A CLOSED-FORM SOLUTION OF A BERNOULLI-EULER BEAM ON A VISCOELASTIC FOUNDATION UNDER HARMONIC LINE LOADS

Abstract

Fourier transform is used in this paper to solve the problem of steady state response of a beam on a viscoelastic foundation subjected to a harmonic line load. The solution is constructed in the form of the convolution of the Green function of the beam. The theorem of residue is employed to evaluate the generalized integral such that a closed-form solution can be achieved. All the different combinations of damping and vibration frequency are discussed and analytical solutions are presented. As a special case, the solution of the beam on a Winkler foundation is also discussed. The validation of the solution is verified by considering the static solution of the beam and comparing the degraded solution to a well-known result. The closed-form expression of the result can be used to construct algorithms for the inverse problems of non-destructive testing of pavement structures using vibration devices.