Applied Mathematics and Mechanics

, Volume 24, Issue 3, pp 363–372 | Cite as

Method of model analysis for flexible head impacting with elastic plane

  • Zhao Gui-fan
  • Tan Hui-feng
  • Du Xing-wen


To consider the head is a flexible multi-layer structure and the contact-impact is flexible, the Hertz Contact Law is unsuitable for analyzing the dynamic response of human head impacts elastic plane with initial speed. In this paper, the process of head impacting with elastic plane is modeled as a response of vibrant system, and methods like mechanical network figure and mechanical impedance is taken to resolve this dynamic response problem. Based on the actual head structure, head is modeled as a vibrant model, which concludes the masses of scalp and bone in the impact area, the masses in the other part of the head and the brain, the stiffness of the head, and the damp coefficient of the scalp and brain. At the same time, the elastic plane is simplified as a vibrant model including mass, stiffness and damp. These two vibrant models are linked into one vibrant systematic model. In order to calculate the elastic deformation and the impact acceleration of the head, the models are transformed into mechanical girding figure at violent vibration point. The dynamic impact force of the system, the impact acceleration of the head, the elastic deformation of the plane and the fixed frequency of the system can be worked out by calculating the velocity impedance at the violent vibration point when the initial impact speed is known. The results fit the test data well, which proves that this method is available for the analysis of the dynamic response of the system under impact.

Key words

mechanical impedance dynamic response head impact 

Chinese Library Classification


2000 MR Subject Classification



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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Zhao Gui-fan
    • 1
  • Tan Hui-feng
    • 1
  • Du Xing-wen
    • 1
  1. 1.Research Center for Composite MaterialsHarbin Institute of TechnologyHarbinP.R. China

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