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This study presents an analytical investigation of the dynamic behavior of a simply supported uniform Bernoulli-Euler beam resting on both constant and variable Pasternak foundations subjected to concentrated moving load with damping. The governing equations of motion were formulated by incorporating the effects of foundation stiffness, shear interaction, damping and load inertia. Analytical solutions were obtained for both moving-force and moving-mass problems. For the constant foundation case, the Generalized Finite Integral Transform technique (GFIT) combined with Laplace transformation and convolution theory is employed, while Galerkin’s method was utilized for the variable foundation case, in place of GFIT. Numerical simulations were performed to compare the responses of the beam under the different loading and foundation conditions. The results showed that moving-mass responses exhibit larger amplitudes than the corresponding moving-force responses and that beams resting on variable Pasternak foundations experience greater deflections than those on constant foundations. The study further demonstrates that the moving-force model cannot be considered a reliable approximation for the moving-mass problem and that constant Pasternak foundations provide a stiffer and safer structural response. The findings contribute to a better understanding of beam-foundation interaction and provide useful information for the design and analysis of engineering structures subjected to moving loads.

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