The interactive vibration behavior in a suspension bridge system under moving vehicle loads and vertical seismic excitations

In this paper, the vibration behavior of a suspension bridge due to moving vehicle loads with vertical support motions caused by earthquake is studied. The suspension bridge system is presented here by two coupled nonlinear cable–beam equations aiming to describe both the dynamic characteristics for the supporting cable and the roadbed, respectively. The dynamic effect of traffic vehicles are modeled as a row of equidistant moving forces, while the earthquake movement is simulated as the vertical oscillation of boundary supports. The governing integro-differential equations are transferred into a set of ordinary differential equations, which can be solved analytically in the present study. Furthermore, the world’s largest designed suspended bridge – Messina Bridge – is examined (central span of length 3.3 km) and the modified Kobe earthquake records is applied to the calculations in order to validate the present study and the proposed methodology. As a result, the deformation of the cable produces more oscillations than that of the beam since the material property of the cable is more flexible. It is shown that the interaction of both the moving loads and the seismic forces can substantially amplify the response of long-span suspension bridge system especially in the vicinity of the end supports.     

Multiple periodic oscillations in a nonlinear suspension bridge system

In this paper, we study periodic oscillations in a suspension bridge system governed by the coupled nonlinear wave and beam equations describing oscillations in the supporting cable and roadbed under periodic external forces. By applying a variational reduction method, it is proved that the suspension bridge system has at least three periodic oscillations.     

Initial-boundary value problem for the nonlinear string-beam system

This paper deals with a nonlinear string-beam system describing the torsional-vertical oscillations of a suspension bridge. We consider the initial-boundary value problem and study the existence and uniqueness question. We assume time independent right hand sides, but allow quite general nonlinear terms. Using the Faedo-Galerkin method we prove the existence of a unique solution on an arbitrary large time interval.     

Couple stress fluid improve rub-impact rotor-bearing system – Nonlinear dynamic analysis

This study performs a dynamic analysis of the rub-impact rotor supported by two couple stress fluid film journal bearings. The strong nonlinear couple stress fluid film force, nonlinear rub-impact force and nonlinear suspension (hard spring) are presented and coupled together in this study. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The numerical results show that the dynamic behaviors of the system vary with the dimensionless speed ratios, the dimensionless unbalance parameters and the dimensionless parameter, l^∗. Inclusive of the periodic, sub-harmonic, quasi-periodic and chaotic motions are found in this analysis. The results of this study contribute to a further understanding of the nonlinear dynamics of a rotor-bearing system considering rub-impact force existing between rotor and stator, nonlinear couple stress fluid film force and nonlinear suspension. We also prove that couple stress fluid used to be lubricant do improve dynamics of rotor-bearing system.     

Linear and nonlinear response of pipeline suspension bridge due to moving fluid

Basing on the nonlinear dynamic model of flexible pipeline suspended by spatial system of cables, described in Ref. [1], the linear and nonlinear vibrations are investigated in order to estimate the nonlinear effects. The model is based on substructure technique and formulated including features specific to analyzed structure, for example large displacements and time dependent parameters appearing in equations of motion due to fluid flowing inside the pipeline. Due to the fact that modelling problem for the analyzed structure is one's own complicated, a simple case when the conveying fluid is idealized simply as a ballast moving inside the pipe is considered. This paper presents a short numerical analysis of linear and nonlinear, static and dynamic response of exemplary structure for three different cases: during filling the pipe with fluid, when the pipeline is completely filled and during emptying the pipe. Moreover, for the linear problem, the influence of a speed of the fluid on the stability of the pipeline suspension bridge is investigated. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The global structure of periodic solutions to a suspension bridge mechanical model

We study two systems of nonlinearly coupled ordinary differentialequations that govern the vertical and torsional motions ofa cross-section of a suspension bridge. We observe numericallythat the structure of the set of periodic solutions changesconsiderably when we smooth the nonlinear terms. The smoothednonlinearities describe the force that we wish to model morerealistically and the resulting periodic solutions more accuratelyreplicate the phenomena observed at the Tacoma Narrows Bridgeon the day of its collapse. The main conclusion is that purelyvertical periodic forcing can result in subharmonic primarilytorsional motion.     

一类非线性桥梁方程解的多重性

本文主要利用变分方法得出一类非线性桥梁方程Lu bu~ -au~-=1 εh(x,t)在H中至少存在三个解,其中3相似文献   

Multiple periodic solutions for a nonlinear suspension bridge equation

We investigate nonlinear oscillations in a fourth-order partialdifferential equation which models a suspension bridge. Previouswork establishes multiple periodic solutions when a parameterexceeds a certain eigenvalue. In this paper, we use Leray-Schauderdegree theory to prove that if the parameter is increased further,beyond a second eigenvalue, then additional solutions are created.     

