This paper presents a study of multi-objective optimization of elastic beams with minimum weight and radiated sound power. The goal of this research is to discover the potentials to design multi-objective optimal elastic structures for better acoustic performance. We discuss various structural-acoustic properties of the Pareto solutions of the multi-objective optimization problem (MOP). We have found that geometrical and dynamic constraints can substantially reduce the volume fraction of feasible solutions in the design space, which can make it difficult to search for the optimal solutions. Several case studies with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure.
The acoustic black hole (ABH) structure has gradually become a research hotspot in recent years due to its ascendant capacity of vibration attenuation and energy accumulation. To further improve the performance of vibration and noise reduction, the ultra-low frequency broadband gap of a one-dimensional structure embedded ABHs with power-law material properties is investigated in this paper. Based on the Euler-Bernoulli theory, the Transfer Matrix Method (TMM) is used to establish the dynamic model of the dual power-law ABH (DP-ABH) beam. The band structure results obtained by TMM and the finite element method are compared with each other to verify the ultra-low broadband gap of the structure. Comparison with the traditional ABH show that the ultra-low frequency performance of the DP-ABH is due to the enhanced local resonator properties with reduction of dual power-law local stiffness. Parameter analysis served as a guide for optimization is carried out and a method of combining NSGA-II and TMM is applied to optimize the ABH section with full parameters, to consider a trade-off between lower bandgaps and higher stiffness. The investigation shows that the ultra-low broadband gaps of the periodic DP-ABHs structure, which meets adequate stiffness requirements, can be designed by optimized configuration.
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