Dynamic Response of Clamped-Clamped Uniform Bernoulli-Euler Beam Resting on a Pasternak Foundation Subjected to Concentrated Moving Load with Damping Term

The dynamic response of a clamped-clamped uniform Bernoulli–Euler beam resting on a Pasternak foundation under the action of a concentrated moving load with a damping term was investigated in this paper. To solve the governing equation, the Dirac, delta function was expressed as a Fourier cosine series and the generalized finite integral transform, the Struble’s asymptotic technique and the Laplace transform method were used. Thereafter, the clamped-clamped support condition was used to obtain the dynamic response of the beam. The study showed that, the moving force problem is structurally unsafe to approximate the moving mass problem in the design of the dynamical system. In addition, as the values of the damping term, axial force, foundation modulus and shear modulus increases, the deflection profiles of the beam decreases. This implies that the beam’s safety and performance are ensured when the values of each parameter are increased. Finally, the results showed that the damping term had a far higher effect on the beam’s deflection.