Dynamic optimization of a sandwich beam

Abstract Analytical procedure for the determination of the least weight design sandwich beam which satisfies a specific frequency requirement is presented. The approach is to modify an initial design by varying the thickness of each of its different layers. This is accomplished using gradient equations to first obtain the correct beam fundamental frequency and then, while this frequency is held constant, to minimize the weight. The gradient equations are derived in matrix notation suitable for the use of digital computers. For practical as well as other considerations, imposing lower bounds on layers' thicknesses have been found necessary. The equations of motion used include all the higher order effects like inertia, extension and shear of all the layers. Hence the procedure is applicable for short as well as long, soft or stiff cored beams. The design procedure has been completely automated in a computer program. Results of numerical examples show that the method is convergent and that optimized configurations can be determined in a few redesign cycles.