Free vibration analysis and design optimization of nanocomposite‐laminated beams using various higher order beam theories and imperialist competitive algorithm

In this article, two goals are followed. First, free vibrations of laminated beams reinforced by Single‐Walled Carbon Nanotubes (SWCNTs) are studied based on various Higher order Shear Deformation Beam Theories (HSDBTs) and using an analytical method. The SWCNTs are assumed to be aligned and straight with a uniform layout. The extended rule of mixture is applied to describe the effective material properties of the structure. The natural frequencies of the nanocomposite beam are compared with the existing solutions to verify the validity of the theories. Results show the simplicity and accuracy of the method for free vibration analysis of nanocomposite beams. The effects of Carbon Nanotube (CNT) volume fractions in the layers and span‐to‐depth ratio on the fundamental frequency of the structure are also studied. As for the second goal of this study, optimization of nanocomposite‐laminated beams is presented. The main objective of the optimization problem is maximizing the fundamental frequency of the structure. The total amount of CNT in the structure is considered as a constraint on the optimization problem. The primary optimization variables are the values of CNT volume fraction in layers of a 10‐layer laminated nanocomposite beam. Since the search space of the optimization problem is large, the optimization processes becomes so complicated and time consuming. Thus, a novel meta–heuristic approach called Imperialist Competitive Algorithm (ICA), which is a socio‐politically motivated global search strategy, is applied to find the optimal solution. Results show the success of ICA for the design of nanocomposite structures. POLYM. COMPOS., 37:2442–2451, 2016. © 2015 Society of Plastics Engineers