I work on some eigenfrequencies analysis of that kind of beams, and still search for ''good'' dimension ratio.
I think if you changed the aspect ratio of the beam from thin(~
The "ideal" aspect ratio or slenderness will depend on the maximum frequency you are interested in; high frequencies probably imply some transverse shear deformation, thus the Timoshenko formulation can give you a better solution. Indeed, I think that there isn't some aspect ratio measure that can guarantee good results, also density and cross sections geometry can affect your results. By the way, it also necessary to define what "good" means.
Martin, when I say "good", I mean on the dimension ratio for which is obvious difference between results in first 3 or 5 frequencies for these two theories.
Aleksandar, I understand, but then I must ask what is obvious in terms of numbers. You need to define percentile changes or some objective measure in order to address accuracy. I strongly think that there isn't a slenderness ratio from which results change from good to bad.
Martin, maybe I didn't explain my question very well. I know that there is no example for which some results change from ''good'' to ''bad'', or vice versa. But, I would like to compare some my new results with example from paper:
D. Cekus, “FREE VIBRATION OF A CANTILEVER TAPERED TIMOSHENKO BEAM”, Scientific Research of the Institute of Mathematics and Computer Science 4, Vol. 11, pp. 11-17, (2012.)
In this paper, author works under Timoshenko beam assumptions, and hi developed some approximate metod for determining natural frequencies. Also, he made an experiment for verification of the method, and there is a relatively good agreemenet betweeen results.
However, I work in the same example, and I got almost identical results when used both assumptions, Euler and Timoshenko. After changing the thickness of the beam from h=0.005m to h=0.1m (beam lenght is l=0.5m), on the advice of Ramy, there is a difference in results, and results based on the Timoshenko assumptions are beter (error as compared to the results of the experiment is smaller).
Thank you on suggestions Martin. It would be usefull for my research.
A pinned-pinned beam has a pure shear mode under Timoshenko theory but not present under Euler-Bernoulli. Furthermore, all beams have a spectrum of frequencies under Timoshenko theory that are not predicted by Euler-Bernoulli theory. Whether or not these additional modes are physical has been settled by comparison with 3D finite element calculations and by experiment. The relative size of these frequencies depends on material properties, but it's not unusual for isotropic beams to see a few of the extra modes show up in the first ten modes. See A. Dixit's paper, "Mechanics-Based Explanation of the Second Frequency Branch of Timoshenko Beam Theory," at http://scholar.google.com/citations?view_op=view_citation&hl=en&user=5FJoYCkAAAAJ&citation_for_view=5FJoYCkAAAAJ:W7OEmFMy1HYC.
You can refer to the following paper comparing four beam theories :
Journal of Sound and
Thank you François. In the meantime, I've found mention paper, and I use in my research examples from there.
Aleksandar, I recently published a paper giving comparison between the frequencies of Timoshenko and Euler-Bernoulli beams theories. Although the paper deals primarily with damaged beams, there are a lot of results for undamaged beams too. The paper is given here: https://www.researchgate.net/publication/262690994_Single-beam_analysis_of_damaged_beams_Comparison_using_EulerBernoulli_and_Timoshenko_beam_theory
Article Single-beam analysis of damaged beams: Comparison using Eule...
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