. allowable charge weight per delay on positing front of the free face can be more used about 2.61 times than that on positing back of the free face, in case of 3.0mm/sec within about 78m more about 2.38 times, in case of 5.0mm/sec within 60m more about 2.10 times. In case of 2.0~5.0mm/sec when a protection structure is within about 200m front from the free face, the max. allowable charge weight per delay can become about 1.52 times than the case on back to the free face.

Effect of axial stretching on large amplitude free vibration of a suspended cable

  • Chucheepsakul, Somchai;Wongsa, Sanit
    • Structural Engineering and Mechanics
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    • v.11 no.2
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    • pp.185-197
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    • 2001
  • This paper presents the effect of axial stretching on large amplitude free vibration of an extensible suspended cable supported at the same level. The model formulation developed in this study is based on the virtual work-energy functional of cables which involves strain energy due to axial stretching and work done by external forces. The difference in the Euler equations between equilibrium and motion states is considered. The resulting equations govern the horizontal and vertical motion of the cables, and are coupled and highly nonlinear. The solution for the nonlinear static equilibrium configuration is determined by the shooting method while the solution for the large amplitude free vibration is obtained by using the second-order central finite difference scheme with time integration. Numerical examples are given to demonstrate the vibration behaviour of extensible suspended cables.

In-Plane Free Vibration Analysis of Plates (평판의 면내 자유진동 해석)

  • Choi, Myung-Soo;Yeo, Dong-Jun;Byun, Jung-Hwan;Jang, Duck-Jong;Moon, Deok-Hong
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.291-296
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    • 2007
  • To analyze accurately the free vibration of a structure by using the finite element method (FEM), we model the structure as a numerical model with many degrees-of-freedom. However the FEM needs much computation time and storage in this case. The authors developed the finite element-transfer stiffness coefficient method (FE-TSCM) for overcoming the drawback of the FEM. In this paper, the authors apply the FE-TSCM to the in-plane free vibration analysis of plates with various shapes. Two numerical examples, a rectangular plate and a triangular plate, are used to compare the results of the FE-TSCM and the FEM. Through the numerical calculation, we confirm that the FE-TSCM can be applied to the plates with various shapes and is effective to in-plane free vibration analysis of plates.

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Free Vibration Analysis of Plate Structures Using Finite Element-Transfer Stiffness Coefficient Method

  • Park, Myung-Soo
    • Journal of Mechanical Science and Technology
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    • v.17 no.6
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    • pp.805-815
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    • 2003
  • In order to execute efficiently the free vibration analysis of 2-dimensional structures like plate structures, the author developed the finite element-transfer stiffness coefficient method. This method is based on the combination of the modeling techniques in the FEM and the transfer technique of the stiffness coefficient in the transfer stiffness coefficient method. Numerical results of the simply supported and the elastic supported rectangular plates showed that the present method can be successfully applied to the free vibration analysis of plate structures on a personal computer. We confirmed that, in the case of analyzing the free vibration of rectangular plate structures, the present method is superior to the FEM from the viewpoint of computation time and storage.

Frequency-Phase Method to Measure Material Damping in a Nonlinear Range (비선형 영역에서의 재료감쇠비 측정을 위한 주파수-위상각법)

  • 우규석;조성호
    • Proceedings of the Korean Geotechical Society Conference
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    • pp.533-540
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    • 2001
  • Material damping is an important parameter to evaluate the site response by a dynamic loading. Currently the material damping of the subgrade is mainly determined by a resonant column testing. Typical methods to evaluate material damping include half-power bandwidth method and free-vibration decay method. In the large strain range, the half-power bandwidth method gives an erratic damping factor, because the method is based on the assumption of the linear behavior of a specimen. The free-vibration decay method has also limitations in that the damping factors vary with the range of cycles in calculation, and also in that the specific shear strain can not be designated for the free vibration. In this study, the frequency-phase method, which was developed to evaluate material damping of a beam simply supported, is introduced to evaluate the material damping by the resonant column testing. Also, the comparison among half-power method, free-vibration decay method and the frequency-phase method is provided for a remolded sand.

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Vibration Characteristics of Thin-Walled Beams (두께가 얇은 단면을 갖는 보의 진동특성)

  • Oh, Sang-Jin;Lee, Jae-Young;Mo, Jeong-Man;Park, Kwang-Kyou
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.709-712
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    • 2004
  • A study of the coupled flexural-torsional vibrations of thin-walled beams with monosymmetric cross-section is presented. The governing differential equations for free vibration of such beams are solved numerically to obtain natural frequencies and their corresponding mode shapes. The beam model is based on the Bernoulli-Euler beam theory and the effect of warping is taken into consideration. Numerical results are given for two specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints both including and excluding the effect of warping stiffness. The effect of warping stiffness on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

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Modal Vibration Characteristics of an Annular Disk Containing Evenly Spaced Narrow Radial Slots (등간격의 좁은 반경방향 슬롯을 가진 환형 박판의 고유진동 특성)

  • Lee, Hyeong-Ill
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.6
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    • pp.560-568
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    • 2009
  • Modal vibration characteristics of a thin annular disk containing narrow radial slots are studied numerically and experimentally. Existing analytical solution is examined based on these results revealing that it can not precisely predict eigenvalues of the disk with slots since it does not accurately consider change in the vibration modes and change in strain energy density distributions due to the slots. Parametric study on slot length found that distortions in the mode shape as well as changes in the corresponding natural frequencies are proportional to the slot length. Consequently, errors in the calculated eigenvalues are also proportional to the slot length and accurate data can not be obtained with existing analytical solution above a certain level of slot length. Same phenomena can be observed in both free-free disk and fixed-free disk.