The mechanical characteristics of a laminated plate can be tailored by adjusting the fiber orientation angle of each orthotropic lamina. To find the fiber orientation angle of each lamina that maximizes the fundamental frequency, previous works analyses using various optimization algorithms have been performed so far. However, the solution space becomes significantly larger as the number of combinations in orientation angles increases. Thus the optimization process takes much more time. This paper sets up the orientation angles to discrete design variables, such as 15°, 30°, etc. Genetic algorithm is employed to find the optimal solutions. The CFRP rectangular composite plates with 8, 12 and 16 layers are considered as an example using the Ritz method for finding the eigenvalues. Two sets of classical boundary conditions are used as edge conditions. It was revealed that the fundamental frequency makes about 5% difference from the optimal value if it is in 30° steps and about 24% in 90° steps.
This paper deals with effects of using different sets of material constants on the natural frequencies of laminated composite rectangular plates. The plate is symmetrically laminated by thin layers composed of recently developed carbon fiber reinforced plastic (CFRP) materials. Numerical experiments are conducted by using a semi-analytical solution based on the thin plate theory and the lamination theory. The displacements are assumed to accommodate any combination of classical boundary conditions. The material property is expressed by a set of four elastic constants, and some typical sets of values are cited from the recent literature. Furthermore, a new standard set of discretized constants is proposed to uncover the underlying characteristics of the existing constants. The convergence study is carried out first, and the lowest five natural frequencies are calculated for five sets of classical boundary conditions including totally free through totally clamped cases. Next, a new definition of frequency parameters is introduced to promote more physically meaningful comparison among the obtained results, and the effect of using slightly different constants is clarified for unified comparison and insights. It is also discussed to derive approximate frequency formulas by linear regression analysis and to test accuracy of the formulas.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.