Structural Engineering and Mechanics

  • 제12권1호
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  • Pages.85-100
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  • 2001
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Classes of exact solutions for several static and dynamic problems of non-uniform beams

  • Li, Q.S. (Department of Building and Construction, City University of Hong Kong)
  • 발행 : 2001.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

키워드

참고문헌

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피인용 문헌

  1. Buckling of Non-Uniform Columns with an Arbitrary Number of Cracks vol.220, pp.6, 2006, https://doi.org/10.1243/09544062C04505
  2. A spatial displacement model for horizontally curved beams vol.15, pp.1, 2003, https://doi.org/10.12989/sem.2003.15.1.151
  3. A new functional perturbation method for linear non-homogeneous materials vol.42, pp.5-6, 2005, https://doi.org/10.1016/j.ijsolstr.2004.08.010
  4. Torsional vibration of multi-step non-uniform rods with various concentrated elements vol.260, pp.4, 2003, https://doi.org/10.1016/S0022-460X(02)01010-6