Cracks Interaction Effect on the dynamic stability of beams under conservative and nonconservative forces

This study is an extension of the paper by E. Viola and A. Marzani [1] where the eigenfrequencies and critical loads of a single cracked beam subjected to conservative and nonconservative forces have been investigated. Here the aim is to analyze the dynamic stability of T cross section beams with multiple cracks. A doubly cracked Euler-Bernoulli beam subjected to triangularly distributed subtangential forces, which are the combination of axial and tangential forces, is considered. The governing equation of the system is derived via the extended Hamilton’s principle in which the kinetic energy, the elastic potential energy, the conservative work and the nonconservative work are taken into account. The local flexibility matrix for a beam with T cross-section is used to model the cracked section. The results show that for given boundary conditions cracked beams become unstable in the form of either flutter or divergence depending on the crack parameters, the nonconservativeness of the applied load as well as the interaction of the two cracks.