Perez-Martinez, Angel M.

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Analytical approximations for parabolic curved beams
(2018) Perez-Martinez, Angel M.; Santana, Samuel; College of Agricultural Sciences; Fernandez, Felix; Marrero, Pablo; Ramos, Rafael; Department of Physics; Castillo, Paul
Analytical approximations for the tangential and radial degrees of freedom for curved beams were found by restricting the rotation of the curved beam. Results showed that only the restriction in the rotational degree of freedom uncouples the differential equations in the radial and tangential component. Simplifications by graphical analysis in the region of interest allowed us to find approximated solutions in the radial and tangential displacement of the curved beam. A generalized shape function for the curved beam, a non-dimensional radius of curvature and its derivative were presented. Two recurrence formulas for a series solution in the tangential displacement were found. One approximated solution for the radial displacement and five approximations for the tangential displacement are presented.