Crack effect on dynamic stability of beams under conservative and nonconservative forces

Abstract

The purpose of this paper is to investigate the dynamic stability of beams containing a single crack subjected to conservative and nonconservative forces. The governing equation of the system can be derived from the extended Hamilton’s principle in which the kinetic energy, the elastic potential energy, the conservative work and the nonconservative work must be taken into account. The local flexibility matrix of a beam of a rectangular cross-section with a single edge crack is employed in order to perform numerical analysis. The investigated cracked beams are subjected to triangularly distributed subtangential forces, which are the combination of axial and tangential forces. The studied cracked beams become unstable in the form of either flutter or divergence, depending on crack parameters and on the degree of nonconservativeness of the load, when boundary conditions are fixed.