On travelling waves in a suspension bridge model as the wave speed goes to zero

2011 ◽  
Vol 74 (12) ◽  
pp. 3998-4001 ◽  
Author(s):  
A.C. Lazer ◽  
P.J. McKenna
Keyword(s):  
Wave Speed ◽  
Travelling Waves ◽  
Suspension Bridge ◽  
Bridge Model

Vibration based damage localization using MEMS on a suspension bridge model

2013 ◽  
Vol 12 (6) ◽  
pp. 679-694 ◽  
Author(s):  
Marco Domaneschi ◽  
Maria Pina Limongelli ◽  
Luca Martinelli
Keyword(s):  
Suspension Bridge ◽  
Damage Localization ◽  
Bridge Model

scholarly journals Propagation of stochastic travelling waves of cooperative systems with noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hao Wen ◽  
Jianhua Huang ◽  
Yuhong Li
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Wave Speed ◽  
Travelling Waves ◽  
Equilibrium Points ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Cooperative System ◽  
Wave Solutions ◽  
Suitable Marker

<p style='text-indent:20px;'>We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of the travelling wave solutions are proven. With a moderately strong noise, the travelling wave solutions are constricted by choosing a suitable marker of wavefront. Moreover, the stochastic Feynman-Kac formula, sup-solution, sub-solution and equilibrium points of the dynamical system corresponding to the stochastic cooperative system are utilized to estimate the asymptotic wave speed, which is closely related to the white noise.</p>

On the instability of inextensible elastic bodies: nonlinear evolution of non-neutral, neutral and near-neutral modes

1993 ◽  
Vol 443 (1917) ◽  
pp. 59-82 ◽  
Keyword(s):  
Linear Theory ◽  
Wave Speed ◽  
Nonlinear Evolution ◽  
Initial Conditions ◽  
Travelling Waves ◽  
Nonlinear Effects ◽  
Elastic Bodies ◽  
Zero Growth ◽  
Main Action ◽  
Amplitude Growth

For inextensible elastic bodies, linear theory predicts that if the reaction stress is compressive and sufficiently large, a transverse progressive wave travelling in the direction of inextensibility may have an imaginary wave speed and grow without bound as a standing wave (Chen & Gurtin 1974). The development of these growing standing waves under the influence of nonlinearity is considered in this paper. Attention is focused on the case for which the negative reaction stress deviates by a small amount from the value corresponding to the zero wave speed, so that the question addressed is how the evolution of the near-neutral waves is (slowly) modulated by nonlinear effects. It is shown, both numerically and analytically, that depending on initial conditions, nonlinearity can make a near-neutral wave grow, decay or have constant amplitude (growth occurs even in the neutral case for which linear theory predicts zero growth), but in every case its main action is to distort the wave profile and make it evolve into a shock within a finite time. It is found that the evolution of some near-neutral waves (corresponding to certain initial conditions) is governed by analytical solutions, with the aid of which we can show that any shock, once it has formed, will eventually decay to zero algebraically. For general initial conditions, the further evolution of the shock cannot be determined from the present analysis, but we may conjecture that the shock thus formed will also decay to zero. Hence nonlinearity stabilizes near-neutral waves through the formation of shocks. However, an important result found for near-neutral waves is that corresponding to some initial conditions, high values of strain (and thus stress) may obtain just before the shock forms, so that there is the possibility that the elastic body may fracture before the decay of shock amplitude occurs. The effects of nonlinearity on non-neutral travelling waves are also studied and it is shown that nonlinearity also makes non-neutral travelling waves evolve into shocks, but in contrast with the situation for near-neutral waves it does not change their amplitudes as time evolves. The present analysis is also applicable to surface waves in pre-stressed materials where zero wave speed may be induced by large enough pre-stresses.

scholarly journals Modelling nonlinear hydroelastic waves

2011 ◽  
Vol 369 (1947) ◽  
pp. 2942-2956 ◽  
Author(s):  
P. I. Plotnikov ◽  
J. F. Toland
Keyword(s):  
Wave Speed ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Lagrangian Description ◽  
Two Dimensional ◽  
Cosserat Theory ◽  
Elastic Sheet ◽  
Eulerian Description ◽  
Eulerian Coordinates ◽  
Special Case

This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff’s hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two-dimensional travelling waves with two wave speed parameters, one for the sheet and another for the fluid, is developed only in terms of Eulerian coordinates.

