International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000414

Topological Sensitivity Analysis of Structural Sound Radiation in a Thermal Environment

Xiongwei Yang, Gang Chen and Yueming Li^a State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China. liyueming@mail.xjtu.edu.cn

ABSTRACT

Sensitivity analysis is carried out in this paper to minimize structural sound radiation in thermal environments. The structure studied is subjected to a uniform temperature rise and excited by a time-harmonic surface loading. The compressive thermal stress can reduce the stiffness of the structure, thus changing the radiation property and optimal design. The thermal stress is first evaluated and considered in the following analysis as pre-stress. The dynamic response is calculated through a linear stress-stiffening finite element equation, and the radiated sound power compliance further using Rayleigh integral. The uniform temperature is chosen to be lower than the critical buckling temperature to ensure a linear condition, which needs to be monitored and guaranteed at every iteration during the optimization. Thereafter, the sensitivity analysis is carried out. The particularity of the problem is that if the design variable of one element changes, thermal stress field of the whole structure will vary; thus stress stiffness of each element will be different. This will significantly increase the difficulty of the sensitivity analysis and the numerical implementation. The equivalent thermal force which is known as design-dependent load should also be carefully dealt with. Both direct and adjoint methods are discussed, and the latter is implemented to keep the computational cost at a relatively low level. A bi-material rectangular plate is studied and several numerical cases are discussed.

Keywords: Topology optimization, Acoustic power, Thermal environment.

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