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.
