Stability maps of a cracked Timoshenko beam resting on elastic soils under sub-tangential forces

The goal of this paper is to generate the stability maps for an elastic cracked beam resting on elastic soils and loaded by a constant distribution of sub-tangential forces. The soil behavior is simulated by a two-parameter Pasternak model. Firstly, the extend version of the Hamilton principle is used to formulate the weak form of the governing equation for the undamaged beam problem. Secondly, a finite element procedure, in which the effect of an open surface crack is computed via the Line-spring model, leads to the discrete governing equation for the cracked beam. Finally, the effect of several parameters on divergence or flutter instability, such as the crack depth and location, the non-conservativeness of the applied load as well as the stiffness of the two soil parameters, is highlighted.