Abstract
Introducing the concept of basic displacement functions (BDFs), a new beam element is presented for the analysis of rotating tapered beams. BDFs are obtained using the energy method; i.e., the unit-load method. Following the basic principles of structural mechanics, it is shown that the shape functions and consequently the structural matrices can be derived in terms of BDFs. The method is a combination of flexibility and stiffness methods and is considered as the logical extension of the conventional finite element method. The method is employed for both static and free vibration analyses of different types of tapered beams, and the results compare well with those in the literature. Finally, the effects of the taper ratio, hub radius and rotating speed parameter on the natural frequencies and static deflection are investigated. The results obtained are satisfactory even for only a few elements.
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