Structural Engineering and Mechanics Volume 19, Number 5, March 30 2005, pages 551566
DOI: http://dx.doi.org/10.12989/sem.2005.19.5.551  
Exact natural frequencies of structures consisting of twopart beammass systems  
H. Su and J. R. Banerjee


Abstract [Full Text]  
Using two different, but related approaches, an exact dynamic stiffness matrix for a twopart beammass system is developed from the free vibration theory of a BernoulliEuler 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 twopart beammass 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 twopart beammass systems. The twopart beammass 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 WittrickWilliams algorithm is applied to compute the natural frequencies of some frameworks consisting of twopart beammass systems. Numerical results are discussed and the paper concludes with some remarks.  
Key Words  
dynamic stiffness method; beammass systems; free vibration; WittrickWilliams algorithm.  
Address  
School of Engineering and Mathematical Sciences, City University, London, Northampton Square, London, EC1V OHB, England, U.K.  