Analytical approximations for parabolic curved beams

Abstract

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.

Aproximaciones analiticas para el desplazamiento tangencial y radial se encontraron al restringir la rotacion de vigas curvas. Analisis de restriccion de movimiento mostro que solo la restriccion rotacional de la viga permite el desacoplamiento de las ecuaciones diferenciales que la modelan. Al simplicar el modelo por medio de analisis grafico se encontraron soluciones aproximadas para el desplazamiento tangencial y radial. Una funcion generalizada, un radio de curvatura adimensional y su derivada fueron desarrolladas. Dos soluciones de recurrencia para una solucion en serie del desplazamiento tangencial fueron encontradas. Una solucion aproximada al desplazamiento radial y cinco aproximaciones para el desplazamiento tangencial son presentadas.