Out-of-plane Vibrations of Inhomogeneous Curved Bars Having Varying Cross-sections

Abstract

An exact method using power series expansions is presented for solving out-of-plane free vibrations of inhomogeneous curved bars with varying curvatures and cross-sections. Equations of motion and boundary conditions are derived from the stationary conditions of the Lagrangian of curved bars. Natural frequencies and mode shapes are presented for elliptical and circular arc bars having both ends clamped and clamped-free ends.