Structural Engineering and Mechanics

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Exact natural frequencies of structures consisting of two-part beam-mass systems

  • Su, H. (School of Engineering and Mathematical Sciences, City University) ;
  • Banerjee, J.R. (School of Engineering and Mathematical Sciences, City University)
  • Received : 2004.06.17
  • Accepted : 2005.01.13
  • Published : 2005.03.30
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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.

Keywords

References

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