Simultaneous optimization of materials and fiber angles on laminated composite shells for reducing transient sound radiation

Researchers generally study optimization problems against noise using frequency-domain analysis. Nonetheless, ubiquitous transient behaviors indicate that time-domain optimization approaches cannot be ignored. Thus, this paper investigates a simultaneous optimization performed on fiber, material, and layer scales to reduce the transient noise from laminated shells with variable stiffness design. The optimization goal is to minimize the integral of the squared sound pressure from structures over a time interval of interest; the Heaviside Penalization of Discrete Material Optimization (HPDMO) model is employed to choose an adequate fiber angle or soft material for each element and determine its stacking sequence. The transient sound pressure is predicted by the finite element/time-domain boundary element method (FEM/TDBEM). Considering that vibration response on each boundary node needs to be known beforehand in TDBEM, an efficient combination scheme is proposed to derive the sensitivity formulation. Namely, the direct method is applied to obtain the dynamic response sensitivities of all nodes at once; and the results are input into the sensitivity calculation of transient sound radiation addressed by using the adjoint variable method. Numerical examples discuss the influences of the number of candidate fiber angles, usage of soft material, size of patches, selection of objective function, eccentric excitation, asymmetric layers, and geometric feature on optimal design.