FREE VIBRATION OF NON-PRISMATIC BEAMS

Abstract eng:
The analysis of non-prismatic beams by the displacement based formulations (stiffness method) includes the inherent approximations due to the fundamental assumptions of the displacement fields in those methods. These assumptions usually lead to the violation of one of the three fundamental equations as the necessary and sufficient conditions for the problem solution. One of the most convenient methods for overcoming this problem is to use a flexibility based formulation (force method) in the analysis. In this paper, a new formulation for the non-prismatic Euler–Bernoulli Beams based on the implicit derivation of exact shape functions is presented. Utilizing this method, the stiffness and consistent mass matrices of these beams have been obtained in an exact fashion, and the vibration properties of the beam have been studied. The results obtained show the competency of the proposed formulation in both exactness and economy in comparison to the methods present in technical literature.

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