Universal analytical solution of the steady-state response of an infinite beam on a Pasternak elastic foundation under moving load. (February 2018) - Froio, Diego; Rizzi, Egidio; Simões, Fernando M.F.; Costa, António Pinto Da
Highlights: Exact derivation by Fourier transform of a universal, explicit closed-form parametric analytical solution of the steady-state response of a uniform infinite Euler–Bernoulli elastic beam on a Pasternak elastic foundation subjected to a concentrated load moving at constant velocity. Rigorous mathematical procedure for classification of the parametric behavior of the solution, by varying the mechanical parameters of the beam-foundation system, based on the parametric nature of the Fourier transform poles. Different types of bending wave shapes are shown to propagate within the beam, including for new solution instances that may be obtained for given values of the physical parameters, such as for a high Pasternak modulus. Original re-derivation and reinterpretation of steady-state physical characteristics, such as critical velocity and two-branch critical damping. Highlighting of characteristic features of the physical steady-state response by a parametric analysis involving normalized deflection, cross-section rotation, bending moment and shear force. Abstract: In this paper, the steady-state response of a uniform infinite Euler-Bernoulli elastic beam resting on a Pasternak elastic foundation and subjected to a concentrated load moving at a constant velocity along the beam is analytically investigated. A universal closed-form analytical solution is derived through Fourier transform, apt to represent the response for all possible beam-foundation parameters. A rigorous mathematical procedure is formulated for classifying the parametric behavior of the solution, including for viscous damping. Depending on such a classification, different types of bending wave shapes are shown to propagate within the beam, ahead and behind the moving load position, and crucial physical characteristics, such as critical velocity and critical damping, are reinterpreted into a wholly exact and complete mathematical framework. Mechanical features of the solution are revealed for the steady-state response in terms of normalized deflection, cross-section rotation, bending moment and shear force.