I want to model the bending mode vibrations along with the first 3 or 4 shell modes in case of pipes with high L/R ratios and low R/h ratios. Please suggest the way to model it?
Hello Shashihar,
For thick shell structures, we have Reissner Mindlin model. If you want to study the mechanical behavior of thin membranes, the Kirchhoff-Love model is employed.
Bests,
Thai.
Thank you Tran Quoc Thai . There are various shell theories which considers the shear deformation (Reissner-Mindlin) like Love's, Donnell's, Sander's,.. etc. Each theory has its own restrictions on L/R and R/h ratios. So if I have higher L/R ratios and lower R/h ratios, which theory will be suitable to apply?
Thank you Victor J. Аdlucky . If I use the beam theory it can not take shell modes into account. I need at least first 3 or 4 shell modes to be accounted.
Hello,
Love's simplifications may work well. It assumes that the strain of the thickness is negligible and that the displacements vary linearly over the thickness.
In your case, being the L/R ratio high and the R/h ratio low, radial-tangential plane is the one to be concerned about. Applying Love's theory and taken into account shear deflection and rotary inertia in that plane, you can obtain accurate results for quite thick shells. I have carried out some analytical calculations like this and I'd say you can obtain reasonable results even for R/h ratios close to 5.
I don't think more complex models, like the most general Byrne, Flügge, Goldenveizer and Novozhilov's equations, will show a significant difference.
Br,
Alex.
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