Vibrations of Elliptic Arc Bar Perpendicular to its Plane

Abstract

We have researched the vibrations of elliptic arc bar perpendicular to its plane. We obtain the Lagrangian of curved bars expressed by arc length, and then by using a new variable we reconstruct the Lagrangian, from which we obtain the equations of motion and the boundary conditions. We solve the equations of motion in the case of elliptic bar and show in graphs the frequencies and the modes of vibrations of symmetric elliptic arc bars. Their boundary conditions are built-in, rolled and supported at both ends. This method is also useful to research other curved bars as cosine, catenary and parabolic bars.