Abstract
The use of the dynamic stiffness method has been extended to permit optimum (minimum mass) design of nonuniform composite beams subject to frequency constraints. The beams are modeled as a series of elements, stepped in thickness at discrete nodes, and are constrained to have a minimum separation between ® rst bending and ® rst torsional frequencies. The frequency constraints are supplied to the optimizer, DOT (design optimization tools), using the dynamic stiffness method, which incorporates a mode tracking routine to ensure that the ® rst bending and ® rst torsional natural frequencies are located at each design iteration. An optimum design has been manufactured from a carbon ® ber/epoxy composite and subjected to an experimental modal analysis to validate the results. The dynamic stiffness method has a maximum difference of 11% from the experimentally obtained natural frequencies. In addition, a ® nite element model of the optimum design has been developed and showed a maximum difference of 13% from the experimental results. Analysis using the dynamic stiffness method is as accurate, much faster (in excess of 2 orders ofmagnitude),and considerably simpler than the ® nite elementmethod for this type of problem.
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