A SAFE formulation for modeling stress waves in elastic waveguides subjected to an initial 3D prestress

The importance of Ultrasonic Guided Waves in the field of nondestructive testing and structural health monitoring has increased considerably in recent years. Lately, researchers are trying to use guided waves to reveal the state of prestress in waveguides. Such information can be relevant, for example, in the buckling prediction of continuously welded rails due to high temperature, as well as for tuning guided wave ultrasonic set-up in deep underwater pipeline inspections. To proficiently exploit Guided Waves their dispersive characteristics, i.e. the solutions of the guided wave equation at several frequencies, must be known for the given waveguide. Even though various formulations can be founded in literature for wave propagations in prestressed structures [1, 2], to date the use of Semi Analytical Finite Element (SAFE) formulations is limited only to axially loaded elastic waveguides [3]. The aim of this work is to extend SAFE formulations in order to account for a generic threedimensional prestress field. To this end, the guided wave equation is derived in incremental form, based on a Lagrangian formulation in which the small displacement field associated to the wave motion is superimposed on the initially stressed state of the waveguide. The prestress enters the problem as a second order effect and leads to additional terms in the system potential energy. Expressions for the computation of fundamental quantities associated to guided waves [4], such as the energy velocity, are revisited in order to account for levels of prestress and different material behaviours. By means of some examples the effect of prestress on the dispersive behaviour of guided waves is shown