Vibration modes and wave propagation of the rail under fastening constraint

•A methodology is proposed to study rail vibrations and control by fastening constraints.•Vibration modes of rail-fastening are identified by operating deflection shapes.•Waves of rail-fastening are measured by synchronized multiple-acceleration wavelet.•A 3D finite element model of rail-fastening is developed and validated.•Sensitivity analysis of fastening parameters provide insights into rail vibration control. This paper investigates three-dimensional (3D) rail vibrations under fastening constraint up to 5000 Hz and provides insights into rail vibration control by fastening parameters. A methodology is proposed, including experimental investigation and numerical simulations of rail vibrations. Three steps are considered: 1) experimental investigation of rail vibrations under fastening constraint; 2) validation and analysis of 3D finite element (FE) modeling of rail-fastening systems; 3) rail vibration control by fastening parameters. In Step 1, operating deflection shape (ODS) and synchronized multiple-acceleration wavelet (SMAW) measurements are applied to identify rail vibration modes and measure wave propagation characteristics under fastening constraint. In Step 2, a 3D FE model capable of reproducing the dynamic behaviors of rail-fastening up to 5000 Hz is developed to analyze rail vibrations and validated using measurements from Step 1. In Step 3, insights into the control of rail vibrations are gained by sensitivity analysis of fastening parameters using the validated 3D FE model from Step 2. The results indicate that (1) under fastening constraint, ODS measurement identifies vertical bending modes, longitudinal compression modes, and lateral bending modes of the rail with shifted frequencies and significantly reduced vibration amplitude compared to that of free rail. (2) Vertical wave attenuation of rail-fastening is relatively small between 1800 and 3600 Hz, and lateral wave attenuation presents a dominant peak at about 3800 Hz. (3) Compared to the vertical and lateral directions, the fastening system constrains the longitudinal rail vibrations less strongly. (4) The change of fastening stiffness and damping can control rail mode frequencies and their vibration amplitude, and influence the wave propagation velocities and attenuation along the rail.