Active Vertical Vibration Control of Railway Vehicle Carbody with Variable Cross-Section Using Secondary and Piezoelectric Actuators

The longitudinal non-uniformities in mass and stiffness distributions of railway vehicle carbodies, caused by doors, windows, and equipment compartments, significantly affect elastic vibrations and ride comfort. This paper establishes a vertical elastic vibration model based on the Euler–Bernoulli beam theory for variable cross-section carbodies, using piecewise uniform beam segments to represent actual cross-sectional properties. The transfer matrix method combined with the Newton–Raphson iteration is employed to solve natural frequencies and mode shapes. A hybrid active control strategy integrating secondary vertical electro-hydraulic actuators and distributed piezoelectric actuators is proposed. Based on a decentralised control architecture, a H∞ robust optimal controller is designed to suppress both rigid-body motions and the first two elastic modes. Simulation results at 250 km/h with a 20% centre-mass proportion show that the combined control reduces the vertical acceleration power spectral density (PSD) at the first vertical bending frequency to 5% of the passive suspension level, and to 35% at bounce and pitch frequencies. The Sperling ride index increases monotonically with speed, with the 20% mass proportion of the middle sub-beam yielding the best performance. The piezoelectric actuator voltage PSD reaches a peak of approximately 4000 V2·Hz−1 near the first bending frequency (0–15 Hz), demonstrating effective elastic vibration suppression, while the secondary actuator force PSD at the second bending frequency remains at around 103 N2·Hz−1, indicating limited contribution. The proposed variable cross-section beam model combined with hybrid control provides a theoretical foundation and engineering reference for lightweight design and active vibration reduction of high-speed trains.