Using energy methods to compare linear vibration models

D. Civin, N.F.J. van Rensburg and A.J. van der Merwe

Applied Mathematics and Computation, 2018, vol. 321, issue C, 602-613

Abstract: In this paper, it is proved that the series representation of the solutions of the general linear vibration model with modal damping, is valid with respect to the energy norm. The partial sums of the series representation of solutions may therefore be used to compare different models. Parseval-type relationships are obtained for the eigenfunction expansions of functions. These relationships are used to derive expressions for the relative error in energy for partial sum approximations of functions. An example is included where a string model (wave equation model) and a modified Euler–Bernoulli beam model for the transverse vibration of a steel wire are compared.

Keywords: Linear vibration models; Eigenfunction expansion; Energy norm (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317307816
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:321:y:2018:i:c:p:602-613

DOI: 10.1016/j.amc.2017.11.008

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().