[1] 黄志诚, 秦朝烨, 褚福磊. 附加粘弹阻尼层的薄壁构件振动问题研究综述[J]. 振动与冲击, 2014, 33(7):105-113. HUANG Z C, QIN Z Y, CHU F L. A review about vibration problems of thin-walled structures with viscoelastic damping layer[J]. Journal of Vibration and Shock, 2014, 33(7):105-113. [2] KANG Z, ZHANG X P, JIANG S G, et al. On topology optimization of damping layer in shell structures under harmonic excitations[J]. Structural and Multidisciplinary Optimization, 2012, 46:51-67. [3] KIM S Y, CHRIS K M, KIM I Y. Optimal damping layout in a shell structure using topology optimization[J]. Journal of Sound and Vibration, 2013, 332:2873-2883. [4] YAMAMOTO T, YAMADA T, IZUI K S, et al. Topology optimization of free-layer damping material on a thin panel for maximizing modal loss factors expressed by only real eigenvalues[J]. Journal of Sound and Vibration, 2015, 358:84-96. [5] 郑玲, 谢熔炉, 王宜, 等. 基于优化准则的约束阻尼材料优化配置[J]. 振动与冲击, 2010, 29(11):156-159. ZHENG L, XIE R L, WANG Y, et al. Optimal placement of constrained damping material in structures based on optimality criteria[J]. Journal of Vibration and Shock, 2010, 29(11):156-159. [6] TAKEZAWA A, DAIFUKU M, NAKANO Y, et al. Topology optimization of damping material for reducing resonance response based on complex dynamic compliance[J]. Journal of Sound and Vibration, 2015, 358:84-96. [7] EI-SABBAGH A, BAZ A. Topology optimization of unconstrained damping treatments for plates[J]. Engineering Optimization, 2014, 46(9):1153-1168. [8] ZHANG X P, KANG Z. Vibration suppression using integrated topology optimization of host structures and damping layers[J]. Journal of Vibration and Control. 2016, 22(1):66-76. [9] YUN K S, YOUN S K. Topology optimization of viscoelastic damping layers for attenuating transient response of shell structures[J]. Finite Elements in Analysis & Design, 2018, 141:154-165. [10] YUN K S, YOUN S K. Multi-material topology optimization of viscoelastically damped structures under time-dependent loading[J]. Finite Elements in Analysis & Design, 2017, 123:9-18. [11] YI Y M, PARK S H, YOUN S K. Asymptotic homogenization of viscoelastic composites with periodic microstructures[J]. International Journal of Solids and Structures, 1998, 35(17):2039-2055. [12] YI Y M, PARK S H, YOUN S K. Design of microstructures of viscoelastic composites for optimal damping characteristics[J]. International Journal of Solids and Structures, 2000, 37(35):4791-4810. [13] ANDREASSEN E, JENSEN J S. Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials[J]. Structural and Multidisciplinary Optimization, 2014, 49:695-705. [14] CHEN W, LIU S. Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus[J]. Structural and Multidisciplinary Optimization, 2014, 50(2):287-296. [15] CHEN W, LIU S. Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures[J]. Structural and Multidisciplinary Optimization, 2016, 53:1-14. [16] ANDREASEN C S, ANDREASSEN E, JENSEN J S, et al. On the realization of the bulk modulus bounds for two-phase viscoelastic composites[J]. Journal of the Mechanics and Physics of Solids, 2014, 63:228-241. [17] HUANG X, ZHOU S, SUN G, et al. Topology optimization for microstructures of viscoelastic composite materials[J]. Computer Methods in Applied Mechanics & Engineering, 2015, 283:503-516. [18] LIU Q, DONG R, HUANG X. Topology optimization of viscoelastic materials on damping and frequency of macrostructures[J]. Computer Methods in Applied Mechanics & Engineering, 2018, 337:305-323. [19] ANDREASSEN E, JAKOB S J. A practical multiscale approach for optimization of structural damping[J]. Structural & Multidisciplinary Optimization, 2015, 53(2):1-10. [20] RODRIGUES H, GUEDES J M, BENDSOE M P. Hierarchical optimization of material and structure[J]. Structural and Multidisciplinary Optimization, 2002, 24(1):1-10. [21] ZHANG W, SUN S. Scale-related topology optimization of cellular materials and structures[J]. International Journal for Numerical Methods in Engineering, 2006, 68(9):993-1011. [22] NIU B, YAN J, CHENG G. Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency[J]. Structural and Multidisciplinary Optimization, 2009, 39(2):115-132. [23] ZUO Z H, HUANG X, RONG J H, et al. Multi-scale design of composite materials and structures for maximum natural frequencies[J]. Materials & Design, 2013, 51:1023-1034. [24] VICENTE W M, ZUO Z H, PAVANELLO R, et al. Concurrent topology optimization for minimizing frequency responses of two-level hierarchical structures[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 301:116-136. [25] JOHNSON C D, KIENHOLZ D A. Finite element prediction of damping in structures with constrained viscoelastic layers[J]. AIAA Journal, 1982, 20(9):1284-1290. [26] ZHANG H, DING X, WANG Q, et al. Topology optimization of composite material with high broadband damping[J]. Computers & Structures, 2020, 239:106331. [27] SVANBERG K. The method of moving asymptotes:A new method for structural optimization[J]. International Journal for Numerical Method on Engineering, 1987, 24:359-373. |