Strategies for the optimum design of quiet structures: Use of material tailoring and/or active vibration control

Two strategies are developed successfully for achieving structures that radiate minimum sound power. Both strategies are based on altering the vibration characteristics of a structure, one passively by tailoring its material properties, and the other actively by altering its vibration response.; In the first strategy, quadratic optimization of the acoustic power written in terms of the structural surface velocity vector at a single frequency leads to a surface velocity profile that radiates minimum sound power. This weak radiator velocity profile is based on the acoustic considerations alone. Next, the distribution of structural material properties are found such that the structure exhibits the weak radiator velocity profile as one of its natural mode shapes at the prescribed frequency. An example of a clamped-clamped beam is used to demonstrate this strategy. It is shown that although the goal of this development is to achieve a weak radiator at one particular natural mode of the beam, other modes of the beam are weak radiators as well. The weak radiator mode shapes are shown to exhibit three unusual characteristics: (1) lower vibration amplitudes near the beam boundaries than at other points on the beam, (2) lower wavenumber content within the supersonic region, and (3) very small surface acoustic intensity values at every point along the length of the beam.; In the second strategy, quadratic optimization of acoustic power expression written in terms of the force vector exciting the structure leads to a set of actuator forces that, once activated, result in minimum radiated sound power. The effect of these actuator forces is to alter the vibration response of the structure to produce a weak radiator behavior. The characteristics of weak radiators achieved via this strategy are shown to be similar to those exhibited by the weak radiators achieved via material tailoring. This strategy is verified experimentally using a clamped-clamped beam excited with a shaker. Four PZT actuators bonded to the surface of this beam provide the control forces necessary to achieve the weak radiator response. Excellent correlation is found between the experimental results and the numerical predictions.