Structural Engineering and Mechanics

  • 제63권4호
  • /
  • Pages.551-565
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  • 2017
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of cracked Timoshenko beams carrying spring-mass systems

  • Tan, Guojin (College of Transportation, Jilin University) ;
  • Shan, Jinghui (College of Transportation, Jilin University) ;
  • Wu, Chunli (College of Transportation, Jilin University) ;
  • Wang, Wensheng (College of Transportation, Jilin University)
  • 투고 : 2017.01.16
  • 심사 : 2017.06.14
  • 발행 : 2017.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Jilin University

참고문헌

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피인용 문헌

  1. Free Vibration of the Cracked Non-uniform Beam with Cross Section Varying as Polynomial Functions vol.22, pp.11, 2017, https://doi.org/10.1007/s12205-018-1833-5
  2. Vibratory characteristics of cracked non-uniform beams with different boundary conditions vol.33, pp.1, 2019, https://doi.org/10.1007/s12206-018-1238-x
  3. Free vibration of multi-cracked beams vol.79, pp.4, 2017, https://doi.org/10.12989/sem.2021.79.4.441