Dynamic amplification factor and interactions of a beam under compressive axial force and load travelling at varying velocity

Abstract

In this article, the deflection profile and response characteristic of axially prestressed continuous beam under the actions of load travelling at non-uniform velocity is explored. To achieve this, The governing equation is transformed using weighted residual method to obtain a set of coupled second-order Ordinary Differential Equations (ODEs) governing the amplitude factors of the beam-mass system. This set of ODEs is further simplified by applying a modified asymptotic method of Struble. Impulse response function is finally employed to obtain solutions representing the responses of this structural member to accelerating masses. Dynamic time history is carried out. Deformation and responses due to the stress in the structure are evaluated for different parameters. Dynamic effects of decelerating, accelerating and uniform velocity-type of motions on the dynamic amplification factor (DAF) and response characteristics are extensively studied for various vital structural parameters such as the beam span length, foundation stiffness, prestress, rotatory inertia correction factor, load position and velocity. The values of the amplification factors (DAF) against various pertinent parameters are presented in plotted curves for the pinned-pinned beam. It is found that, for accelerating, decelerating and constant velocity-type of motion, the value of the dynamic amplification factor increases as the values of axial force, foundation subgrade, and rotatory inertia factor increase. Various useful results in perfect agreement with existing studies are presented. It is further established that variations of the various structural parameters of interest significantly alter the response characteristics of the vibrating system.

Keywords

• Beam-mass system
• Response characteristics
• Simply supported
• Moving load
• Duhamel’s integral
• Galerkin’s method