Free vibration analysis of Timoshenko beams reinforced by BNNTs and a comparison with CNT-reinforced composite

Abstract

This paper studies free vibration of composite beams reinforced by boron nitride nanotubes (BNNTs), lying on an elastic foundation. The beam matrix is taken as poly methyl methacrylate. The nanotubes have different layouts in the matrix (aligned and randomly oriented) and are also distributed through the beam thickness as one uniform and three different functionally graded distributions. A micromechanical model is applied to estimate the properties of BNNT-reinforced composite (BNNTRC). Equations of motion are achieved by means of Hamilton's principle as well as Timoshenko beam theory. Natural frequencies are gained by introducing generalized differential quadrature method to the equations. Investigating the influence of different parameters as diverse as nanotube volume fraction, nanotubes distribution type, the elastic foundation, boundary conditions and the beam's slenderness ratio on the natural frequency, reveals that any changes in aforementioned parameters has a significant impact on the natural frequency. Furthermore, the results for aligned BNNTRC beam are measured against the results of similar CNT-reinforced beam in the literature, illustrating that natural frequency of BNNTRC beam is lower than CNTRC beam. Finally, the comparison between natural frequencies of two BNNTRC beams with two different alignments of BNNTs, illustrates their different behavior due to different factors.