A design method for achieving minimum sound radiation from a beam is presented. The strategy is to form a series of cylindrical dimples on the beam surface in order to make one or more vibration modes of this dimpled beam have the same shape as the weak modes. Consequently, the dimpled beam behaves as a weak radiator when one or more vibration modes are excited. Instead of minimizing the radiated sound power at a specific frequency or in a bandwidth, the objective is to maximize the modal assurance coefficient (MAC) which quantifies resemblance between the vibration mode of a dimpled beam and a weak mode. To perform this strategy, two key issues are addressed in this paper. The first is to determine the so-called weak mode of a beam. And the second is how to determine the required dimple size and the dimple location on this beam so that the dimpled beam may have vibration modes resembled to the weak modes. A methodology to do so based on the finite element method and the mode assurance criteria is proposed. Results show that the radiation efficiency of the dimpled beam after optimization using MAC as the objective is generally lower than the uniform beam. However, the effectiveness of this strategy depends on how close in shape between the vibration mode of the dimpled beam and the designated weak mode.

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