The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized ...by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.
In this paper, a higher-order element based on the unified and integrated approach of Timoshenko beam theory is developed. A two-node beam element with Hermitian functions of a 5th-degree polynomial ...(4 DOFs per node) called UI element is proposed to solve the problems of static and free vibration. In this proposed element, the Timoshenko beam theory is modified in such a way to prevent shear locking while taking account of the transverse shear effect. The static and free vibration analyses are used to obtain the displacements and natural frequencies of rectangular Functionally Graded Material (FGM) beam for hinged-roll, clamped-free and clamped-clamped boundary conditions and to study the effects of the power-law exponent (coupling of the anisotropic material) on the displacements and natural frequencies. Results of the present work are compared with the published data to learn the effectiveness of the proposed element and to verify the validity of the model theory. The numerical analysis shows that the coupling of axial-bending should be taken into consideration in static and vibration analysis of FGM. The comparison study confirms the accuracy and the efficiency of the proposed element for static and vibration analysis of FGM beam.
•Exploited a bottom to up modelling nano-mechanics theory to investigate the nonlinear stability of CNTs.•Micro-strain and micro-stress effects are included by Doublet Mechanics theory.•The ...nonclassical sixth order nonlinear integro-partial-differential equation of CNTs is derived.•Analytical solutions are derived for static and dynamic analysis.•Static and dynamic stablity of perfect and imperfect CNTs are investigated.
This manuscript exploited a bottom to up modelling nano-mechanics theory to investigate the nonlinear stability and dynamic behaviors of perfect and imperfect carbon nanotubes (CNTs) in pre-buckling and post-buckling domains, for the first time. The Doublet Mechanics (DM) theory is exploited to induce the length scale of CNTs, micro-strain, and micro-stress effects, which are negligible in classical continuum theory. The Euler-Bernoulli kinematic and nonlinear mid-plane stretching effect are considered through analysis. The imperfection of CNTs is described by a harmonic function through spatial direction. The nonclassical sixth order nonlinear integro-partial-differential equation of CNTs is derived in detail. Based on the static equilibrium equation, analytical solutions for smallest buckling loads, as well as, nonlinear static response of perfect and imperfect CNTs in pre-buckling and post-buckling regimes are deduced. The equation of motion of linear vibration problem is solved analytically to get natural frequencies and corresponding mode shapes. Numerical studies investigate the impact of length scale parameter, imperfection amplitude and shear foundation constant on static and dynamic stabilities of CNTs with both fully clamped and simply supported conditions. The current model is effective in designing of NEMS, nano-sensor and nano-actuator manufactured by CNTs.
Abstract Spontaneous rhythmic movements are part of everyday life, e.g., in walking, clapping or music making. Humans perform such spontaneous motor actions at different rates that reflect specific ...biomechanical constraints of the effector system in use. However, there is some evidence for intra-individual consistency of specific spontaneous rates arguably resulting from common underlying processes. Additionally, individual and contextual factors such as musicianship and circadian rhythms have been suggested to influence spontaneous rates. This study investigated the relative contributions of these factors and provides a comprehensive picture of rates among different spontaneous motor behaviors, i.e., melody production, walking, clapping, tapping with and without sound production, the latter measured online before and in the lab. Participants ( n = 60) exhibited high intra-individual stability across tasks. Task-related influences included faster tempi for spontaneous production rates of music and wider ranges of spontaneous motor tempi (SMT) and clapping rates compared to walking and music making rates. Moreover, musicians exhibited slower spontaneous rates across tasks, yet we found no influence of time of day on SMT as measured online in pre-lab sessions. Tapping behavior was similar in pre-lab and in-lab sessions, validating the use of online SMT assessments. Together, the prominent role of individual factors and high stability across domains support the idea that different spontaneous motor behaviors are influenced by common underlying processes.
•The operational dynamic strains of a steel bridge are monitored with FBGs for one year.•The modal characteristics of the bridge are systematically identified from the dynamic strains.•The mode ...selection process in automated with the use of hierarchical clustering.•The influence of temperature on modal strains and natural frequencies is investigated.•The influence of retrofitting on modal strains and natural frequencies is investigated.
