A Method for Linearization of a Beam Problem
The bending vibrations of an elastic shaft under action of compression are considered. Taking into account the beam torsion, the eigenparameter appears nonlinearly into the model fourth-order differential equation. We propose an approach for avoiding this nonlinearity using an appropriate mixed formulation and thus some variational numerical methods could be applied in a standard way.
The possibility for symmetrization of the weak mixed formulation and corresponding finite element analysis are presented. Different matrix structures related to the proposed approach and its finite element implementation are discussed. Finally, we illustrate the method by numerical example.
This work was partially supported by the Technical University of Gabrovo under grant D1602E/2016.
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