Dinamica di una mensola con impatti soffici: confronto del modello infinito dimensionale con quello equivalente ad un grado di liberta ́ (SDOF)

Non-smooth dynamics of a cantilever beam subjected to a transverse harmonic force and impacting onto a soft obstacle will be presented in the talk. Upon formulating the equations of motion of the beam, proper attention will be paid to identifying the mechanical properties of an equivalent single-degree-of-freedom (SDOF) piecewise linear impacting model. A multidegree-of-freedom (MDOF) model of the impacting beam will also be derived via standard finite elements. An “optimal” identification curve of the obstacle spring rigidities in the two models will be obtained by comparing the relevant pseudo-resonance frequencies. The identification will then be exploited in the nonlinear dynamic regime to get hints on some main, mostly regular, features of nonlinear dynamic response of the impacting beam by the actual investigation of the behavior of the sole equivalent SDOF model, with a definitely lower computational effort. Sample regular and non-regular responses of the MDOF model will also be presented where the identification does not work. Overall, useful points will be made as regards the possibility and the limitations of referring to a SDOF impacting model to investigate the nonlinear response of the underlying infinite-dimensional system