Vibration monitoring from strain data is a promising alternative to the more conventional acceleration-based monitoring because a dense measurement grid can be achieved at a relatively low cost and because strain mode shapes are more sensitive to local stiffness changes than displacement mode shapes. However, the feasibility of monitoring strain mode shapes of full-scale civil structures, where the operational dynamic strain levels are of very low amplitude and temperature changes can influence the modal characteristics, has remained an open question. The present work provides a proof of concept in which the deck of a steel tied arch railway bridge is instrumented with eighty Fiber-optic Bragg Grating strain sensors, multiplexed in four fibers, that are interrogated with a technique that achieves high accuracy and precision. For more than a year, the natural frequencies and strain mode shapes of ten modes have been automatically identified from operational strain time histories, with typical root-mean-square values of 0.01 microstrain, on an hourly basis. Furthermore, using these modal data, the influence of temperature fluctuations and that of a retrofitting of the hangers connecting the bridge deck and the arches, which took place during the monitoring period, are extensively investigated. Both have an influence on the overall stiffness of the bridge and therefore they result in clear changes in the natural frequencies. They do not have an influence on the local stiffness and therefore they do not influence the strain mode shapes, except when the retrofitting induces an interaction between previously well-separated modes.
Reduced-order models (ROMs) are developed for obtaining the natural frequencies of offshore wind turbines (OWTs) considering the soil–structure interaction (SSI) by distributed springs along the ...monopile and employing three different modeling strategies. The ROM is derived considering a non-prismatic beam with mass at the tip. Once the mathematical model is obtained, the natural frequencies of the NREL 5 MW reference wind turbine are analytically obtained and the results are compared with those obtained by higher-order hierarchical models based on the Finite Element Method (FEM). The novelty here is the presentation of a mathematical model for this SSI representation that allows obtaining different natural frequencies and the vibration modes representation in an analytical scheme. The analyses developed raise a discussion about the choice of the shape function in the use of Galerkin’s method. The results show that, depending on the modeling strategy, the fundamental frequency of the OWT studied is obtained with great accuracy when compared to the FEM analysis (considered as a reference value), with difference below 3.5%. The ROMs obtained allow evaluating the natural frequencies and mode shapes with very low computational cost, a feature that can be useful especially in the early stages of design.
•Reduced-order models (ROMs) considering the soil-structure interaction are obtained.•The ROMs obtained allow evaluating the natural frequencies and mode shapes for offshore wind turbines.•A discussion about the choice of the shape function in the use of Galerkin’s method is carried out.
•Using the FG-X graphene pattern in channel section struts boosts the critical buckling temperature by 12 % for clamped and 9 % for simply-supported struts, compared to the FGO pattern.•For a shape ...factor of bf/bw=0.2, changing graphene in the flanges minimally affects strut buckling temperature. However, altering the web's graphene pattern, with consistent flange reinforcement, can alter the temperature by up to 12 %.•The study on thermal pre- and post-buckling vibrations in struts with various graphene patterns reveals FGX configurations yield the highest frequencies through the pre-buckling state, though this trend shifts in the post-buckling.•Integrating an asymmetric graphene pattern (FGV) or embedding geometric imperfections sustain the primary natural frequencies of FG-GRC channel section struts above zero as they approach the critical buckling temperature.
This study explores the effect of local buckling on the compressive performance of slender structural elements, particularly those with thin-walled sections. The phenomenon of local buckling significantly reduces the axial compressive stiffness, leading to a notable decrease in the load-bearing capacity of these elements. The main goal of this research is to examine how the post-buckling characteristics of polymeric composite channel section struts can be improved under thermal loading by incorporating multi-layer graphene reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To ascertain the precision and computational performance of the results derived from LW-TSDT, a three-dimensional (3D) finite element model is created in ABAQUS for comparative evaluation. An extensive analysis of nonlinear thermal instability in perfect and geometrically imperfect FG-GRC laminated channel section struts is undertaken to discern the graphene distribution patterns that are most and least effective in elevating the critical buckling temperature and natural frequencies through pre- and post-buckling conditions. The comparative analysis indicates that employing the FG-X graphene distribution pattern across the thickness of the web and flanges in channel section struts leads to a projected increase of 12 % in the critical buckling temperature for clamped channel section struts, in contrast to those that adopt the FGO graphene distribution pattern. For cases with simply-supported boundary conditions, this increase is noted to be approximately 9 %. Moreover, findings confirm that incorporating an asymmetric graphene distribution pattern (FGV) or introducing geometrical imperfections in the flanges and web that generate a bending moment within the structure from the beginning of thermal loading effectively prevents the primary natural frequencies of FG-GRC channel section struts from declining to zero close to the critical buckling temperature. This is significantly different from scenarios involving perfectly structured and symmetrically reinforced graphene distribution patterns such as FGX.
