Details
Title
A comparative study of the sensitivity analysis for systems with viscoelastic elementsJournal title
Archive of Mechanical EngineeringYearbook
2023Volume
vol. 70Issue
No 1Affiliation
Łasecka-Plura, Magdalena : Poznan University of Technology, Institute of Structural Analysis, Poznan, PolandAuthors
Keywords
sensitivity analysis ; viscoelastic damping elements ; dynamic characteristics ; fractional derivativesDivisions of PAS
Nauki TechniczneCoverage
5-25Publisher
Polish Academy of Sciences, Committee on Machine BuildingBibliography
[1] M. Zhang and R. Schmidt. Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection. Journal of Sound and Vibration, 333(26):7352–7363, 2014. doi: 10.1016/j.jsv.2014.08.020.[2] T.W. Kim and J.H. Kim. Eigensensitivity based optima distribution of a viscoelastic damping layer for a flexible beam. Journal of Sound and Vibration, 273(1-2):201–218, 2004. doi: 0.1016/S0022-460X(03)00479-6.
[3] F. van Keulen, R.T. Haftka, and N.H. Kim. Review of options for structural design sensitivity analysis. Part 1: Linear systems. Computer Methods in Applied Mechanics and Engineering, 194(30-33):3213–3243, 2005. doi: 0.1016/j.cma.2005.02.002.
[4] D.A. Tortorelli and P. Michaleris. Design sensitivity analysis: Overview and review. Inverse Problems in Engineering, 1(1):71–105, 1994, doi: 10.1080/174159794088027573.
[5] R.L. Fox and M.P. Kapoor. Rates of change of eigenvalues and eigenvectors. AIAA Journal, 6(12):2426–2429, 1968. doi: 10.2514/3.5008.
[6] S. Adhikari and M.I. Friswell. Eigenderivative analysis of asymmetric non-conservative systems. International Journal for Numerical Methods in Engineering, 51(6):709–733, 2001. doi: 10.1002/NME.186.
[7] R.B. Nelson. Simplified calculation of eigenvector derivatives. AIAA Journal, 14(9):1201–1205, 1976. doi: 10.2514/3.7211.
[8] M.I. Friswell and S. Adhikari. Derivatives of complex eigenvectors using Nelson’s method. AIAA Journal, 38(12):2355–2357, 2000. doi: 10.2514/2.907.
[9] S. Adhikari and M.I. Friswell. Calculation of eigenrelation derivatives for nonviscously damped systems using Nelson’s method. AIAA Journal, 44(8):1799–1806, 2006. doi: 10.2514/1.20049.
[10] L. Li, Y. Hu, X. Wang, and L. Ling. Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues. Finite Elements in Analysis and Design, 72:21–34, 2013. doi: 10.1016/j.finel.2013.04.006.
[11] L. Li, Y. Hu, and X. Wang. A study on design sensitivity analysis for general nonlinear eigenproblems. Mechanical Systems and Signal Processing, 34(1-2):88–105, 2013. doi: 10.1016/j.ymssp.2012.08.011.
[12] T.H. Lee. An adjoint variable method for structural design sensitivity analysis of a distinct eigenvalue problem. KSME International Journal, 13(6):470–476, 1999. doi: 10.1007/BF02947716.
[13] T.H. Lee. Adjoint method for design sensitivity analysis of multiple eigenvalues and associated eigenvectors. AIAA Journal, 45(8):1998–2004, 2007. doi: 10.2514/1.25347.
[14] S. He, Y. Shi, E. Jonsson, and J.R.R.A. Martins. Eigenvalue problem derivatives computation for a complex matrix using the adjoint method. Mechanical Systems and Signal Processing, 185:109717, 2023. doi: 10.1016/j.ymssp.2022.109717.
[15] R. Lewandowski and M. Łasecka-Plura. Design sensitivity analysis of structures with viscoelastic dampers. Computers and Structures, 164:95–107, 2016. doi: 10.1016/j.compstruc.2015.11.011.
