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: ryszard.holubowski@pwr.edu.pl

Abstract

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.