Free Vibration of a Simply Supported Bar With a Linearly Variable Height of Cross Section

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Abstract
The problem of vibration of nonhomogeneous bars or bars of variable cross section1 leads to differential equations, which are generally unsolvable by formal integration. It is known that functional coefficients occur in these equations, which make it difficult, if not impossible, to obtain exact solutions by simple integration. Several exact solutions obtained for a few special cases and also some interesting approximate solutions are mentioned in the paper.

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