scholarly journals Emergence of the London Millennium Bridge instability without synchronisation

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Igor Belykh ◽  
Mateusz Bocian ◽  
Alan R. Champneys ◽  
Kevin Daley ◽  
Russell Jeter ◽  
...  
Keyword(s):  
Mathematical Models ◽  
General Formula ◽  
Limit Cycle ◽  
Positive Feedback ◽  
Natural Frequencies ◽  
Foot Placement ◽  
Wide Range ◽  
Negative Damping ◽  
Millennium Bridge

AbstractThe pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians’ foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies. We present a simple general formula that quantifies this effect, and illustrate it through simulation of three mathematical models, including one with strong propensity for synchronisation. Despite subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger. More broadly, we describe an alternative to Kuramoto theory for emergence of coherent oscillations in nature; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

scholarly journals The simulation model for a flood management by flood control facilities

2018 ◽  
Vol 245 ◽  
pp. 15002 ◽  
Author(s):  
Roman Davydov ◽  
Valery Antonov ◽  
Dmitry Molodtsov ◽  
Alexey Cheremisin ◽  
Vadim Korablev
Keyword(s):  
Mathematical Models ◽  
Flood Control ◽  
Flood Management ◽  
Hydroelectric Power Station ◽  
Hydroelectric Power ◽  
Operating Characteristics ◽  
Hydro Power ◽  
Operation Modes ◽  
Wide Range ◽  
Environmental Requirements

The rapid spread of storm floods over large areas requires flood management throughout the river basin by the creation an innovative system of flood control facilities of various functional purposes distributed in the area. The central part of the system is the hydro system with hydro power plant. In addition, the flood control facilities on the side tributaries with self-regulating reservoir are included in the system. To assess the effect of controlling extreme water discharges by flood control facilities, it is necessary to develop special mathematical models reflecting the specifics of their operation. Unified mathematical models of the operation modes of a hydro complex with hydroelectric power station and flood control facility are created. They are implemented in a computer program that provides the ability to determine the main parameters and operating characteristics of hydro systems when performing multivariate calculations in a wide range of initial data. This makes possible specifying the parameters and operation modes of each hydro system with the current economic and environmental requirements, to assess the energy-economic and environmental consequences in the operation of the system of flood control facilities distributed in the area. The article analyses the results of the extreme water discharge’s regulation by the hydro system on the main river and flood control facilities on the side tributaries, considering environmental requirements.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

Preparation of Functionalized Diorganomagnesium Reagents in Toluene via Bromine or Iodine/Magnesium-Exchange Reactions

Synthesis ◽  
2021 ◽  
Author(s):  
Alexandre Desaintjean ◽  
Fanny Danton ◽  
Paul Knochel
Keyword(s):  
Exchange Reaction ◽  
Nitro Group ◽  
General Formula ◽  
Functional Groups ◽  
Exchange Reactions ◽  
Acyl Chlorides ◽  
Aryl Iodides ◽  
Highly Sensitive ◽  
Wide Range ◽  
Magnesium Exchange

A wide range of polyfunctionalized di(hetero)aryl- and dialkenyl-magnesium reagents were prepared in toluene within 10 to 120 min between −78 °C and 25 °C via an I/Mg- or Br/Mg-exchange reaction using reagents of the general formula R2Mg (R = sBu, Mes). Highly sensitive functional groups, such as a triazene or a nitro group, were tolerated in these exchange reactions, enabling the synthesis of various functionalized (hetero)arenes and alkenes derivatives after quenching with several electrophiles including allyl bromides, acyl chlorides, aldehydes, ketones, and aryl iodides.

Vibration Suppression of an Elastically Supported Beam With Closely Spaced Natural Frequencies

2020 ◽  
Author(s):  
Haizhou Liu ◽  
Hao Gao
Keyword(s):  
Natural Frequencies ◽  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Dynamic Performance ◽  
Point Theory ◽  
Primary System ◽  
Computationally Efficient ◽  
Wide Range ◽  
Univariate Optimization ◽  
Elastically Supported

Abstract Vibration suppression of distributed parameter systems is of great interest and has a wide range of applications. The dynamic performance of a primary system can be improved by adding dynamic vibration absorbers (DVA). Although the relevant topics have been studied for decades, the trade-off between capability of suppressing multiple resonant peaks and complexity of absorbers has not been well addressed. In this paper, the vibration suppression problem of a uniform Euler-Bernoulli beam with closely spaced natural frequencies is investigated. To achieve desired vibration reduction, a two-DOF DVA is connected to the beam through a pair of a spring and a dashpot. By introducing a virtual ground spring, the parameters of the absorber are determined via extended fixed point theory. The proposed method only requires univariate optimization and is computationally efficient. Numerical examples conducted verify the viability of the proposed method and the effectiveness of a two-DOF DVA in suppressing double resonances.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

scholarly journals Multiple sources of signal amplification within the B cell Ras/MAPK pathway

