Summary
In this paper, we present a solution to the problem of free vibrations of the human head system taking into account the dissipative behaviour of the brain. The mathematical model is based on the three-dimensional theory of viscoelasticity and the representation of the displacement field in terms of the Navier eigenvectors. The frequency equation is solved numerically and the results for eigenfrequencies and damping coefficients are presented for various geometrical and physical parameters of the system. The results obtained are in excellent agreement with the measured eigenfrequencies, and the predicted damping coefficients are within the order of magnitude of the measured ones. From the proposed analysis we have obtained the information that the role of the viscoelastic neck as well as the viscoelastic properties of the skull-brain system have to be simultaneously taken into account in the study of the frequency spectrum of the human head. The analysis of the realistic model is under preparation.
Similar content being viewed by others
References
Misra, J. C., Chakravarty S.: A free-vibration analysis for the human cranial system. J. Biomech.15, 635–645 (1982).
Guarino, J. C., Elger, D. F.: Modal analysis of a fluid-filled elastic shell containing an elastic sphere. J. Sound Vibr.156, 461–479 (1992).
Advani, S. H., Owings, R. P.: Structural modelling of human head. J. Eng. Mech. Div., Am. Soc. Civil Engng101, 257–266 (1975).
Charalambopoulos, A., Dassios, G., Fotiadis, D. I., Kostopoulos, V., Massalas, C. V.: On the dynamic characteristics of the human skull. Int. J. Eng. Sci.34, 1339–1348 (1996).
Charalambopoulos, A., Dassios, G., Fotiadis, D. I., Massalas, C. V.: The dynamic characteristics of the human skull-brain system. Math. Comp. Modelling27, 81–101 (1998).
Charalambopoulos, A., Dassios, G., Fotiadis, D. I., Massalas, C. V.: The dynamic characteristics of the human head-neck system. Int. J. Eng. Sci.35, 753–768 (1997).
Charalambopoulos, A., Fotiadis, D. I., Massalas, C. V.: The effect of geometry on the dynamic characteristics of the human skull. Int. J. Eng. Sci. in print (1998).
Charalambopoulos, A., Fotiadis, D. I., Massalas, C. V.: Frequency spectrum of the bispherical hollow system: the case of the nonuniform thickness human skull. Acta Mech.130, 249–278 (1998).
Charalambopoulos, A., Fotiadis D. I., Massalas, C. V.: Free vibrations of the human viscoelastic skull. Int. J. Eng. Sci. in print (1998).
Håkanson B., Brandt, A., Carlsson, P.: Resonance frequencies of the human skull in vivo. J. Acoust. Soc. Am.95, 1474 (1994).
Hansen, W. W.: A new type of expansion in radiation problem. Phys. Rev.47, 139–143 (1935).
Zhang, S., Jin, J.: Computation of special functions. New York: Wiley-Interscience 1996.
McElhaney, J. H., Fogle, J. L., Melvin, J. W., Haynes, R. R., Roberts, V. L., Alem, N. M.: Mechanical properties of cranial bone. J. Biomech.3, 495–511 (1970).
Schuck, L. Z., Advani, S. H.: Rheological response of human brain tissue in shear. Trans. ASME, J. Basic Eng. 905–911 (1972).
Hickling, R., Wenner, M. L.: Mathematical model of a head subjected to an axisymmetric impact. J. Biomech.6, 115–132 (1973).
Landkoff, B., Goldsmith, W., Sackman, J. L.: Impact on a head-neck structure. J. Biomech.9, 141–151 (1976).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Charalambopoulos, A., Fotiadis, D.I., Ktena, A. et al. The effect of viscoelastic brain on the dynamic characteristics of the human skull-brain system. Acta Mechanica 130, 159–173 (1998). https://doi.org/10.1007/BF01184308
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01184308