Vibration Analysis of Cracked Structures as a Roving Body Passes a Crack Using the Rayleigh-Ritz Method

Sinniah Ilanko (School of Engineering, The University of Waikato)
Yusuke Mochida (School of Engineering, The University of Waikato)
Julian De Los Rois (School of Engineering, The University of Waikato)

EPI International Journal of Engineering
Vol 1 No 2 (2018): Volume 1 Number 2, August 2018 with Special Issue on Railway Engineering

The natural frequencies of a cracked plate with a roving mass were computed using the Rayleigh-Ritz Method for various sets of boundary condition. The obtained frequencies exhibit a sudden shift as a roving body crosses a crack. If the crack is only partial and continuity of translation is maintained, then the frequency shift occurs only when the body possesses a rotary inertia. If the crack is a complete one (through thickness) which permits differential translation to occur on either side of the crack, a particle having mass only (translatory inertia) is sufficient to cause a sudden shift. There is no need for a rotary inertia. This is potentially useful in detecting cracks in structures, as it is possible to track the changes in the natural frequencies of a structure as a test body such as a vehicle on a bridge moves and identify points where sudden frequency changes occur.