桥梁动态响应

1
Introduction
This paper assesses a fundamental engineering problem of the vibrations of axially prestressed thick beam resting on elastic foundation and traversed by concentrated masses traveling with nonuniform velocity. A basic understanding of the complexity of the dynamic interactions between structural members and the masses traversing them is very vital as it helps in controlling structural vibrations and saves operations of such dynamical system. Thus, on this subject, a lot exists in the literature especially when only the force effect on the vibrating system is considered. Few examples of these studies are found in Refs. ͓1–14͔. In most of the existing works in literature, applications of the solution techniques and the theories developed by several researchers are limited to the cases where the velocity or the acceleration of the traveling masses is held constant throughout its motion on the structures. However, situation arises when the mass accelerates by a forward force or decelerates reduces speed and comes to rest at any desired position on the beam, causing the friction between the mass and the beam to increase considerably. Under such condition, the vibrating system exhibits dynamic behavior, which may be more complicated. Among few authors in recent times who made effort to tackle the problem of the elastic beam undergoing flexural vibrations under the passage of accelerating loads are Wang ͓15͔ who studied the dynamical analysis of a finite inextensible beam with an attached accelerating mass. He employed the Galerkin procedure in conjunction with the method of numerical integration to tackle the partial differential equations, which describe the transient vibrations of the beam-mass system. He concluded that the applied forward force amplifies the speed of the mass and the displacement of the beam. Muscolino and Palmeri ͓16͔ investigated the response of beams resting on viscoelastiContributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 3, 2009; final manuscript received December 8, 2010; published online April 7, 2011. Assoc. Editor: Wei-Hsin Liao.
cally damped foundation to moving oscillators. They proposed a novel state-space formulation in which a number of internal variables are introduced with the aim of representing the frequencydependent behavior of the viscoelastic foundation. In their study, they figured-out that the inaccuracy associated with the use of effective values of stiffness and damping for the foundation, widely adopted in the conventional techniques, could be unacceptable for engineering purposes. Hilal and Zibdeh ͓17͔ investigated the vibration analysis of beams with general boundary conditions traversed by a single point force traveling with variable velocity. They obtained analytical solution to the beam problem and compared the results with the same beam under the actions of a concentrated force traveling at constant velocity. The dynamical problem tackled here disregards the inertial effects of the moving load as it traverses the beam ͓18͔. Thus, the model is limited to the case when the mass of the moving load is assumed very small compared with the mass of the structure. The model in which the moving load has commensurate value with that of the structure is not covered by their theory and analysis. In such case, inertia effect of the moving load cannot be neglected and the mathematical analysis becomes more complex. The authors also limited their studies to the Bernoulli–Euler theory of flexure. Nevertheless, it is easy to see that a typical element of an elastic system performs not only a translatory motion but also rotates ͓19͔. Thus, this work therefore investigates the dynamic response of a prestressed Rayleigh beam resting on elastic foundation and traversed by mass traveling at nonuniform velocity ͓20͔. Effects of some very important beam parameters on the motions of the vibrating system are investigated.
Dynamic Response of Prestressed Rayleigh Beam Resting on Elastic Foundation and Subjected to Masses Traveling at Varying Velocity
In this study, the dynamic response of axially prestressed Rayleigh beam resting on elastic foundation and subjected to concentrated masses traveling at varying velocity has been investigated. Analytical solutions representing the transverse-displacement response of the beam under both concentrated forces and masses traveling at nonuniform velocities have been obtained. Influence of various parameters, namely, axial force, rotatory inertia correction factor, and foundation modulus on the dynamic response of the dynamical system, is investigated for both moving force and moving mass models. Effects of variable velocity on the vibrating system have been established. Furthermore, the conditions under which the vibrating systems will experience resowk.baidu.comance effect have been established. Results arrived at in this paper are in perfect agreement with existing results. ͓DOI: 10.1115/1.4003405͔ Keywords: axially prestressed, elastic foundation, concentrated masses, rotatory inertia, dynamic response
S. T. Oni B. Omolofe
e-mail: babatope_omolofe@yahoo.com Department of Mathematical Sciences, School of Sciences, Federal University of Technology, PMB 704, Ondo State, Akure 234000, Nigeria