• Title/Summary/Keyword: free vibration

Search Result 1,257, Processing Time 0.091 seconds

Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation

  • Civalek, Omer;Ozturk, Baki
    • Geomechanics and Engineering
    • /
    • v.2 no.1
    • /
    • pp.45-56
    • /
    • 2010
  • The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

Free Vibration Analysis of Timoshenko Arcs with Elastic Supports Using Transfer of Influence Coefficient (영향계수의 전달을 이용한 탄성 지지된 티모센코 호의 자유진동 해석)

  • Choi, Myung-Soo;Yeo, Dong-Jun
    • Journal of Power System Engineering
    • /
    • v.21 no.2
    • /
    • pp.70-76
    • /
    • 2017
  • When Timoshenko arcs considering the shear deformation and rotatory inertia have elastic supports, the authors analyze in-plane free vibration of them by the transfer influence coefficient method. This method finds the natural frequencies of them using the transfer of influence coefficient after obtaining the transfer matrix of arc element from numerical integration of the differential equations governing the vibration of arc. In this study, two computer programs were made by the transfer influence coefficient method and the transfer matrix method for analyzing free vibration of Timoshenko arcs. From numerical results of four computational models, we confirmed that the transfer influence coefficient method is a reliable method when analyzing the free vibration of Timoshenko arcs. In particular, the transfer influence coefficient method is a effective method when analyzing the free vibration of arcs with rigid supports.

Application of Numerical Differentiations in Free Vibration Analysis (자유진동 해석에서 수치미분의 응용)

  • 이병구;안대순;강희종;김권식
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
    • /
    • /
    • pp.814-818
    • /
    • 2003
  • This paper deals with the application of numerical differentiation in free vibration analysis. In the free vibration analysis, the derivative values of the given function are certainly used in calculation of structural parameters. For deriving the derivative values, both the time and labor are needed when the structures consist of non-linear geometries such as arches or curved beams. From this viewpoint, the numerical differentiation scheme is applied into the free vibration analysis. The numerical results obtained from the numerical differentiations are agreed very well with those obtained from the exact derivatives by analytical method. It is expected that the numerical differentiations can be utilized practically in the free vibration analysis.

  • PDF

Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study

  • AlSaid-Alwan, Hiyam Hazim Saeed;Avcar, Mehmet
    • Computers and Concrete
    • /
    • v.26 no.3
    • /
    • pp.285-292
    • /
    • 2020
  • In engineering structures, to having the projected structure to serve all the engineering purposes, the theory to be used during the modeling stage is also of great importance. In the present work, an analytical solution of the free vibration of the beam composed of functionally graded materials (FGMs) is presented utilizing different beam theories. The comparison of supposed beam theory for free vibration of functionally graded (FG) beam is examined. For this aim, Euler-Bernoulli, Rayleigh, Shear, and Timoshenko beam theories are employed. The functionally graded material properties are assumed to vary continuously through the thickness direction of the beam with respect to the volume fraction of constituents. The governing equations of free vibration of FG beams are derived in the frameworks of four beam theories. Resulting equations are solved versus simply supported boundary conditions, analytically. To verify the results, comparisons are carried out with the available results. Parametrical studies are performed for discussing the effects of supposed beam theory, the variation of beam characteristics, and FGM properties on the free vibration of beams. In conclusion, it is found that the interaction between FGM properties and the supposed beam theory is of significance in terms of free vibration of the beams and that different beam theories need to be used depending on the characteristics of the beam in question.

Eight-node field-consistent hexahedron element in dynamic problems

  • Rajendran, S.;Prathap, G.
    • Structural Engineering and Mechanics
    • /
    • v.8 no.1
    • /
    • pp.19-26
    • /
    • 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.

Static and free vibration behaviour of orthotropic elliptic paraboloid shells

  • Darilmaz, Kutlu
    • Steel and Composite Structures
    • /
    • v.23 no.6
    • /
    • pp.737-746
    • /
    • 2017
  • In this paper the influence of aspect ratio, height ratio and material angle on static and free vibration behaviour of orthotropic elliptic paraboloid shells is studied by using a four-node hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. A parametric study is carried out for static and free vibration response of orthotropic elliptic paraboloid shells with respect to displacements, internal forces, fundamental frequencies and mode shapes by varying the aspect and height ratios, and material angle.

A hybrid 8-node hexahedral element for static and free vibration analysis

  • Darilmaz, Kutlu
    • Structural Engineering and Mechanics
    • /
    • v.21 no.5
    • /
    • pp.571-590
    • /
    • 2005
  • An 8 node assumed stress hexahedral element with rotational degrees of freedom is proposed for static and free vibration analyses. The element formulation is based directly on an 8-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 20-node element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on Hellinger-Reissner variational principle. Numerical examples are presented to show the validity and efficiency of the present element for static and free vibration analysis.

An assumed-stress finite element for static and free vibration analysis of Reissner-Mindlin plates

  • Darilmaz, Kutlu
    • Structural Engineering and Mechanics
    • /
    • v.19 no.2
    • /
    • pp.199-215
    • /
    • 2005
  • An assumed stress quadrilateral thin/moderately thick plate element HQP4 based on the Mindlin/Reissner plate theory is proposed. The formulation is based on Hellinger-Reissner variational principle. Static and free vibration analyses of plates are carried out. Numerical examples are presented to show that the validity and efficiency of the present element for static and free vibration analysis of plates. Satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis.

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

  • Park, Myung-Soo
    • Journal of Mechanical Science and Technology
    • /
    • v.17 no.6
    • /
    • pp.805-815
    • /
    • 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.

Free Vibration Analysis of Double Cylindrical Shells Using Transfer of Influence Coefficent (영향계수의 전달에 의한 2중 원통형 셸의 자유진동해석)

  • Choi, Myung-Soo;Yeo, Dong-Jun
    • Journal of Power System Engineering
    • /
    • v.21 no.5
    • /
    • pp.48-54
    • /
    • 2017
  • The transfer influence coefficient method which is an vibration analysis algorithm based on the transfer of influence coefficient is applied to the free vibration analysis of double cylindrical shells. After the computational programs for the free vibration analysis of double cylindrical shells were made using the transfer influence coefficient method and the transfer matrix method, we compared the results using the transfer influence coefficient method with those by the transfer matrix method. The transfer influence coefficient method provided the good computational results in the free vibration analysis of double cylindrical shells. In particular, The results of the transfer influence coefficient method are superior to those of the transfer matrix method when the stiffness of internal springs connecting a inside cylindrical shell and a outside cylindrical shell is very large.