[16] Z. Ding, L. Li, G. Zou, and J. Kong. Design sensitivity analysis for transient response of non-viscously damped systems based on direct differentiate method. Mechanical Systems and Signal Processing, 121:322–342, 2019. doi: 10.1016/j.ymssp.2018.11.031.
[17] Z. Ding, J. Shi, Q. Gao, Q. Huang, and W.H. Liao. Design sensitivity analysis for transient responses of viscoelastically damped systems using model order reduction techniques. Structural and Multidisciplinary Optimization, 64:1501–1526, 2021. doi: 10.1007/s00158-021-02937-9.
[18] R. Haftka. Second-order sensitivity derivatives in structural analysis. AIAA Journal, 20(12):1765–1766, 1982. doi: 10.2514/3.8020.
[19] M.S. Jankovic. Exact nth derivatives of eigenvalues and eigenvectors. Journal of Guidance, Control, and Dynamics, 17(1):136–144, 1994. doi: 10.2514/3.21170.
[20] J.Y. Ding, Z.K. Pan, and L.Q. Chen. Second-order sensitivity analysis of multibody systems described by differential/algebraic equations: adjoint variable approach. International Journal of Computer Mathematics, 85(6):899–913, 2008. doi: 10.1080/00207160701519020.
[21] M. Martinez-Agirre and M.J. Elejabarrieta. Higher order eigensensitivities-based numerical method for the harmonic analysis of viscoelastically damped structures. International Journal for Numerical Methods in Engineering, 88(12):1280–1296, 2011. doi: 10.1002/nme.3222.
[22] H. Kim and M. Cho. Study on the design sensitivity analysis based on complex variable in eigenvalue problem. Finite Elements in Analysis and Design, 45:892–900, 2009. doi: 10.1016/j.finel.2009.07.002.
[23] A. Bilbao, R. Aviles, J. Aguirrebeitia, and I.F. Bustos. Eigensensitivity-based optimal damper location in variable geometry trusses. AIAA Journal, 47(3):576–591, 2009. doi: 10.2514/1.37353.
[24] R.M. Lin, J.E. Mottershead, and T.Y. Ng. A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives. Mechanical Systems and Signal Processing, 138:106536, 2020. doi: 10.1016/j.ymssp.2019.106536.
[25] R. Lewandowski, A. Bartkowiak, and H. Maciejewski. Dynamic analysis of frames with viscoelastic dampers: a comparison of dampers models. Structural Engineering and Mechanics, 41(1):113–137, 2012. doi: 10.12989/sem.2012.41.1.113.
[26] S.W. Park. Analytical modeling of viscoelastic dampers for structural and vibration control. International Journal of Solids and Structures, 38(44-45):8065–8092, 2001. doi: 10.1016/S0020-7683(01)00026-9.
[27] R. Lewandowski. Sensitivity analysis of structures with viscoelastic dampers using the adjoint variable method. Civil-Comp Proceedings, 106, 2014.
[28] J.S. Arora and J.B. Cardoso. Variational principle for shape design sensitivity analysis. AIAA Journal, 30(2):538–547, 1992. doi: 10.2514/3.10949.
[29] Z. Pawlak and R. Lewandowski. The continuation method for the eigenvalue problem of structures with viscoelastic dampers. Computers and Structures, 125:53–61, 2013. doi: 10.1016/j.compstruc.2013.04.021.
[30] R. Lewandowski and M. Baum. Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model. Archive of Applied Mechanics, 85(12):1793–1814, 2015. doi: 10.1007/s00419-015-1019-2.
[31] R. Lewandowski, P. Litewka and P. Wielentejczyk. Free vibrations of laminate plates with viscoelastic layers using the refined zig-zag theory – Part 1: Theoretical background. Composite Structures, 278:114547, 2021. doi: 10.1016/j.compstruct.2021.114547.
[32] M. Kamiński, A. Lenartowicz, M. Guminiak, and M. Przychodzki. Selected problems of random free vibrations of rectangular thin plates with viscoelastic dampers. Materials, 15(19): 6811, 2022. doi: 10.3390/ma15196811.