Free in-plane vibration of cracked curved beams: Experimental, analytical, and numerical analyses

Abstract

In this study, free vibration of a cracked curved beam utilizing analytical, numerical, and experimental methods is investigated. The differential quadrature element method is used to solve the equations of motion numerically. The governing equations are also solved analytically. The crack, which is considered to be open, is modeled as a rotational spring. Furthermore, the effect of curvature on mode shapes is studied. To verify the validity of the proposed methods of determining frequencies and mode shapes, an experimental modal analysis test is conducted on a sample beam having crack with some different depths. This study revealed that the behavior of curved beams toward the mode transition phenomenon depends greatly on the boundary conditions of the beam. Also, both the location and depth of crack have considerable effects on natural frequencies.