Abstract
We show that for some non-uniform rods and beams the equation of motion can be transformed into the equation of motion for a uniform rod or beam. Then, when the ends are completely fixed, the eigenvalues of the non-uniform continuum are the same as those of uniform rods or beams. For other end support conditions, exact solutions are obtained. An efficient procedure is used to analyze the free vibration of non-uniform beams with general shape and arbitrary boundary conditions. Simple formulas are presented for predicting the fundamental natural frequency of non-uniform beams with various end support conditions.
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