Analytical-numerical modelling of bending vibrations of a modernized hydro-friction torsion damper for high-speed electric rolling stock

An analytical-numerical model is developed for the variable-section shaft of a modernized hydro-friction torsion damper for high-speed electric rolling stock. The spatial coefficients are derived explicitly from line mass m z , flexural rigidity D z = E z I z , and separate restoring and rotational terms. The source model uses 100 sections, piecewise-linear approximation, Fourier separation and a one-sided Laplace transform. A variable-coefficient benchmark with 50-400 Hermite elements verifies the spatial discretization: at 100 elements the curvature-energy and bending-moment errors are 0.00368 % and 0.00822 %, or 0.00529 % and 0.01234 % with linearly interpolated properties. These results verify the benchmark, not the complete damper model. Field observations of 3-5 Hz horizontal and 7-12 Hz vertical vibrations and piston velocities up to 520/580 mm/s are used only as operating context because calibrated transmitted loads and shaft-strain histories are unavailable. No unsupported stress-reduction percentage is claimed.