Global dynamics perspective on macro- to nano-mechanics

Rega, Giuseppe; Settimi, Valeria

doi:10.1007/s11071-020-06198-x

Cited by 19 publications

(6 citation statements)

References 96 publications

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“…Furthermore, in view of an iterative procedure, the LIM provides the important advantage that, if at an iteration step a particular value of the LIM is defined, all the phase space external to the hypersphere defined by the LIM (that we call hypersphere of convergence) can be immediately disregarded; this is not true for the IF. As illustrated in [48] and in [45], in most cases the various integrity measures provide qualitatively similar results. This fact allows us to use the most convenient one for our purposes, which is the LIM.…”

Section: Basic Idea and Objectivementioning

confidence: 60%

“…Later, in a series of papers, Rega and Lenci [31,44] carefully evaluated the relevance of these integrity measures and proposed new ones, such as the integrity factor (IF) and the actual global integrity measure (AGIM). These dynamical integrity measures proved to be a valuable tool to quantitatively investigate phenomena of BOA erosion, particularly important for safe engineering design [32,40,45].…”

Section: Dynamical Integrity Measuresmentioning

confidence: 99%

“…However, it is computationally very costly since it requires a large number of numerical simulations, which increases exponentially with the dimension of the system, becoming practically infeasible even for medium size systems. For this reason, BOA repre-sentations are often limited to bidimensional sections [45]. This method is intrinsically very inefficient since from each numerical simulation it extracts only one bit of information.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure

Habib

2021

Nonlinear Dyn

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A new algorithm for the estimation of the robustness of a dynamical system’s equilibrium is presented. Unlike standard approaches, the algorithm does not aim to identify the entire basin of attraction of the solution. Instead, it iteratively estimates the so-called local integrity measure, that is, the radius of the largest hypersphere entirely included in the basin of attraction of a solution and centred in the solution. The procedure completely overlooks intermingled and fractal regions of the basin of attraction, enabling it to provide a significant engineering quantity in a very short time. The algorithm is tested on four different mechanical systems of increasing dimension, from 2 to 8. For each system, the variation of the integrity measure with respect to a system parameter is evaluated, proving the engineering relevance of the results provided. Despite some limitations, the algorithm proved to be a viable alternative to more complex and computationally demanding methods, making it a potentially appealing tool for industrial applications.

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Section: Basic Idea and Objectivementioning

confidence: 60%

Section: Dynamical Integrity Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure

Habib

2021

Nonlinear Dyn

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“…It has been widely used in sewage treatment, biotechnology, human health, automatic control, aerospace, and other engineering fields. The basic components of micro-/nano electromechanical systems (MEMS/NEMS) are widely used in chemical and biological fields thanks to their excellent mechanical properties, which can be simplified into micro-/nano scale beams or plates [2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of graded porous circular micro/nanoplates with various boundary conditions based on the nonlocal elasticity theory

Wang

Zhang

2022

Z Angew Math Mech

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In this article, the free vibrations of graded porous circular nanoplates subjected to various boundary conditions have been investigated. It is assumed that the performance of graded porous materials varies continuously in the whole thickness, and two cosine forms of non‐uniform porosity distribution along its thickness are considered. In order to capture the size effect, the Eringen's nonlocal elastic theory is applied. Then, Mindlin plate theory, combined with Hamilton's principle, is utilized to derive the governing equations of motion. Various types of boundary conditions are assumed for the plate with a combination of clamped, simply supported and free edges. Finally, the governing equations of motion are solved numerically using the shooting technique. The effects of various factors such as porosity coefficient, porosity distribution pattern, thickness‐diameter ratio, and the nonlocal scale effect and boundary conditions on the natural frequencies of grade porous circular nanoplates are discussed in detail.

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“…Its practical implementation is far from trivial since there exists no simple connection between the coexisting asymptotic states and their basins of attraction, and its development emerged into the research field now known as dynamical integrity [16,18,21]. Changing the paradigm from local to global dynamics leads to a deeper knowledge of system safety, despite the growing difficulties in terms of numerical costs of the simulations as the number of dof increases [22,23].…”

Section: Introductionmentioning

confidence: 99%

Global Analysis of Stochastic Nonlinear Dynamical Systems. Part 2: Influence of Uncertainties and Noise on Basins/Attractors Topology and Integrity

Benedetti

Gonçalves

Lenci

et al. 2022

Preprint

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This paper explores the influence of uncertainties and noise on the global dynamics of nonlinear systems, with emphasis on the basins and attractors’ topology and on the dynamic integrity of coexisting solutions. For this, the adaptive phase-space discretization strategy proposed in Part I [1] is employed. Two well-known archetypal oscillators found in engineering applications, the Helmholtz and Duffing oscillators under harmonic or parametric excitation with uncertain parameters or added load noise, are studied. The results demonstrate the adaptive capability of the proposed method, increasing the resolution without increasing the computational cost. Mean basins of attraction and attractors’ distributions are obtained. The time-dependency of stochastic responses is demonstrated, with long-transients influencing the short-term behavior. Finally, the effect of uncertainties and noise on the basins areas, attractors distributions and basin boundaries is discussed, which can be used to evaluate the dynamic integrity of the competing basins.

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Global dynamics perspective on macro- to nano-mechanics

Cited by 19 publications

References 96 publications

Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure

Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure

Free vibration analysis of graded porous circular micro/nanoplates with various boundary conditions based on the nonlocal elasticity theory

Global Analysis of Stochastic Nonlinear Dynamical Systems. Part 2: Influence of Uncertainties and Noise on Basins/Attractors Topology and Integrity

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