MATEC Web Conf.
Volume 285, 201916th Symposium of Structural Dynamics (DYNKON 2019)
|Number of page(s)||6|
|Published online||12 July 2019|
Application of the two-parameter single shooting method for natural vibration analysis of Euler-Bernoulli beams
Wroclaw University of Science and Technology, Faculty of Civil Engineering, Wroclaw, Poland
* Corresponding author: firstname.lastname@example.org
The paper presents a new method of calculating the natural frequencies and modes of Euler-Bernoulli beams. The formulated algorithm is based on the fourth order homogeneous ordinary differential equation of motion that allows different support conditions to be considered. The idea of the method is to replace a two-point boundary value problem with an initial value problem. Distinct from the classic approach, where only one unknown parameter is considered, the method enables problems with two parameters to be solved. The proposed two-parameter version of the single shooting method is verified on the example of a non-prismatic simply supported beam and a prismatic propped cantilever beam resting on Winkler foundation and loaded by axial force. The obtained results confirm the correctness and high effectiveness of the presented method.
© The Authors, published by EDP Sciences, 2019
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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