Load carrying capacity of systems within a global safety perspective. Part II. Attractor/basin integrity under dynamic excitations

Abstract

. Load carrying capacity of systems within a global safety perspective Part II. Attractor/basin integrity under dynamic excitations. International Journal of Non-Linear Mechanics, Elsevier, 2011, 46 (9) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. 1 LOAD CARRYING CAPACITY OF SYSTEMS WITHIN Abstract:The effects of the dynamic excitation on the load carrying capacity of mechanical systems are investigated with reference to the archetypal model addressed in Part I, which permits to highlight the main ideas without spurious mechanical complexities. First, the effects of the excitation on periodic solutions are analyzed, focusing on bifurcations entailing their disappearance and playing the role of Koiter critical thresholds. Then, attractor robustness (i.e., large magnitude of the safe basin) is shown to be necessary but not sufficient to have global safety under dynamic excitation. In fact, the excitation strongly modifies the topology of the safe basins, and a dynamical integrity perspective accounting for the magnitude of the solely compact part of the safe basin must be considered. By means of extensive numerical simulations, robustness/erosion profiles of dynamic solutions/basins for varying axial load and dynamic amplitude are built, respectively. These curves permit to appreciate the practical reduction of system load carrying capacity and, upon choosing the value of residual integrity admissible for engineering design, the Thompson practical stability. Dwelling on the effects of the interaction between axial load and lateral dynamic excitation, this paper supports and, indeed, extends the conclusions of the companion one, highlighting the fundamental role played by global dynamics as regards a reliable estimation of the actual load carrying capacity of mechanical systems.

Load carrying capacity of systems within a global safety perspective. Part I. Robustness of stable equilibria under imperfections

“…In fact, only the basic aspect of the dynamical integrity perspective, which consists of allowing for finite size perturbations, has been used in this paper, since it is sufficient for highlighting the actual robustness of stable equilibria. As it will be shown in Part II of this work [17], the issue of system load carrying capacity and global safety in the presence of actual dynamic excitations requires full consideration of its highly variable dynamic response, with the ensuing effects in terms of reduction of dynamical integrity due to the erosion phenomena entailed by the possible occurrence of fractal basins of attraction.…”

“…the finite magnitude of the area of the safe basin) is not enough to guarantee the real dynamical integrity of the system, as it will be clarified in Part II of this work [17]. However, it is a sufficient concept for the goal pursued herein.…”

“…This issue, which constitutes the second point of the Thompson achievements, entails properly addressing the dynamical integrity concept in all of its implications, which are indeed quite delicate because of the strange dynamical phenomena (e.g., fractals) which may occur. This will be considered in the companion paper [17], by also addressing the so-called integrity (or basin erosion) profiles, which are very useful instruments to achieve the reliability threshold, as well as the most important practical information ensuing from the analysis of system dynamics. Part II [17] complements this one and concludes the analysis of the global safety.…”

“…This will be considered in the companion paper [17], by also addressing the so-called integrity (or basin erosion) profiles, which are very useful instruments to achieve the reliability threshold, as well as the most important practical information ensuing from the analysis of system dynamics. Part II [17] complements this one and concludes the analysis of the global safety.…”

The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics

“…In [28], it is shown that the requirement of a large basin also applies in the absence of dynamical excitation, because close to the static bifurcation point the basin of attraction shrinks to zero and thus the associated equilibrium point is no longer robust, the situation being unsafe. In [29], on the other hand, the dynamical excitation is added, and the interactions between the excitation amplitude and the axial load in reducing the global safety are investigated, analysing in-depth both the basin extent and its compactness.…”