Comprehensive analysis of periodic regimes of forced vibration for structures with nonlinear snap-through springs

In this paper a comprehensive analysis of steady-state forced response is performed for the case of a system with snap-through nonlinear springs. Stiffness characteristics of these springs include cubic and linear terms and the linear stiffness term is negative. There are a very restricted number of solutions found in literature for such type of nonlinearity. Because of that, the primary goal of the study is to obtain a full set of possible solutions providing stable and unstable periodic forced response regimes. The solutions sought include three major groups of the periodic response: (i) vibrations having a period coinciding with the excitation; (ii) subharmonic vibrations; and (iii) superharmonic vibrations. A multi-harmonic balance method is applied for highly efficient and accurate frequency-domain analysis of steady-state forced responses in a wide range of excitation frequency variation. Time-marching integration methods are used for validation and further analysis, including assessment of stability for the solutions found by the multi-harmonic balance method. The numerical studies performed reveal a wide variety of periodic regimes which are inherent for structures with snap-through springs