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Biomaterials and Biomedical Engineering
  Volume 4, Number 1, March 2019 , pages 45-58

Analysis of the size-dependent wave propagation of a single lamellae based on the nonlocal strain gradient theory
Farzad Ebrahimi, Farin Zokaee and Vinyas Mahesh

    In the present article, the general wave propagation behavior of a single lamellae biological system was analyzed. The Lamellae is the main component of cortical bone. Its shape can be approximated by a cylindrical shell; so with using shell theories as displacement relations and the nonlocal strain gradient theory (NSGT) as constitutive relation was obtained the equation of motion. Using the NSGT leads to the effectiveness of scale parameter on equations of motion and the obtained results. The governing equations are derived by Hamilton\'s principles. The results are showing the variations of the overall trend of wave velocity toward wave vector have descending scheme and wave frequency against wave vector have ascending scheme; also were investigated effects of size and geometrical parameters on wave velocity and wave frequency. It was shown uptrend of types of wave velocities for wave vectors greater than 105.
Key Words
    bone; lamellae, osteon; wave propagation; size effect
Farzad Ebrahimi and Farin Zokaee: Faculty of engineering, Imam Khomeini International University, Qazvin, Iran
Vinyas Mahesh: Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, India

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