Resonance of a rectangular plate influenced by sequential moving masses

In this work, an improved semi-analytical technique is adopted to track the dynamic response of thin rectangular plates excited by sequential traveling masses. This technique exploits a so-called indirect definition of inertial interaction between the moving masses and the plate and leads to a reduction, in the equations of motion, of the number of time-varying coefficients linked to the changing position of the masses. By employing this optimized method, the resonance of the plate can be obtained according to a parametric study of relevant maximum dynamic amplification factor. For the case of evenly spaced, equal masses travelling along a straight line, the resonance velocity of the masses themselves is also approximately predicted via a fast methodology based on the fundamental frequency of the system only

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