Optimization of Fundamental Frequency of NonSymmetric Functionally Grade Beams Using Particle Swarm Optimization

In this paper, particle swarm optimization (PSO) is used to find the volume fraction that maximizes the first natural frequency of a functionally graded beam (FGB). The properties of the beam are considered to vary from two ceramic surfaces at the top and bottom of the beam to an interior metal surface according to two different power law functions. First, using Hamilton s principle governing equations and boundary conditions are derived. Next, differential quadrature method (DQM) is hired and the set of governing equations are solved numerically for all boundary conditions and natural frequencies are derived. Finally, using particle swarm optimization (PSO) an optimization is presented for increase fundamental frequency of the beam. Convergence and accuracy of the proposed solution are investigated and two different examples for optimization are presented.