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Structural Engineering and Mechanics Volume 21, Number 3, October20 2005 , pages 351-367 DOI: https://doi.org/10.12989/sem.2005.21.3.351 |
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On the natural frequencies and mode shapes of a uniform multi-span beam carrying multiple point masses |
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Hsien-Yuan Lin and Ying-Chien Tsai
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| Abstract | ||
| 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. | ||
| Key Words | ||
| single-span beam; multi-span beam; numerical assembly method (NAM); natural frequency; mode shape. | ||
| Address | ||
| Hsien-Yuan Lin; Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-Sen University,70 Lien-hai Rd. Kaohsiung 804, Taiwan, Republic of China Ying-Chien Tsai; Department of Mechanical Engineering, Cheng Shiu University, Kaohsiung, Taiwan 800, Republic of China | ||