Clustered natural frequencies in multi-span beams with constrained characteristic functions

Article type: Research Article

Authors: Saeedi, Khodabakhsh | Bhat, Rama B.

Affiliations: Mechanical and Industrial Engineering Department, Concordia University, Montreal, QC, H3G1M8, Canada

Note: [] Corresponding author. Tel.: +1 514 848 2424 Ext. 7268; E-mail: k_saeedi@encs.concordia.ca

Abstract: A study of the natural frequencies and mode shapes of a multi-span beam is carried out by introducing constrained beam characteristic functions. The conventional method used for the dynamic analysis of such a beam is to consider span-wise characteristic function solution and then to solve it by using compatibility conditions such as the continuity in the a slope and bending moment at the intermediate supports and boundary conditions at the ends. In the method proposed here, the matrix size is reduced and, if the support conditions are symmetric about the midpoint, the symmetry and anti-symmetry conditions at the midpoint can be conveniently exploited for computational economy. The natural frequencies occur in clusters, each one containing the number of natural frequencies equal to the number of spans. The results are presented and discussed.

Keywords: Multi-span beam, vibration, intermediate support, reaction force

DOI: 10.3233/SAV-2010-0592

Journal: Shock and Vibration, vol. 18, no. 5, pp. 697-707, 2011