Simplified modeling of beam vibrations induced by a moving mass by regression analysis

In this paper, we propose a fast computation of beam-type dynamic response to a moving mass. Dynamics of a single-span beam is first accurately computed with a semi-analytical procedure based on characteristic orthogonal polynomials (COPs), in the case of a force or a mass traveling across. A regression analysis is then adopted to automatically define the effects of the moving mass once the effects of the moving force are known. Best-fitting multivariable correlation splines, with strictly given coefficients, are obtained. The provided correlation splines conveniently interpolate the maximum design parameters of the base beam over a wide range of load inertia and velocity. Results provided are valid for any geometry and elastic stiffness of the beam, thanks to a properly set normalization factor here defined. Hence, practitioners are provided with an effortless and highly simplified direct prediction of design parameters when inertial interactions are taken into consideration