2018 ◽  
Author(s):  
Justin D. Mclaurin ◽  
Orion D. Weiner
Keyword(s):  
Positive Feedback ◽  
Signal Amplification ◽  
Mapk Pathway ◽  
Threshold Level ◽  
Cell Types ◽  
Multiple Sources ◽  
Analog To Digital ◽  
Ras Activation ◽  
Wide Range ◽  
Erk Activity

AbstractThe Ras-Map kinase (MAPK) cascade underlies functional decisions in a wide range of cell types and organisms. In B cells, positive feedback-driven Ras activation is the proposed source of the digital (all-or-none) MAPK responses following antigen stimulation. However, an inability to measure endogenous Ras activity in living cells has hampered our ability to test this model directly. Here we leverage biosensors of endogenous Ras and ERK activity to revisit this question. We find that BCR ligation drives switch-like Ras activation and that lower BCR signaling output is required for the maintenance versus the initiation of Ras activation. Surprisingly, digital ERK responses persist in the absence of positive feedback-mediated Ras activation, and digital ERK is observed at a threshold level of Ras activation. These data suggest an independent analog-to-digital switch downstream of Ras activation, and reveals that multiple sources of signal amplification exist within the Ras-ERK module of the BCR pathway.

scholarly journals Robot Modeling for Physical Rehabilitation

Robotics ◽  
2013 ◽  
pp. 1212-1232 ◽  
Author(s):  
Rogério Sales Gonçalves ◽  
João Carlos Mendes Carvalho
Keyword(s):  
Mathematical Models ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Industrial Robots ◽  
Limb Movements ◽  
Rehabilitation Robots ◽  
Wide Range ◽  
Movable Platform ◽  
Human Limb ◽  
Robot Modeling

The science of rehabilitation shows that repeated movements of human limbs can help the patient regain function in the injured limb. There are three types of mechanical systems used for movement rehabilitation: robots, cable-based manipulators, and exoskeletons. Industrial robots can be used because they provide a three-dimensional workspace with a wide range of flexibility to execute different trajectories, which are useful for motion rehabilitation. The cable-based manipulators consist of a movable platform and a base, which are connected by multiple cables that can extend or retract. The exoskeleton is fixed around the patient's limb to provide the physiotherapy movements. This chapter presents a summary of the principal human limb movements, a review of several mechanical systems used for rehabilitation, as well as common mathematical models of such systems.

scholarly journals Originals of operating images for generalized problems of unsteady heat conductivity

2019 ◽  
Vol 14 (4) ◽  
pp. 77-86 ◽  
Author(s):  
E. M. Kartashov
Keyword(s):  
Mathematical Models ◽  
Bessel Functions ◽  
Applied Mathematics ◽  
Operational Calculus ◽  
Polymeric Materials ◽  
Thermal Reaction ◽  
Heaviside Step Function ◽  
External Influences ◽  
Wide Range ◽  
Variable Function

A series of operating (Laplace) non-standard images, the originals of which are absent in well-known reference books on operational calculus, are considered. By reducing one of the basic images to the Riemann-Mellin contour integral for the modified Bessel functions and analyzing the corresponding inversion formula using the approaches of the complex variable function theory, an analytical form of the original original is found, which is abrupt in nature with a break point. It is shown that analytical solutions of the corresponding mathematical models using the found originals have a wave character, which is expressed by the presence of the Heaviside step function in the solutions. The latter means that at any time there is a region of physical disturbance to the point of discontinuity and an unperturbed area after the point of discontinuity. The images studied are included in the operational solutions of mathematical models in many areas of applied mathematics. physics, thermomechanics, thermal physics, in particular in the theory of thermal shock of viscoelastic bodies, in the study of the thermal reaction of solids based on the classical Maxwell-Cattaneo-Lykov-Vernott phenomenology, taking into account the final rate of heat propagation. These models are needed to study the thermal reaction of relatively new consolidated structurally sensitive polymeric materials in structures exposed to high-intensity external influences. The analytical relations obtained for the originals and the original improper integrals resulting from them, containing combinations of Bessel functions, can be used in the general methodology of constructing and applying various mathematical models in a wide range of external influences on materials in many fields of science and technology.

Some Results on Axisymmetric Vibration of Spherical Shells of Variable Thickness

1990 ◽  
Vol 112 (4) ◽  
pp. 432-437 ◽  
Author(s):  
A. V. Singh ◽  
S. Mirza
Keyword(s):  
Variable Thickness ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Spherical Shells ◽  
Varying Thickness ◽  
Wide Range

Natural frequencies and mode shapes are presented for the free axisymmetric vibration of spherical shells with linearly varying thickness along the meridian. Clamped and hinged edges corresponding to opening angles 30, 45, 60 and 90 deg have been considered in this technical brief to cover a wide range from shallow to deep spherical shells. Variations in thickness are seen to have very pronounced effects on the frequencies and mode shapes.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

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