Thermal Vibration Analysis of Cracked Nanobeams Embedded in an Elastic Matrix Using Finite Element Analysis

AI Aria (Tabriz University, Iran), MI Friswell (Swansea University) & T Rabczuk (Bauhaus University Weimar, Germany)

Composite Structures, Vol. 212, 15 March 2019, pp. 118-128


In this study, a finite element (FE) model is proposed to study the thermal transverse vibrations of cracked nanobeams resting on a double-parameter nonlocal elastic foundation. Hamilton's principal is employed to derive the governing equations for the free vibrations of the nanobeam. The cracked section of the beam is modelled by dividing the cracked element into two classical beam sections connected via a rotational spring positioned at the crack. The Galerkin method of weighted residuals is used to solve the equations of motion and calculate the natural frequencies. The effect of the crack length/position, the temperature gradient, the boundary conditions and the foundation stiffness, on the vibration response of the cracked nanobeams supported by elastic foundations is considered by including thermal effects. The FE results are compared to the available benchmark studies in the literature.

Paper Availability

This material has been published in the Composite Structures, Vol. 212, 15 March 2019, pp. 118-128. Unfortunately the copyright agreement with Elsevier does not allow for the PDF file of the paper to be available on this website.

Link to paper using doi: 10.1016/j.compstruct.2019.01.040

Composite Structures