<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natural vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material parameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse distribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.</p></abstract>

In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natural vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material parameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse distribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.

Effect of Kerr Foundation and in-Plane Forces on Free Vibration of FGM Nanobeams with Diverse Distribution of Porosity

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natural vibrations of nanobeams...

Effect of Kerr Foundation and in-Plane Forces on Free Vibration of FGM Nanobeams with Diverse Distribution of Porosity

Published Online: Nov 20, 2020

Page range: 135 - 143

Received: Jun 19, 2020

Accepted: Oct 23, 2020

DOI: https://doi.org/10.2478/ama-2020-0020

Keywords
Porosity distribution, nanobeam, Reddy beam theory, free vibrations, nonlocal strain gradient theory

© 2020 Piotr Jankowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Effect of Kerr Foundation and in-Plane Forces on Free Vibration of FGM Nanobeams with Diverse Distribution of Porosity

Published Online: Nov 20, 2020

Page range: 135 - 143

Received: Jun 19, 2020

Accepted: Oct 23, 2020

DOI: https://doi.org/10.2478/ama-2020-0020

KeywordsPorosity distribution, nanobeam, Reddy beam theory, free vibrations, nonlocal strain gradient theory

© 2020 Piotr Jankowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Porosity distribution, nanobeam, Reddy beam theory, free vibrations, nonlocal strain gradient theory