This paper presents a design method to optimize the material distribution of functionally graded beams with respect to some\nvibration and acoustic properties. The change of thematerial distribution through the beamlength alters the stiffness and the mass\nof the beam. This can be used to alter a specific beam natural frequency. It can also be used to reduce the sound power radiated\nfrom the vibrating beam. Two novel volume fraction laws are used to describe the material volume distributions through the\nlength of the FGM beam.The proposed method couples the finite elementmethod (for the modal and harmonic analysis), Lumped\nParameterModel (for calculating the power of sound radiation), and an optimization technique based on Genetic Algorithm. As a\ndemonstration of this technique, the optimization procedure is applied to maximize the fundamental frequency of FGM cantilever\nand clamped beams and to minimize the sound radiation from vibrating clamped FGM beam at a specific frequency.
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