刘晓峰等：基于虚拟材料复模量非均匀分布的螺栓连接薄板结构半解析建模 851· [14]Yang Y,Cheng H,Liang B,et al.A novel virtual material layer [21]Chisari C,Bedon C,Amadio C.Dynamic and static identification model for predicting natural frequencies of composite bolted of base-isolated bridges using genetic algorithms.Eng Struct, joints.Chin Jeron,https://doi.org/10.1016/j.cja.2020.05.028 2015,102:80 [15]Shi K,Zhang G P.A parameterized model of fixed joint interface [22]Liu Q,Yang J P,Wang B L,et al.Genetic optimization model of based on virtual material.J Mech Sci Technol,2019,33(11):5209 steelmaking-continuous casting production scheduling based on [16]Ye H,Huang Y M.Li P Y,et al.Virtual material parameter the "fumace-caster coordinating"strategy.Chin J Eng,2020, acquisition based on the basic characteristics of the bolt joint 42(5):645 interfaces.Tribol Int,2016,95:109 (刘倩，杨建平，王柏琳，等.基于“炉-机对应”的炼钢-连铸生产 [17]Zhao Y S,Yang C,Cai L G,et al.Surface contact stress-based 调度问题遗传优化模型.工程科学学报，2020,42(5)：645) nonlinear virtual material method for dynamic analysis of bolted [23]Papkov S O,Banerjee J R.Dynamic stiffness formulation and free joint of machine tool.Precis Eng,2016,43:230 vibration analysis of specially orthotropic Mindlin plates with [18]Shi Y M,Sol H,Hua H X.Material parameter identification of arbitrary boundary conditions.J Sound Vib,2019,458:522 sandwich beams by an inverse method.J Sound Vib,2006,290 [24]Xue J,Wang Y F,Chen L H.Nonlinear vibration of cracked (3-5:1234 rectangular Mindlin plate with in-plane preload.J Sound Vib, [19]Gao Y,Sun W,Piao Y H,et al.Inverse identification of support 2020,481:115437 stiffness and damping of hoop based on measured FRF. [25]Mahi A,Bedia E AA,Tounsi A.A new hyperbolic shear Aerospace Power,2019,34(3):664 deformation theory for bending and free vibration analysis of (高晔，孙伟，朴玉华，等.基于实测频响函数反推管路卡箍支承 isotropic,functionally graded,sandwich and laminated composite 刚度与阻尼.航空动力学报，2019,34(3)：664) plates.Appl Math Modell,2015,39(9):2489 [20]Miller B,Ziemianski L.Optimization of dynamic behavior of thin- [26]Sun W,Wang Z,Yan X F,et al.Inverse identification of the walled laminated cylindrical shells by genetic algorithms and deep frequency-dependent mechanical parameters of viscoelastic neural networks supported by modal shape identification.Ad Eng materials based on the measured FRFs.Mech Syst Signal Process, Software,.2020,147:102830 2018,98:816Yang Y, Cheng H, Liang B, et al. A novel virtual material layer model  for  predicting  natural  frequencies  of  composite  bolted joints. Chin J Aeron, https://doi.org/10.1016/j.cja.2020.05.028 [14] Shi K, Zhang G P. A parameterized model of fixed joint interface based on virtual material. J Mech Sci Technol, 2019, 33（11）: 5209 [15] Ye  H,  Huang  Y  M,  Li  P  Y,  et  al.  Virtual  material  parameter acquisition  based  on  the  basic  characteristics  of  the  bolt  joint interfaces. Tribol Int, 2016, 95: 109 [16] Zhao  Y  S,  Yang  C,  Cai  L  G,  et  al.  Surface  contact  stress-based nonlinear  virtual  material  method  for  dynamic  analysis  of  bolted joint of machine tool. Precis Eng, 2016, 43: 230 [17] Shi  Y  M,  Sol  H,  Hua  H  X.  Material  parameter  identification  of sandwich  beams  by  an  inverse  method. J Sound Vib,  2006,  290 （3-5）: 1234 [18] Gao Y, Sun W, Piao Y H, et al. Inverse identification of support stiffness  and  damping  of  hoop  based  on  measured  FRF. J Aerospace Power, 2019, 34（3）: 664 （高晔, 孙伟, 朴玉华, 等. 基于实测频响函数反推管路卡箍支承 刚度与阻尼. 航空动力学报, 2019, 34（3）：664） [19] Miller B, Ziemiański L. Optimization of dynamic behavior of thin￾walled laminated cylindrical shells by genetic algorithms and deep neural networks supported by modal shape identification. Adv Eng Software, 2020, 147: 102830 [20] Chisari C, Bedon C, Amadio C. Dynamic and static identification of  base-isolated  bridges  using  genetic  algorithms. Eng Struct, 2015, 102: 80 [21] Liu Q, Yang J P, Wang B L, et al. Genetic optimization model of steelmaking-continuous  casting  production  scheduling  based  on the “ furnace-caster  coordinating” strategy. Chin J Eng,  2020, 42（5）: 645 （刘倩, 杨建平, 王柏琳, 等. 基于“炉−机对应”的炼钢−连铸生产 调度问题遗传优化模型. 工程科学学报, 2020, 42（5）：645） [22] Papkov S O, Banerjee J R. Dynamic stiffness formulation and free vibration  analysis  of  specially  orthotropic  Mindlin  plates  with arbitrary boundary conditions. J Sound Vib, 2019, 458: 522 [23] Xue  J,  Wang  Y  F,  Chen  L  H.  Nonlinear  vibration  of  cracked rectangular  Mindlin  plate  with  in-plane  preload. J Sound Vib, 2020, 481: 115437 [24] Mahi  A,  Bedia  E  A  A,  Tounsi  A.  A  new  hyperbolic  shear deformation  theory  for  bending  and  free  vibration  analysis  of isotropic, functionally graded, sandwich and laminated composite plates. Appl Math Modell, 2015, 39（9）: 2489 [25] Sun  W,  Wang  Z,  Yan  X  F,  et  al.  Inverse  identification  of  the frequency-dependent  mechanical  parameters  of  viscoelastic materials based on the measured FRFs. Mech Syst Signal Process, 2018, 98: 816 [26] 刘晓峰等： 基于虚拟材料复模量非均匀分布的螺栓连接薄板结构半解析建模 · 851 ·