Research Papers

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

[+] Author and Article Information
Reem Yassine, Samir Mustapha

Mechanical Engineering Department,
American University of Beirut,
P.O. Box 11-0236,
Riad El-Solh,
Beirut 1107 2020, Lebanon

Ali Fakhreddine, Mohammad Sayegh

Mechanical Engineering Department,
American University of Beirut,
P.O. Box 11-0236,
Riad El-Solh,
Beirut 1107 2020, Lebanon

Ramsey F. Hamade

Mechanical Engineering Department,
American University of Beirut,
P.O. Box 11-0236,
Riad El-Solh,
Beirut 1107 2020, Lebanon
e-mail: rh13@aub.edu.lb

1Corresponding author.

Manuscript received November 30, 2017; final manuscript received July 5, 2018; published online August 16, 2018. Assoc. Editor: Fabrizio Ricci.

ASME J Nondestructive Evaluation 1(4), 041006 (Aug 16, 2018) (9 pages) Paper No: NDE-17-1111; doi: 10.1115/1.4040797 History: Received November 30, 2017; Revised July 05, 2018

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.

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Fig. 1

Experimental setup for mode shape (M-L plane shown)

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Fig. 2

(a) Two respective cross sections B-B and A-A used for dimensional measurements and (b) sections BB and AA, respectively, from left to right

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Fig. 3

Sample frequency response plots for bone 6 generated using the data from the four accelerometers—lateral direction; acc: accelerometer

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Fig. 4

Schematic of the analysis procedure based on the CMIF

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Fig. 5

Sample CMIF plots versus FRF at different impact locations for Bone 6 generated using the data from each accelerometer—C-C direction; reconstructed CMIF (a); FRF- (b) location 1; (c) location 2; and (d) location 3

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Fig. 6

Sample CMIF plots versus FRF at different impact locations for bone 6 generated using the data from each accelerometer—ML direction; reconstructed CMIF (a); FRF- (b) location 1; (c) location 2; and (d) location 3

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Fig. 7

Experimentally found modes 1 and 2 of tibia bone 6 in the C-C (a) and ML (b) planes

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Fig. 8

Fit representions of (a) mode 1 in the C-C and ML planes and (b) mode 2 in the C-C and M-L planes



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