The classical finite element and finite difference formulation in structural dynamics leads to an algebraic eigenvalue problem whereas the continuous model however leads to a transcendental eigenvalue problem. This paper demonstrates the discrepancies between continuous systems and their discrete approximations and, introduces a finite dimensional transcendental eigenvalue method, which approximates the spectrum of the continuous system accurately. Illustration of the effectiveness and applicability of such a model has been shown with an example of an axially vibrating tapered rod.

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