A comparative study of the sensitivity analysis for systems with viscoelastic elements

• Autorzy: Łasecka-Plura Magdalena

Identyfikatory

DOI

10.24425/ame.2022.144077

• Języki publikacji: EN

Abstrakty

EN

This paper discusses the different methods used for calculating first- and second-order sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.

Słowa kluczowe

EN

sensitivity analysis; viscoelastic damping elements; dynamic characteristics; fractional; derivatives

PL

analiza wrażliwości; lepkosprężyste elementy tłumiące; charakterystyka dynamiczna

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2023
• Tom: LXX, nr 1
• Strony: 5--25
• Opis fizyczny: Bibliogr. 32 poz., rys., tab.

Twórcy

autor

Łasecka-Plura Magdalena

• Poznan University of Technology, Institute of Structural Analysis, Poznań, Poland

• https://orcid.org/0000-0002-5229-9361

Bibliografia

• [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.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).