in this paper, an analytical study of the forced vibrations of hexapod table is studied. considering external force as a time sinusoid force, forced vibrations of the platform are investigated. resonance frequencies and vibrations of the moving platform are also calculated in different directions. the results of the analytical approach are verified using fem simulation. modelling the harmonic m...

In his technical report~\cite[sec. 6]{barrontech}, Barron states that the de Bruijn's identity for Gaussian perturbations holds for any RV having a finite variance. In this report, we follow Barron's steps as we prove the existence of $J_{\alpha}\left(X + \sqrt[\alpha]{\eta}N\right)$, $\eta>0$ for any Radom Variable (RV) $X \in \mathcal{L}$ where \begin{equation*} \mathcal{L} = \left\{ \text{RV...

the vibrations produced by trains include two parts which are deterministic and random vibrations. due to variation of dynamic loads and patterns of load-time, the random vibration of moving train is one of the most important issues in the field of railway engineering. one of the important sources in producing the train vibrations is rail roughness and irregularities. in this paper, responses o...