Vibration control of beams subjected to a moving mass using a successively combined control method

• Vibration of an Euler beam excited by a moving mass is analysed.
• Active control of such vibration is studied.
• Sliding mode control is shown to reduce vibration when the moving mass on the beam.
• Sliding mode control and positive position control are combined to suppress vibration effectively.

This study addresses the vibration control of beams subjected to a moving mass, which represent real applications such as vehicle–bridge interaction. Positive position feedback control (PPF) which has been successfully used in vibration control of flexible structures is found not suitable for the current control problem when the moving mass is travelling on the beam as it makes the structure more flexible but is found capable of reducing free vibration after the moving mass leaves the beam. Sliding mode control (SMC) is known to be a robust method to deal with parameter uncertainties and disturbances in vibration, however it is found to be likely to introduce some higher-frequency vibration which is detrimental to the beam. A method combining SMC and PPF is proposed to suppress the vibration of the beam when the moving mass is on and off the beam, which overcomes the above problems and possesses the benefits of both SMC control and PPF control. Simulated numerical examples demonstrate the effectiveness of the proposed method.