Effect of damping on the nonlinear modal characteristics of a piecewice-smooth system through harmonic forced response

Abstract

Several engineering systems present piecewise-linear characteristics, among them, the damaged beams with breathing cracks are of particular interest. The dynamics of such systems exhibits bifurcations at internal resonances characterized by the onset of superabundant nonlinear normal modes with their individual modal shapes. In this paper, a 2-DOF system with piecewise linear stiffness, representative of a damaged system with a breathing crack, is analyzed by means of a numerical and theoretical investigation. The oscillator is forced by a harmonic base excitation and the role of damping on the modification of the nonlinear modal characteristics is investigated. The outcomes are compared with the reference behavior of the undamped system which allows for semi-analytical solution. It is found that the damping, on one hand, softens the abrupt transitions from one behavior to another, typical of undamped systems, on the other, affects the bifurcations of the nonlinear modes causing some of them to completely disappear and leaving others largely unaffected.