Abstract
Propose
Investigation of mathematical solutions for including the self-weight of a column for calculating buckling critical load. The complexity of including self-weight resides in the fact that the mathematical formulation depends on elliptical integral solutions related to differential equations of the problem.
Method
Comparing the analytical solutions with computation modeling. The obtained results with these computational models are approximate since they depend on the discretization of the domain of the problem while analytical solutions tend to be exact. An experimental activity was carried out for analyzing mathematical accuracy.
Results
The investigation of buckling was performed through static as well as dynamic analysis. The results found shown differences smaller than 5% among the mathematical investigated solution. Besides that, all solutions represented well the problem in comparison with a laboratory test.
Conclusion
It has been evaluated solutions for stability analyses of bars under self-weight, using Euler–Greenhill analytical approach, solutions with the eigenvalues from FEM analysis, and also a dynamic solution based on the Rayleigh’s method, comparing them with dynamic laboratory tests. Can be concluded that the mathematical ways and the experimental investigation had a good agreement.
Level of evidence
IV, evidence obtained from multiple mathematical methods, static and dynamic, is experimentally confirmed.
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Wahrhaftig, A.d.M., Magalhães, K.M.M., Brasil, R.M.L.R.F. et al. Evaluation of Mathematical Solutions for the Determination of Buckling of Columns Under Self-weight. J. Vib. Eng. Technol. 9, 733–749 (2021). https://doi.org/10.1007/s42417-020-00258-7
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DOI: https://doi.org/10.1007/s42417-020-00258-7