The natural frequency facilitation effect describes the finding that people are better able to solve descriptive Bayesian inference tasks when represented as joint frequencies obtained through ...natural sampling, known as natural frequencies, than as conditional probabilities. The present meta-analysis reviews 20 years of research seeking to address when, why, and for whom natural frequency formats are most effective. We review contributions from research associated with the 2 dominant theoretical perspectives, the ecological rationality framework and nested-sets theory, and test potential moderators of the effect. A systematic review of relevant literature yielded 35 articles representing 226 performance estimates. These estimates were statistically integrated using a bivariate mixed-effects model that yields summary estimates of average performances across the 2 formats and estimates of the effects of different study characteristics on performance. These study characteristics range from moderators representing individual characteristics (e.g., numeracy, expertise), to methodological differences (e.g., use of incentives, scoring criteria) and features of problem representation (e.g., short menu format, visual aid). Short menu formats (less computationally complex representations showing joint-events) and visual aids demonstrated some of the strongest moderation effects, improving performance for both conditional probability and natural frequency formats. A number of methodological factors (e.g., exposure to both problem formats) were also found to affect performance rates, emphasizing the importance of a systematic approach. We suggest how research on Bayesian reasoning can be strengthened by broadening the definition of successful Bayesian reasoning to incorporate choice and process and by applying different research methodologies.
Public Significance Statement
The present study shows that it is possible to improve people's inferences based on probabilistic information if conditional probabilities are presented as naturally sampled frequencies. Visual aids can help boost performance even further. However, future work is needed to understand why many people continue to have difficulties solving conditional probability problems.
The study focuses on the free vibration analysis of beams composed of functionally graded porous materials and characterized by a variable cross-section along their length. A broad range of beams is ...examined encompassing various tapered configurations, porosity profiles, and porosity content. The equations of motion are derived using Hamilton’s principle within the framework of Timoshenko beam theory. These equations are solved semi-analytically using the differential transform method, which has been adapted to incorporate various boundary conditions such as clamped–clamped, clamped–free, clamped–pinned, and pinned–pinned constraints within a general formulation of the beam eigenvalue problem. To validate the proposed solution technique, computed natural frequencies are compared with existing literature results for tapered inhomogeneous beams and uniform porous beams. Notably, new results are obtained for tapered porous beams. In this regard, a comprehensive parametric study explores the influence of various factors on the natural frequencies and mode shapes of functionally graded porous beams with variable cross-sections. These factors include the type of porosity profiles, a range of porosity parameters, cross-section taper ratios, and specific boundary conditions. The findings deepen our understanding of the modal characteristics of functionally graded porous beams, providing valuable guidance for engineering design and structural optimization in relevant applications. Additionally, they may serve as benchmarks for other researchers.
In this work, high-order beam (1D) finite element models for the modal analysis of structures made of compressible and nearly-incompressible hyperelastic soft materials are presented in the ...well-established framework of Carrera Unified Formulation (CUF). In this investigation, the modal behavior of soft structures subjected to progressively increasing loads can be correctly predicted by higher-order structural theories, and the influence of pre-stress conditions applied on the modal response of structures is investigated. The mathematical formulation of hyperelastic isotropic materials is presented in terms of invariants of the right Cauchy–Green strain tensor, obtaining the most general expression of the Piola–Kirchoff 2 stress tensor and tangent elasticity tensor, both independent of the model adopted for the material strain energy function. Governing equations in matrix forms for the static nonlinear analysis and subsequent vibration problem around non-trivial equilibrium states are derived through the Principle of Virtual Displacements (PVD) under a total Lagrangian formulation, defining the fundamental nuclei of stiffness matrices and internal and external forces vector, all independent of expansion theories and kinematic models adopted in the mathematical modeling of finite elements. Actual numerical results are obtained by an iterative Newton–Raphson linearized scheme coupled with line-search algorithms, and they are compared with results obtained by the commercial code ABAQUS. Our proposed models are tested with large strain problems involving hyperelastic slender and thin-walled structures, for which mode aberration such as crossing or bearing are observed.
•Non-linear vibration analysis of solid and thin-walled structures made of soft material.•High-order finite element models to deal with local effects and cross-section deformation.•Effect of the material compressibility on the mode aberration is investigated.•Mode veering and crossing studied by means of MAC and frequency tracking.•High-order modes and wave propagation characteristics analyzed.
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