Coupled vibrations of beams with lateral loads

Abstract eng:
The objective of this report is to analyse the free vibration and mode shapes of straight beams where the coupling between the bending and torsion is induced by steady state lateral loads. The governing differential equations and boundary conditions for coupled vibrations of Euler-Bernoulli-Vlasov beams are performed by using the virtual work principle which includes the second order terms of finite beam rotations. Closed form solution is derived for the coupled frequencies and mode shapes of a symmetric beam with simply supported ends under uniform bending. A finite element model with seven degrees of freedoms per node is also presented. To illustrate the accuracy of this formulation, numerical solutions are presented and compared with available solutions. The investigation presented in this report is motivated by the fact that for dynamic structural analyses that are sensitive to the modal vibration properties small errors in the natural frequencies and mode shapes may produce sizable errors in the modal time history and associated structural response.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket