Structural Engineering and Mechanics

  • 제21권3호
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  • Pages.351-367
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  • 2005
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On the natural frequencies and mode shapes of a uniform multi-span beam carrying multiple point masses

  • Lin, Hsien-Yuan (Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-Sen University) ;
  • Tsai, Ying-Chien (Department of Mechanical Engineering, Cheng Shiu University)
  • 투고 : 2004.12.10
  • 심사 : 2005.07.05
  • 발행 : 2005.10.20
⟨ 이전 논문 다음 논문 ⟩

초록

Multi-span beams carrying multiple point masses are widely used in engineering applications, but the literature for free vibration analysis of such structural systems is much less than that of single-span beams. The complexity of analytical expressions should be one of the main reasons for the last phenomenon. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-span uniform beam carrying multiple point masses. First, the coefficient matrices for an intermediate pinned support, an intermediate point mass, left-end support and right-end support of a uniform beam are derived. Next, the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the related eigenfunctions respectively. The effects of in-span pinned supports and point masses on the free vibration characteristics of the beam are also studied.

키워드

참고문헌

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  6. Differential transform method and numerical assembly technique for free vibration analysis of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and rotary inertias vol.53, pp.3, 2015, https://doi.org/10.12989/sem.2015.53.3.537