Structural topology optimization on sound radiation at resonance frequencies in thermal environments

Thermal and acoustic environments pose severe challenges to the structural design of hypersonic vehicles. One of them is to find optimal design that exhibits ideal acoustic characteristics in a frequency band, which is discussed in this paper through topology optimization aiming at resonance sound radiation in thermal environments. The sound radiation at resonance frequencies is the main component of response, minimization on which is likely to provide a satisfactory design. A bi-material plate subjected to uniform temperature rise and excited by harmonic loading is studied here. Thermal stress is first evaluated and considered as pre stress in the following dynamic analysis; radiated sound power is then calculated through Rayleigh integral. Sensitivity analysis is carried out through adjoint method considering the complicated relationship between stress-induced geometric stiffness and design variables. As the resonance frequency is constantly changing during the optimization, its sensitivity should be considered. It is also noticed that mode switching may occur, so mode tracking technique is employed in this work. Some numerical examples are finally discussed.