Structural Engineering and Mechanics

  • 제4권5호
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  • Pages.553-568
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  • 1996
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Exact calculation of natural frequencies of repetitive structures

  • Williams, F.W. (Division of Structural Engineering, School of Engineering, University of Wales Cardiff) ;
  • Kennedy, D. (Division of Structural Engineering, School of Engineering, University of Wales Cardiff) ;
  • Wu, Gaofeng (Division of Structural Engineering, School of Engineering, University of Wales Cardiff) ;
  • Zhou, Jianqing (Division of Structural Engineering, School of Engineering, University of Wales Cardiff)
  • 발행 : 1996.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

Finite element stiffness matrix methods are presented for finding natural frequencies (or buckling loads) and modes of repetitive structures. The usual approximate finite element formulations are included, but more relevantly they also permit the use of 'exact finite elements', which account for distributed mass exactly by solving appropriate differential equations. A transcendental eigenvalue problem results, for which all the natural frequencies are found with certainty. The calculations are performed for a single repeating portion of a rotationally or linearly (in one, two or three directions) repetitive structure. The emphasis is on rotational periodicity, for which principal advantages include: any repeating portions can be connected together, not just adjacent ones; nodes can lie on, and members along, the axis of rotational periodicity; complex arithmetic is used for brevity of presentation and speed of computation; two types of rotationally periodic substructures can be used in a multi-level manner; multi-level non-periodic substructuring is permitted within the repeating portions of parent rotationally periodic structures or substructures and; all the substructuring is exact, i.e., the same answers are obtained whether or not substructuring is used. Numerical results are given for a rotationally periodic structure by using exact finite elements and two levels of rotationally periodic substructures. The solution time is about 500 times faster than if none of the rotational periodicity had been used. The solution time would have been about ten times faster still if the software used had included all the substructuring features presented.

키워드

참고문헌

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  22. Wittrick, W.H. and Williams, F.W. (1973), "New procedures for structural eigenvalue calculations", 4th Australasian Conf. on the Mechanics of Structures and Materials, U. of Queensland, Brisbane, Queensland, Austalia, 299-308.

피인용 문헌

  1. A Reduced-Order Model of Detuned Cyclic Dynamical Systems With Geometric Modifications Using a Basis of Cyclic Modes vol.132, pp.11, 2010, https://doi.org/10.1115/1.4000805
  2. Optimal design of infinite repetitive structures vol.18, pp.2-3, 1999, https://doi.org/10.1007/BF01195995