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Structural Engineering and Mechanics Volume 19, Number 5, March 30 2005 , pages 551-566 DOI: https://doi.org/10.12989/sem.2005.19.5.551 |
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Exact natural frequencies of structures consisting of two-part beam-mass systems |
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H. Su and J. R. Banerjee
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| Abstract | ||
| Using two different, but related approaches, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam. The first approach is based on matrix transformation while the second one is a direct approach in which the kinematical conditions at the interfaces of the two-part beam-mass system are satisfied. Both procedures allow an exact free vibration analysis of structures such as a plane or a space frame, consisting of one or more two-part beam-mass systems. The two-part beam-mass system described in this paper is essentially a structural member consisting of two different beam segments between which there is a rigid mass element that may have rotatory inertia. Numerical checks to show that the two methods generate identical dynamic stiffness matrices were performed for a wide range of frequency values. Once the dynamic stiffness matrix is obtained using any of the two methods, the Wittrick-Williams algorithm is applied to compute the natural frequencies of some frameworks consisting of two-part beam-mass systems. Numerical results are discussed and the paper concludes with some remarks. | ||
| Key Words | ||
| dynamic stiffness method; beam-mass systems; free vibration; Wittrick-Williams algorithm. | ||
| Address | ||
| School of Engineering and Mathematical Sciences, City University, London, Northampton Square, London, EC1V OHB, England, U.K. | ||