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

Obara P., Gilewski W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2016

Vol. 64, nr 4

739--750

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.

A boundary integral equation formulation of moderately thick laminated anisotropic shallow shells

Wang J., Schweizerhof K.

Applied Mechanics and Engineering

1999

Vol. 4, no 4

621-639

In this paper, a boundary integral equation formulation of moderately thick laminated anisotropic shallow shells including transverse shear deformation is presented using the method of weighted residuals. Numerical computation of the boundary integral equation presented is discussed in detail. Some of numerical examples are given and compared with the exact solutions and the solutions available in the literature. The numerical results show that the method presented has good accuracy and high efficiency.