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Advances in Nano Research
  Volume 7, Number 2, March 2019 , pages 135-143

Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme
Farzad Ebrahimi, Ali Dabbagh, Timon Rabczuk and Francesco Tornabene

    The important effect of porosity on the mechanical behaviors of a continua makes it necessary to account for such an effect while analyzing a structure. motivated by this fact, a new two-step porosity dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) porous nanobeams. In the introduced homogenization method, which is a modified form of the power-law model, the effects of porosity distributions are considered. Based on Hamilton's principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adapted to put emphasis on the role of each variant on the wave dispersion behaviors of porous FG nanobeams.
Key Words
    wave propagation; porous materials; functionally graded materials (FGMs); nonlocal elasticity theory
(1) Farzad Ebrahimi, Ali Dabbagh:
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran;
(2) Timon Rabczuk:
Institute of Structural Mechanics (ISM), Bauhaus-University Weimar, Weimar 1599423, Germany;
(3) Francesco Tornabene:
Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna, Bologna, Italy.

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