Analytical and numerical studies on the slope inertia-based Timoshenko beam
Abstract
In this work, a comparative study is performed between the slope inertia-based Timoshenko (SIBT) beam and other classical beam theories. We prove that the SIBT beam comprehensively incorporates physical effects of shear deformation, rotary inertia, and shear inertia. The transcendental equations of frequency are derived from the initial parameter solutions, and then used to demonstrate that the frequency spectrum of the SIBT beam theory has only one branch. A finite element implementation of the SIBT beam is developed and verified using closed-form solutions. We find that the SIBT and Love theories predict the same mode shape but different frequencies. Comparisons of frequency spectra obtained from different beam theories also suggest that the shear deformation influences the frequency more than the rotary inertia and that the SIBT beam theory predicts lower frequency values due to its complete consideration of shear deformation, rotary inertia and shear inertia. Parametric studies demonstrate that boundary conditions influence lower order frequencies predicted by the SIBT beam theory significantly, but only marginally influence the high order frequencies; they also show that the frequency spectrum of the SIBT beam theory has an upper bound.
- Publication:
-
Journal of Sound Vibration
- Pub Date:
- May 2020
- DOI:
- 10.1016/j.jsv.2020.115227
- Bibcode:
- 2020JSV...47315227X
- Keywords:
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- Slope inertia;
- Shear inertia;
- Upper bound;
- Wave number;
- Frequency spectrum