DYNAMIC IMPACT FACTOR OF ACCELERATING MASSES ON PRESTRESSED TAPERED BEAM RESTING ON ELASTIC SUBGRADE WITH STIFFNESS VARIATION

Abstract

This study assesses the dynamic impact factor of an accelerating masses on a prestressed tapered beam resting on two parameter elastic subgrade with stiffness variation under the action of accelerating masses. The governing equation of the beam model is a fourth order non-homogeneous partial differential equation which is prescribed according to the Bernoulli-Euler beam theory of flexure. An approximate analytical solution to this complex beam-mass interactions problem is sought. To accomplish this, the Weighted Residual Method in conjunction with series representation of dirac delta function is used in first instance to transform the fourth order partial differential equation governing the flexural motion of the structural member to a system of second order ordinary differential equations. This transformed system of equations is further simplified using the asymptotic method due to Strubble. The simplified system of second order ordinary differential equation obtained through this procedure is then solved using Duhamel Integration Method and the solution representing the response of this vibrating structural member to a moving force and accelerating moving masses is obtained with classical boundary conditions. Analysis of the various results obtained are presented. It was found that an increase in the values of structural parameters such as axial force N, shear modulus S and foundation modulus F reduces the response amplitudes of the tapered Bernoulli-Euler beam subjected to accelerating masses. It is also observed that the larger the span length L of the beam, the lower the magnitude of the dynamic impact factor. For accelerating, decelerating and uniform velocity type of motion, it is found that the value of the dynamic impact factor decreases for all the illustrative examples considered in this study as the values of the various vital structural parameters increases.