Dynamic Assessment and Modeling of the Modal Frequencies and Shapes of Bovine Tibia

Abstract

Thirteen long tibia (bovine) bones were utilized in vitro to experimentally extract modal frequencies in the cranial-caudal (C-C) and medial–lateral (M–L) planes. Bones were instrumented with four single-axis accelerometers uniformly placed along the length of the bone and hammer impacted at different locations in both planes. Frequency response function (FRF) and complex mode indicator function (CMIF) techniques were used to identify the modal frequencies. CMIF has an advantage of detecting closely spaced modes by excluding misinterpreted peaks. It was found that the difference between the two methods did not exceed 2.98%. CMIF data were more consistent when varying impact location. The effect of bone's geometrical attributes on modal frequencies was statistically scrutinized and highly correlated parameters were identified. Bone length exhibited high correspondence to frequencies (p < 0.05) for practically all modes. Also, four simple equations were developed, relating modes 1 and 2 in the C-C and M-L planes to bone length. To determine the first and second modal shapes, subset of 6 tibia bones was further instrumented. Mode shapes were extracted in the C-C and M-L planes.