Tapered Beam elements are of great importance in a wide range of structural applications because of their optimized distribution of strength and weight compared with the uniform ones. Vibration analysis of beams with variable properties has been receiving great interest from engineers and researchers for a long time. This paper presents the way in which new shape functions are constructed and used for analyzing free vibration of Timoshenko beams with linear variation in height or width and various boundary conditions. Fundamental frequencies from the present work are compared with those obtained by different formulation and approaches. The shape functions in the paper are derived for a solid rectangular beam with linearly taper changing in its sectional dimensions. With the aid of the consistently derived shape functions in the finite element calculation, the solution to vibration problems with the least number of elements can be evaluated with high accuracy. A detailed example is presented and compared with a reference work to illustrate the accuracy and computational efficiency for vibration analysis of linearly tapered Timoshenko beams.
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