Influence of Inertial Vlasov Foundation Parameters on the Dynamic Response of the Bernoulli-Euler Beam Subjected to A Group of Moving Forces-Analytical Approach.

The subject of this study is the vibration of the Bernoulli-Euler beam on a three-parameter inertial foundation caused by a group of moving forces. The solution to the problem is obtained analytically. The influence of deformable foundation properties on the dynamic response of the beam in the case of forced vibration and the case of free vibration after the load has left the beam is analysed. The influence of velocity on the dynamic response of the beam is also investigated in both cases. The results can be used as a benchmark for calculating more complex engineering structures under moving loads caused by road or railroad vehicles. The results of the investigation are presented in the figures. It is evident that the coefficient determining the foundation inertia has a significant influence on the dynamic deflection of the beam. Taking shear into account in the Vlasov foundation model has little effect on the dynamic deflections of the beam. The equivalent damping number introduced into the Kelvin-Voigt model takes into account the structure damping and mass damping of the beam.

Analytical solution for bending vibration of a thin-walled cylinder rolling on a time-varying force.

This paper presents the analytical solution of radial vibration of a rolling cylinder submitted to a time-varying point force. In the simplest situation of simply supported edges and zero in-plane vibration, the cylinder is equivalent to an orthotropic pre-stressed plate resting on a visco-elastic foundation. We give the closed-form solution of vibration as a series of normal modes whose coefficients are explicitly calculated. Cases of both deterministic and random forces are examined. We analyse the effect of rolling speed on merging of vibrational energy induced by Doppler's effect for the example of rolling tyre.