A periodic reaction–diffusion system modelling man–environment–man epidemics

2017 ◽  
Vol 10 (05) ◽  
pp. 1750074 ◽  
Author(s):  
Zhenguo Bai
Keyword(s):  
Wave Speed ◽  
Global Attractivity ◽  
Travelling Waves ◽  
Spatial Dynamics ◽  
Reaction Diffusion ◽  
Positive Periodic Solution ◽  
System Modelling ◽  
Periodic Reaction ◽  
Minimal Wave Speed ◽  
Disease Spreading

The purpose of this work is to study the spatial dynamics of a periodic reaction–diffusion epidemic model arising from the spread of oral–faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.

MULTISTABILITY, BASIN BOUNDARY STRUCTURE, AND CHAOTIC BEHAVIOR IN A SUSPENSION BRIDGE MODEL

2004 ◽  
Vol 14 (03) ◽  
pp. 927-950 ◽  
Author(s):  
MÁRIO S. T. DE FREITAS ◽  
RICARDO L. VIANA ◽  
CELSO GREBOGI
Keyword(s):  
Chaotic Behavior ◽  
Vibrational Mode ◽  
Basin Of Attraction ◽  
Elastic Beam ◽  
Suspension Bridge ◽  
Boundary Structure ◽  
Bridge Structure ◽  
Coexisting Attractors ◽  
Bridge Model ◽  
Time Periodic

We consider the dynamics of the first vibrational mode of a suspension bridge, resulting from the coupling between its roadbed (elastic beam) and the hangers, supposed to be one-sided springs which respond only to stretching. The external forcing is due to time-periodic vortices produced by impinging wind on the bridge structure. We have studied some relevant dynamical phenomena in such a system, like periodic and quasiperiodic responses, chaotic motion, and boundary crises. In the weak dissipative limit the dynamics is mainly multistable, presenting a variety of coexisting attractors, both periodic and chaotic, with a highly involved basin of attraction structure.

Fatigue Assessment of Suspension Bridges Carrying Rail and Road Traffic Based on SHMS

2012 ◽  
Vol 204-208 ◽  
pp. 2019-2027
Author(s):  
Zhi Wei Chen ◽  
You Lin Xu ◽  
Kai Yuen Wong
Keyword(s):  
Road Traffic ◽  
Good Condition ◽  
Measurement Data ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Road Vehicles ◽  
Fatigue Assessment ◽  
Long Span ◽  
Bridge Model ◽  
Critical Locations

Many long-span suspension bridges have been built around the world, and many of them carry both of rail and road traffic. Fatigue assessment shall be performed to ensure the safety and functionality of these bridges. This paper first briefly introduces the main procedure of fatigue assessment recommended by British Standard, and then it is applied to the Tsing Ma suspension bridge in Hong Kong. Vehicle spectrum of trains and road vehicles are investigated based on the measurement data of trains and road vehicles recorded by the Structural Health Monitoring System (SHMS) installed on the bridge so that fatigue damage assessment will be more realistic and accurate. Stress influence lines corresponding to railway tracks and highway lanes are established based on a complex finite element bridge model so that an accurate vehicle-induced stress response can be estimated based on them. The fatigue-critical locations for different type of bridge components are identified in terms of the maximum stress range due to a standard train running over the bridge. Finally, the fatigue life at the fatigue-critical locations due to both trains and road vehicles are estimated, and the result indicates the bridge is in very good condition.

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