Center manifold approach to the control of a tethered satellite system

It is well known that in a linearized analysis the in-plane oscillation of a tethered satellite system about the radial earth pointing position decouples from the out-of-plane oscillation. By tension control, therefore, only the in-plane but not the out-of-plane oscillation can be affected. Hence, using tension control linearization of the equations of motion cannot be used and a nonlinear problem must be treated. For a simple mechanical model of a tethered satellite system we show by means of center manifold theory that for the nonlinear system the out-of-plane oscillations can be stabilized by tension control.     

Existence of solitons in the nonlinear beam equation

This paper concerns the existence of solitons, namely stable solitary waves in the nonlinear beam equation with a suitable nonlinearity. An equation of this type has been introduced in [P. J. McKenna and W. Walter, Arch. Ration. Mech. Anal., 98 (1987), 167-177] as a model of a suspension bridge. We prove both the existence of solitary waves for a large class of nonlinearities and their stability. As far as we know this is the first result about stability of solitary waves in nonlinear beam equation.     

Existence and stability of large scale nonlinear oscillations in suspension bridges

A nonlinear model of a suspension bridge is considered in which large-scale, stable oscillatory motions can be produced by constant loading and a small-scale, external oscillatory force. Loud's implicit-function theoretic method for determining existence and stability of periodic solutions or nonlinear differential equations is extended to a case of a non-differentiable nonlinearity.Author partially supported by NSF under Grant DMS 8318204 and AFOSR Grant 85-0330.Author partially supported by NSF under Grant DMS 9519882.Author partially supported by NSF under Grant DMS 8519776.     

Autoresonant asymptotics in an oscillating system with weak dissipation

We study a system of two first-order differential equations arising in averaging nonlinear systems over fast single-frequency oscillations. We consider the situation where the original system contains weak dissipative terms. We construct the asymptotic form of a two-parameter solution with an unbounded increasing amplitude. This result gives a key for understanding autoresonance in weak dissipative systems as a phenomenon of significant increase in the forced nonlinear oscillation initiated by a small external pumping. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 102–111, July, 2009.     

Oscillations and multiple periodic solutions in systems of differential equations with piecewise continous delay

A system of two first-order liner differential equations with piecewise continuous delay is studied. The delay generates unusually interesting oscillation and periodic properties of the system. In particular nonlinear phenomena such as simultaneous existence of periodic solutions with different periods observed in linear delay systems     

具脉冲和时滞影响的非线性抛物系统边值问题的振动结果

研究一类具非线性扩散项的脉冲时滞抛物偏微分系统解的振动性,借助Green公式、垂直相加法和脉冲时滞微分不等式,获得了该类系统在Robin边值条件下振动的充分性条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

Oscillation and stability of nonlinear neutral impulsive delay differential equations

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equation are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.     

Existence of global attractors for the coupled system of suspension bridge equations

A mathematical model of the suspension bridge describes the vibration of the road bed in the vertical plain and that of the main cable. We show the existence of an absorbing set for the solution of the problem. Furthermore, the global attractors of the coupled system of suspension bridge are studied by a new semigroup approach.     

Nonlinear oscillations in a MEMS energy scavenger

The dynamics of an electret-based, capacitive, vibration-to-electric micro-converter (energy scavenger) is described by a set of ODEs where a second-order equation is coupled to two first-order equations through strongly-nonlinear terms. The nonlinear regimes of forced oscillations are analyzed with a semi-analytical approach, finding that the system exhibits features typical of Duffing-like nonlinear oscillators, such as jumps and multivalued frequency-response curves, with both stable and unstable periodic solutions. It is also proved that, for appropriate combinations of parameters, the system acts as a linear, damped oscillator, independently of the oscillation amplitude: in this case, the nonlinear coupling term reduces to a viscous-like term, physically interpretable as electromechanical damping.     

Exponential decay rate of a nonlinear suspension bridge model by a local distributed and boundary dampings

In this paper, we investigate the decay properties of the unconstrained one dimensional suspension bridge model. With only partial damping acting on one or on both equations and with boundary dampings, we prove that the first order energy is decaying exponentially, our method of proof is based on the energy method to build the appropriate Lyapunov functional. Moreover, we develop a numerical algorithm which is based on the finite element method to approximate the spatial variable and the Crank–Nicolson type of symmetric difference scheme to discretize the time derivative, and also a Picard type iteration process for solving the system of nonlinear equations obtained by discretization. At the end, we present some numerical experiments to illustrate our theoretical results.     

一类二阶非线性变时滞微分方程的振动准则

研究二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0,对振动因子p(t)变符号的情况讨论了方程的振动性,通过两个已有引理得到了方程振动的两个充分条件.所得结论推广了原有的二阶非线性微分方程与变时滞微分方程当系数不变号时的振动性结论,完善了具变符号振动因子的二阶非线性变时滞微分方程的研究.