Optimising Natural Frequencies of Functionally Graded Beams Via CPA and TWO Metaheuristic Algorithms

Abstract

This research aims to optimise the lowest natural frequencies of functionally graded beams using the power-law distribution under classical boundary conditions (simply supported, clamped–clamped, and clamped–free) through material gradation across the beam thickness. To include the effect of mechanical properties gradient, the classical Euler–Bernoulli beam theory is expanded, which leads to a local change in mass density and stiffness modulus. The solution is achieved using two modern metaheuristic algorithms. This study investigates the application of metaheuristic algorithms for optimising the dynamic behaviour of functionally graded beams under classical boundary conditions. The two algorithms used are Tug of War optimisation algorithm (TWO), and Cyclical Parthenogenesis algorithm (CPA) to overcome the traditional constraints by using adaptive penalty functions to impose mass and manufacturability constraints, because the highly nonconvex and nonlinear design space. The results show that the CPA algorithm provides high-quality solutions by achieving rapid convergence, making it suitable for time- and mass-sensitive designs. The TWO algorithm, on the other hand, offer greater improvement in natural frequency of up to 25%, but with a longer processing time therefore it is suitable when vibration efficiency is a priority. This research highlights the potential of intelligent algorithms in the design of high-performance composite beams and contributes to laying the foundation for future expansion of the study to 3D panels and shells using 3D printing.