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.
- Petroleum Institute
A Mathematical Model to Overcome the Discrepancies Between Continuous Systems and Their Discrete Approximation
Singh, KV, & Ram, YM. "A Mathematical Model to Overcome the Discrepancies Between Continuous Systems and Their Discrete Approximation." Proceedings of the ASME 2002 Engineering Technology Conference on Energy. Engineering Technology Conference on Energy, Parts A and B. Houston, Texas, USA. February 4–5, 2002. pp. 605-611. ASME. https://doi.org/10.1115/ETCE2002/OT-29157
Download citation file: