Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions
ORCID Identifiers
Document Type
Article
Source of Publication
JVC/Journal of Vibration and Control
Publication Date
9-1-2019
Abstract
© The Author(s) 2019. There are well-known expressions for natural frequencies and mode shapes of a Euler-Bernoulli beam which has classical boundary conditions, such as free, fixed, and pinned. There are also expressions for particular boundary conditions, such as attached springs and masses. Surprisingly, however, there is not a method to calculate the natural frequencies and mode shapes for a Euler–Bernoulli beam which has any combination of linear boundary conditions. This paper describes a new method to achieve this, by writing the boundary conditions in terms of dynamic stiffness of attached elements. The method is valid for any boundaries provided they are linear, including dissipative boundaries. Ways to overcome numerical issues that can occur when computing higher natural frequencies and mode shapes are also discussed. Some examples are given to illustrate the applicability of the proposed method.
DOI Link
ISSN
Publisher
SAGE Publications Inc.
Volume
25
Issue
18
First Page
2473
Last Page
2479
Disciplines
Life Sciences
Keywords
Dynamic stiffness, general boundary condition, mode shape, natural frequency, numerical stable equations
Scopus ID
Recommended Citation
Gonçalves, Paulo J.Paupitz; Brennan, Michael J.; Peplow, Andrew; and Tang, Bin, "Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions" (2019). All Works. 815.
https://zuscholars.zu.ac.ae/works/815
Indexed in Scopus
yes
Open Access
no