Analytical solution for an infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to arbitrary dynamic loads

An analytical solution for the dynamic response of an infinite beam resting on a viscoelastic foundation and subjected to arbitrary dynamic loads is developed in this paper. Fourier and Laplace transforms are utilized to simplify the governing equation of the beam to an algebraic equation, so that the solution can be conveniently obtained in the frequency domain. The convolution theorem is employed to convert the solution into the time domain. Final solutions of beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The validation of the proposed solution is verified by considering the solutions of several special dynamic loads and comparing the degraded solution to the known results. Further complicated dynamic loads, such as impulsive loads and time-lag loads, are also discussed and analytical solutions are presented. These relationships can be an effective tool for practitioners.