PSI - Issue 63

Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 63 (2024) 35–42

Keywords: natural frequency; mode shape; stiffness matrix; mass matrix; bisection method 1. Introduction Knowledge of natural frequencies and mode shapes is necessary for structures that are dynamically loaded. Dynamic effects are caused by inertial forces that arise during the accelerated motion of masses. It can be caused by the movement of the structure itself, the movement of objects placed on the structure, or the movement of the structure surroundings (air, water, soil). A number of papers are focused on solving the natural frequencies and mode shapes of structures. Some present analytical analysis, others numerical analysis, and some present experimental work. 22nd International Conference on Modelling in Mechanics 2024 Numerical Solution of Natural Frequencies and Mode Shapes Lenka Koubova a, * a Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvika Podeste 1875/17, 708 00 Ostrava-Poruba, Czech Republic Abstract Every construction has a set of their natural frequencies (resonant frequencies) and mode shapes that depend on its material, structure, and boundary conditions. A mode shape is a deflection pattern. It is related to a particular natural frequency and represents the relative displacement of all parts of a construction for that particular mode. This paper deals with numerical solutions of natural frequencies and mode shapes. The method of stiffness constants and bisection method is used. The procedure can be used for any planar bar construction. First, the mode shapes of the simple beam are solved, where the solution is compared with the results obtained using known relationships. The article further describes the solution of the parabolic arc. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers

* Corresponding author. Tel.: +420 596 991 919. E-mail address: lenka.koubova@vsb.cz

2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of 22nd International Conference on Modelling in Mechanics 2024 organizers 10.1016/j.prostr.2024.09.006