Nonlinear oscillations and bifurcations of a multistable truss and dynamic integrity assessment via a Monte Carlo approach

Abstract

In the present work, a truss model inspired by von Mises and Bergan trusses is considered. The resulting structure is a phenomenological model that represents the behavior of many engineering structures and may exhibit in-plane snap-through or pitchfork unstable bifurcation and/or lateral buckling, leading two a multiwell potential function. The topology of the resulting potential function generates a complex bifurcation scenario under harmonic forcing with multiple attractors. The first aim of this work is to investigate the nonlinear vibrations of the proposed model. The interaction of the bifurcation phenomena leads to motions in two-, four- and six-dimensional phase-space. The use of different integrity measures is essential for assessing the robustness of the driven structure to unpredictable finite disturbances of a both static and dynamic nature in such cases. However of the various numerical tools for global dynamic analysis, few are well suited for higher-dimensional systems. In particular the evaluation of integrity measures of multidimensional system requires significant computational resources, being a rather time-consuming procedure. Thus the second aim of the paper is to propose numerical methodologies for evaluating the dynamic integrity measures of multidimensional systems by a Monte Carlo approach. Dynamic integrity analysis of the resulting multidimensional system is performed using three integrity measures, global and local integrity measures (GIM and LIM, respectively) and the integrity factor. Three algorithms based on the Monte Carlo method are proposed to estimate these measures by means of sampling initial conditions. We demonstrate that the proposed approach has a major advantage in comparison to classical methods, since basins of attraction are not needed. Computationally expensive procedures, such as simple cell mapping, are not required. Therefore, the proposed approach has the potential to estimative the dynamic integrity of high dimensional systems with less computational effort, as shown by the obtained results.