The present thesis deals with the identification of damages in mechanical structures using the electro-mechanical (E/M) impedance method. The E/M impedance method is a vibration based structural health monitoring (SHM) method. It uses for both the vibration excitation as well as for the measurement of the vibration response piezoelectric elements, so-called piezoelectric wafer active sensors (PWAS). In particular, damages of a mechanical structure are investigated, which produce a nonlinear response to a harmonic excitation. Examples therefore are delamination in laminates or face- layer debonding in sandwich panels, so-called sub-surface cracks. For a crack opening small enough, ideally equal to zero, the crack surfaces get for certain frequencies of the harmonic excitation into mechanical contact, and thus nonlinear response results. The effects of such a structural nonlinearity on the vibration response is initially investigated by means of a simplified two-dimensional model of a beam on a nonlinear elastic foundation. An analytical investigation and a numerical investigation based on the finite element method (FEM) are conducted. The harmonic excitation for this model is realized by a force excitation in the middle of the beam. The dynamic response is evaluated by the displacement at the position of the excitation. Further investigations are carried out on a second and more realistic model, an aluminum beam with rectangular cross-section and a sub-surface crack in the beams lengthwise center. In contrast to the first model, the vibration excitation and the sensing of the response are realized by piezoelectric wafer active sensors (PWAS). The focus for this investigation is mainly on the numerical and experimental investigation. Since experiments are conducted a part within this section deals with the manufacturing of the beam specimen, in particular with the manufacturing of the artificial sub-surface crack, since this crack should have an opening distance of ideally zero to produce a nonlinear response to a harmonic excitation. A manufacturing process of a sub-surface crack in metallic beams, capable to produce structural nonlinearity is presented. For both models the evaluation and assessment of the effects of the sub-surface crack is carried out on the one hand by comparing the dynamic responses of the pristine and damaged structure. On the other hand an evaluation of nonlinear features that occur in the dynamic response of the damaged structure is conducted. The discussed nonlinear features are sub- and higher harmonic oscillations with respect to the excitation frequency.