Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions
Gonçalves, Paulo J.Paupitz ; Brennan, Michael J. ; Peplow, Andrew LU
and Tang, Bin
(2019)
In JVC/Journal of Vibration and Control
25(18).
p.2473-2479
- Abstract
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... (More)
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.
(Less)
- author
- Gonçalves, Paulo J.Paupitz
; Brennan, Michael J.
; Peplow, Andrew
LU
and Tang, Bin
- publishing date
- 2019-09-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Dynamic stiffness, general boundary condition, mode shape, natural frequency, numerical stable equations
- in
- JVC/Journal of Vibration and Control
- volume
- 25
- issue
- 18
- pages
- 7 pages
- publisher
- SAGE Publications
- external identifiers
-
- scopus:85068347170
- ISSN
- 1077-5463
- DOI
- 10.1177/1077546319857336
- language
- English
- LU publication?
- no
- id
- dd276814-8f83-4e7b-9107-9f38c161ba07
- date added to LUP
- 2021-01-20 18:27:01
- date last changed
- 2022-04-26 23:50:48
@article{dd276814-8f83-4e7b-9107-9f38c161ba07,
abstract = {{<p>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.</p>}},
author = {{Gonçalves, Paulo J.Paupitz and Brennan, Michael J. and Peplow, Andrew and Tang, Bin}},
issn = {{1077-5463}},
keywords = {{Dynamic stiffness; general boundary condition; mode shape; natural frequency; numerical stable equations}},
language = {{eng}},
month = {{09}},
number = {{18}},
pages = {{2473--2479}},
publisher = {{SAGE Publications}},
series = {{JVC/Journal of Vibration and Control}},
title = {{Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions}},
url = {{http://dx.doi.org/10.1177/1077546319857336}},
doi = {{10.1177/1077546319857336}},
volume = {{25}},
year = {{2019}},
}