Theoretical and numerical study of symmetric, in-plane, free vibration of Timoshenko portal frame with open crack

Abstract

The local flexibility introduced by cracks changes the vibration behaviour of the structure and by examining this change, crack severity can be identified. This paper presents the natural frequencies of symmetric, in-plane free-vibrations of Timoshenko portal frame with and without open crack for different boundary conditions. Cracked segment is modelled as two segments connected by a massless torsional spring. Considering appropriate compatibility requirements at the crack section in any one of segments and at the junction of two segments, the characteristic equations are established for corresponding boundary conditions and solved for natural frequencies by numerically. Crack location ranging from 20% to 70% of length of segment and crack size ranging from 20% to 60% of depth have been considered. Results obtained analytically are compared numerically using standard commercially available finite element software. The frame has been modelled by using quadratic quadrilateral shell elements and quarter-point singular elements are employed around the crack-tip. It is observed that as expected, with increase in crack depth the change in frequencies of the frame with and without crack increases. The maximum difference between the analytical and numerical results is 7.09% for all the cases considered, which proves usefulness of the data.