Comparison of Design Optimization Formulations for Minimization of Noise Transmission in a Cylinder

A computational design tool was developed to perform a constrained optimization of the acoustic environment within a vibrating cylinder, incorporating e nite element and boundary element methods. This paper presents a comparison of the relative performance and results obtained through the use of four different objective function and constraint formulations within the optimization tool: 1 ) minimize the sum of the squared acoustic pressures at a number of points within the cylinder, 2 ) minimize the weight of the structure with a constraint on the sum of the acoustic pressures, 3 ) minimize the sum of the acoustic pressures with a constraint on weight, and 4 ) minimize weight and summed pressures simultaneously. All four formulations were subject to upper and lower bounds on the design variables, the structural shell element thicknesses. All analyses were performed at a single excitation frequency. These formulations were implemented within the design tool and compared based on their overall pressure and weight reduction and computational efe ciency. Two different cylinder models were used to evaluate the optimization formulations. It was found that the third formulation was the most stable and effective. In addition, a nearly linear relationship was observed between the relative optimal decibel noise level within the cylinder and the optimal cylinder weight.