A Mathematical Model to Overcome the Discrepancies Between Continuous Systems and Their Discrete Approximation

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.