Harmonically Varying Moving Load on Time-Dependent Uniform Beam Resting on Pasternak Foundation - Jimoh A.; A. Joge E.O.; Ajiola D.I.; Oni D.I.; Abiola Kolawole; Adesanmi O.A. (International Journal of Electro-Mechanics and Material Behaviour, 2025)
In this paper, we investigated elastic beam whose properties does not varies with spatial coordinate but constant along the span L of the beam. The moving load considered in this work is harmonically varying moving load with non-classical boundary conditions, time dependent boundary conditions in particular. Also, considered in this work is two parameters foundation which are Winkler and Pasternak foundations. Closed form solutions in plotted form are obtained using Mindlin Goodman [1] method, Fourier series transformation, integral transformation and theorem of convolution. Mindlin Goodman method is used to transformed the non-homogeneous boundary conditions to homogeneous boundary conditions, the Fourier series transformation is used to reduce the fourth order non-homogeneous partial differential equation with singular coefficient describing the dynamical system to second order ordinary differential equation. The resulting equation is solved using integral transformation alongside with the theorem of convolution. The results are presented graphically and it was revealed that, as the structural parameters such as Winkler foundation parameter (K), Pasternak foundation parameter (G), damping coefficient (E), axial force (N), and circular frequency (w), increases, the response amplitude of the time dependent uniform elastic beam reduces. Amongst all the structural parameters, shear modulus (G) and axial force (N) gives more noticeable effects compares to other structural parameters. Higher values of G and N are required in order to reduce the resonance effect in the dynamical system and this could guarantee the safety of lives.
Keywords: Circular frequency of the Moving Load; Damping Coefficient; Harmonically Varying Moving Load; Pasternak foundation; time dependent boundary conditions