Analytical study of the amplitude and phase resonances of a Duffing oscillator

peer reviewedThis paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with a specific attention to phase resonance and to its relation with amplitude resonance. To this end, the different families of resonances, namely primary (1:1), superharmonic (k:1) and subharmonic (1:ν) resonances are carefully studied using first and higher-order averaging. When the phase lag is calculated between the k-th harmonic of the displacement and the harmonic forcing, this study evidences that phase resonance occurs when the phase lag is equal to either π/2 (phase quadrature) or 3π/4ν

Characterizing fundamental, superharmonic and subharmonic resonances using phase resonance nonlinear modes

peer reviewedNonlinear normal modes (NNMs) are often used for the prediction of the backbone of resonance peaks in nonlinear frequency response functions. However, in principle, NNMs require multi-point, multi-harmonic external forcing for their practical realization. The present study proposes a new NNM definition termed phase resonance nonlinear modes. The definition is based on virtual, mono-point, mono-harmonic external forcing proportional to a specific harmonic of the velocity of the forced degree of freedom. Depending on the chosen harmonic, fundamental, superharmonic and subharmonic resonances can be characterized

Phase resonance of an oscillator with polynomial stiffness

peer reviewedThis paper extends the linear concept of phase resonance, which occurs when the damping forces counterbalance exactly the external forces, to oscillators with polynomial stiffness. To this end, a first-order averaging technique is applied to a one degree-of-freedom oscillator with arbitrary polynomial stiffness. We show that phase resonance exists in the vicinity of amplitude resonance and is associated with a phase resonance of π/2

Experimental Characterization of Superharmonic Resonances Using Phase-Lock Loop and Control-Based Continuation

Experimental characterization of nonlinear structures usually focuses on fundamental resonances. However, there is useful information about the structure to be gained at frequencies far away from those resonances. For instance, non-fundamental harmonics in the system's response can trigger secondary resonances, including superharmonic resonances. Using the recently-introduced definition of phase resonance nonlinear modes, a phase-locked loop feedback control is used to identify the backbones of even and odd superharmonic resonances, as well as the nonlinear frequency response curve in the vicinity of such resonances. When the backbones of two resonances (either fundamental or superharmonic) cross, modal interactions make the phase-locked loop unable to stabilize some orbits. Control-based continuation can thus be used in conjunction with phase-locked loop testing to stabilize the orbits of interest. The proposed experimental method is demonstrated on a beam with artificial cubic stiffness exhibiting complex resonant behavior. For instance, the frequency response around the third superharmonic resonance of the third mode exhibits a loop, the fifth superharmonic resonance of the fourth mode interacts with the fundamental resonance of the second mode, and the second superharmonic resonance of the third mode exhibits a branch-point bifurcation and interacts with the fourth superharmonic resonance of the fourth mode

The PRECISE-DYAD neurodevelopmental substudy protocol: neurodevelopmental risk in children of mothers with pregnancy complications

Background: Over 250 million children are not reaching their developmental potential globally. The impact of prenatal factors and their interplay with postnatal environmental factors on child neurodevelopment, is still unclear—particularly in low- and middle-income settings. This study aims to understand the impact of pregnancy complications as well as environmental, psychosocial, and biological predictors on neurodevelopmental trajectories. Open Peer Review Approval Status 1 2 version 2 (revision) 05 Aug 2024 view view version 1 09 Nov 2023 view view Kimford Meador, Stanford University School of Medicine, Palo Alto, CA,, USA 1. Page 1 of 21 Wellcome Open Research 2024, 8:508 Last updated: 09 AUG 2024 Methods: This is an observational cohort study of female and male children ( ≈3,950) born to women (≈4,200) with and without pregnancy complications (pregnancy-induced hypertension, foetal growth restriction, and premature birth) previously recruited into PREgnancy Care Integrating Translational Science, Everywhere study with detailed biological data collected in intrapartum and post-partum periods. Children will be assessed at six weeks to 6 months, 11-13 months, 23- 25 months and 35-37 months in rural and semi-urban Gambia (Farafenni, Illiasa, and Ngayen Sanjal) and Kenya (Mariakani and Rabai). We will assess children\u27s neurodevelopment using Prechtls General Movement Assessment, the Malawi Development Assessment Tool (primary outcome), Observation of Maternal-Child Interaction, the Neurodevelopmental Disorder Screening Tool, and the Epilepsy Screening tool. Children screening positive will be assessed with Cardiff cards (vision), Modified Checklist for Autism in Toddlers Revised, and Pediatric Quality of Life Inventory Family Impact. We will use multivariate logistic regression analysis to investigate the impact of pregnancy complications on neurodevelopment and conduct structural equation modelling using latent class growth to study trajectories and relationships between biological, environmental, and psychosocial factors on child development. Conclusions: We aim to provide information regarding the neurodevelopment of infants and children born to women with and without pregnancy complications at multiple time points during the first three years of life in two low-resource African communities. A detailed evaluation of developmental trajectories and their predictors will provide information on the most strategic points of intervention to prevent and reduce the incidence of neurodevelopmental impairments

The impact of fretting wear on structural dynamics: Experiment and simulation

This paper investigates the effects of fretting wear on frictional contacts. A high frequency friction rig is used to measure the evolution of hysteresis loops, friction coefficient and tangential contact stiffness over time. This evolution of the contact parameters is linked to significant changes in natural frequencies and damping of the rig. Hysteresis loops are replicated by using a Bouc-Wen modified formulation, which includes wear to simulate the evolution of contact parameters and to model the evolving dynamic behaviour of the rig. A comparison of the measured and predicted dynamic behaviour demonstrates the feasibility of the proposed approach and highlights the need to consider wear to accurately capture the dynamic response of a system with frictional joints over its lifetime

The impact of fretting wear on structural dynamics: Experiment and simulation

This paper investigates the effects of fretting wear on frictional contacts. A high frequency friction rig is used to measure the evolution of hysteresis loops, friction coefficient and tangential contact stiffness over time. This evolution of the contact parameters is linked to significant changes in natural frequencies and damping of the rig. Hysteresis loops are replicated by using a Bouc-Wen modified formulation, which includes wear to simulate the evolution of contact parameters and to model the evolving dynamic behaviour of the rig. A comparison of the measured and predicted dynamic behaviour demonstrates the feasibility of the proposed approach and highlights the need to consider wear to accurately capture the dynamic response of a system with frictional joints over its lifetime

Functionally Fractal Urban Networks: Geospatial Co-location and Homogeneity of Infrastructure

Just as natural river networks are known to be globally self-similar, recent research has shown that human-built urban networks, such as road networks, are also functionally self-similar, and have fractal topology with power-law node-degree distributions (p(k) = a k). Here we show, for the first time, that other urban infrastructure networks (sanitary and storm-water sewers), which sustain flows of critical services for urban citizens, also show scale-free functional topologies. For roads and drainage networks, we compared functional topological metrics, derived from high-resolution data (70,000 nodes) for a large US city providing services to about 900,000 citizens over an area of about 1,000 km2. For the whole city and for different sized subnets, we also examined these networks in terms of geospatial co-location (roads and sewers). Our analyses reveal functional topological homogeneity among all the subnets within the city, in spite of differences in several urban attributes. The functional topologies of all subnets of both infrastructure types resemble power-law distributions, with tails becoming increasingly power-law as the subnet area increases. Our findings hold implications for assessing the vulnerability of these critical infrastructure networks to cascading shocks based on spatial interdependency, and for improved design and maintenance of urban infrastructure networks