Acoustic Control Mechanism And Optimization Design Of Curved Edge For Two-dimensional Pentamode Materials

Noise which causes damages to people’s health has become the second largest city public hazard,second only to air pollution.Controlling noise to improve the quality of people’s lives has become one of main research directions at present.With the rise of periodic materials such as pentamode acoustic metamaterial,researchers have found new solutions in controlling acoustic wave and elastic wave.In this thesis,several pentamode materials and its single cell structures are designed and constructed.The sound wave regulation function is proved by the band structure analysis and related simulations,and by conducting relevant structural optimizations to improve its performance.The aim of this research is to explore the method of designing pentamode material structure,and provide a certain reference for related studies.The main research contents of this thesis are as follows:(1)Based on different shapes of arrangement,three kinds of pentamode materials and single cell structures are constructed respectively with two filling materials.After establishing their finite element model,energy band analysis is conducted.According to the band structure and combined with the corresponding scene simulation,the sound wave regulation function of the pentamode material is verified,including the band gap and single-mode transmission.In addition,through analysis and comparison,it is found that the triangular arrangement of pentamode material has better performance and is selected for further research.(2)In the single-mode transmission area of pentamode material,only the propagation of the compressed wave(longitudinal wave)is allowed,while the propagation of shear wave(cross wave)is suppressed,and thus pentamode material exhibits fluid properties in this frequency interval.After analyzing the sound pressure distribution in the water area with or without pentamode material,it is found that the sound wave has almost no scattering which shows the function of "acoustic stealth".In addition,the local resonant band gap is introduced.By calculating the transmission loss of sound waves after passing through the pentamode material,it is found that all sound waves with frequencies in the band gap range will be suppressed and cannot propagate.(3)Using the control variable method,the parameters affecting the acoustic regulation performance of pentamode materials are analyzed respectively.It is found that the influencing parameters mainly include the material density of the filling material in the biconical region,the young’s modulus and Poisson’s ratio of the filling material in the node region,the biconical width and the lattice constant of the single cell.According to the influence law obtained by analyzing the changes of these parameters,the appropriate filling materials and the geometric parameters of single cell structure can be selected to better design the pentamode material structure.(4)Taking the biconical width and node radius of single cell as the design variables and bandwidths of the band gap and single-mode transmission region as the optimization objectives,the multi-objective optimization design of the pentamode material’s single cell structure is carried out.The sample points are selected through the optimal Latin hypercube,and the adaptive Kriging model is established combined with the double-points infilling criterion.NSGA-II algorithm is used to solve the optimization problem and Pareto solution sets are obtained.The final compromise solution is obtained by utilizing the fitness function.The results show that after optimization,the band gap is widened by nearly 2.22 times,and the overall frequency range of acoustic control is increased by 26.73%.(5)By replacing the straight edge of double cone with curved edge and taking different curved lines as biconical curved edge,six kinds of curved pentamode materials with different arrangements or biconical curved edges and their single cell structures are constructed.Through analysis and comparison,the curved pentamode material based on hexagonal arrangement with elliptical arc extraction line as biconical curved edge have better performance.Compared with the originally designed straight edge pentamode material,the band gap width of the finally optimized pentamode material is increased from 9Hz to 1039.6Hz,and the width of the single-mode transmission area is widened from 276.26 Hz to 1456.52 Hz,showing that the regulation performance is significantly improved.