Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

The objective of this paper is to determine dynamic instability areas of moderately thick beams and frames. The effect of moderate thickness on resonance frequencies is considered, with transverse shear deformation and rotatory inertia taken into account. These relationships are investigated using the Timoshenko beam theory. Two methods, the harmonic balance method (HBM) and the perturbation method (PM) are used for analysis. This study also examines the influence of linear dumping on induced parametric vibration. Symbolic calculations are performed in the Mathematica programme environment.