Skip to main content
SpringerLink
Log in

Topology Optimization of Plates with Constrained Layer Damping Treatments Using a Modified Guide-Weight Method

  • Original Paper
  • Published:
Journal of Vibration Engineering & Technologies Aims and scope Submit manuscript

Abstract

Purpose

The full damping treatments have been widely used in many fields for structural vibration and noise reduction. Compared to the partial damping treatments, the full damping treatments have not significantly enhanced the effect of vibration reductions. It is essential to find the optimal damping treatments in lightweight designs. Moreover, the solution methods should be beneficial to engineering applications.

Method

In this work, a layerwise finite element (FE) model of plates with constrain layer damping (CLD) treatments is proposed, based on Kerwin’s hypothesis. The dynamic characteristics of CLD system are analyzed by the modal strain energy (MSE) method. Based on the variable density method and the rational approximation of material properties (RAMP) interpolation scheme, a topology optimization model of the CLD system is built, and the optimal layouts are determined by the proposed modified guide-weight (MGW) method. The results are compared with optimal layouts using other common methods.

Results

The layerwise FE model, the topology optimization model and the MGW method are validated by numerical examples. The proposed layerwise FEM-MSE solutions converge to the analytical or semi-analytical solutions more accurately than the NASTRAN/MSE solutions. The optimization results indicate that the added weight of viscoelastic material (VEM) layer decreases by 50 percent, and meanwhile the modal loss factors can just decrease by 5.18 percent compared to plates with VEM full coverage in some cases.

Conclusion

The results of this work are beneficial to the vibration and sound radiation suppression of plates with CLD treatments in engineering applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Flugge W (1975) Viscoelasticity. Springer

    Book  Google Scholar 

  2. Ferry JD (1980) Viscoelastic properties of polymers. Wiley and Sons

    Google Scholar 

  3. Gutierrez-Lemini D (2014) Engineering viscoelasticity. Springer

    Book  Google Scholar 

  4. Mead DJ (1998) Passive vibration control. Wiley. https://doi.org/10.1017/S0001924000064514

    Book  MATH  Google Scholar 

  5. Christensen RM (1982) Theory of viscoelasticity. An introduction. Academic Press

    Google Scholar 

  6. Nakra BC (1998) Vibration control in machines and structures using viscoelastic damping. J Sound Vib 211(3):449–466. https://doi.org/10.1006/jsvi.1997.1317

    Article  Google Scholar 

  7. El-Sabbagh A, Baz A (2013) Topology optimization of unconstrained damping treatments for plates. Eng Optimiz 46(9):1153–1168. https://doi.org/10.1080/0305215X.2013.832235

    Article  MathSciNet  Google Scholar 

  8. Baker M (2007) Analysis methods to support design for damping. Eng Comput 23:1–10. https://doi.org/10.1007/s00366-006-0022-1

    Article  Google Scholar 

  9. Kerwin EM (1959) Comparison of the vibration damping effectiveness of free and constrained viscoelastic layers. J Acoust Soc Am 31(11):1578–1578. https://doi.org/10.1121/1.1930310

    Article  Google Scholar 

  10. Edawrd M, Kerwin JR (1959) Damping of flexural waves by a constrained viscoelastic layer. J Acoust Soc Am 31(7):952–962. https://doi.org/10.1121/1.1907821

    Article  Google Scholar 

  11. Nokes DS, Nelson FC (1968) Constrained layer damping with partial coverage. Shock Vib Bull 38(3):5–12

    Google Scholar 

  12. Lall AK, Asnani NT, Nakra BC (1988) Damping analysis of partially covered sandwich beams. J Sound Vib 123(2):247–259. https://doi.org/10.1016/S0022-460X(88)80109-3

    Article  Google Scholar 

  13. Plunkett R, Lee CT (1970) Length optimization for constrained viscoelastic layer damping. J Acoust Soc Am 48:150. https://doi.org/10.1121/1.1912112

    Article  Google Scholar 

  14. Chen YC, Huang SC (2002) An optimal placement of CLD treatment for vibration suppression of plates. Int J Mech Sci 44(8):1801–1821. https://doi.org/10.1016/S0020-7403(02)00042-5

    Article  MATH  Google Scholar 

  15. Johnson CD, Kienholz DA (1982) Finite element prediction of damping in structures with constrained viscoelastic layers. AIAA J 20(9):1284–1290. https://doi.org/10.2514/3.51190

    Article  Google Scholar 

  16. Zheng L, Xie R, Wang Y et al (2010) Topology optimization of constrained layer damping on plates using method of moving asymptote (MMA) approach. Shock Vib 18:221–244. https://doi.org/10.3233/SAV-2010-0583

    Article  Google Scholar 

  17. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Meth Eng 24(2):359–373. https://doi.org/10.1002/nme.1620240207

    Article  MathSciNet  MATH  Google Scholar 

  18. Luo Z, Gao W, Song CM (2010) Design of multi-phase piezoelectric actuators. J Intel Mat Syst Str 21(18):1851–1865. https://doi.org/10.1177/1045389X10389345

    Article  Google Scholar 

  19. Araujo AL, Madeira JFA, Mota Soares CA et al (2013) Optimal design for active damping in sandwich structures using the Direct MultiSearch method. Compos Struct 105(8):29–34. https://doi.org/10.1016/j.compstruct.2013.04.044

    Article  Google Scholar 

  20. Kim SY, Mechefske CK, Kim IY (2013) Optimal damping layout in a shell structure using topology optimization. J Sound Vib 332(12):2873–2883. https://doi.org/10.1016/j.jsv.2013.01.029

    Article  Google Scholar 

  21. Fang Z, Zheng L (2015) Topology optimization for minimizing the resonant response of plates with constrained layer damping treatment. Shock Vib PT.2:1–11

    Google Scholar 

  22. Li ZL, Liu ZQ, Sun DG et al (2018) Fractional maxwell model of viscoelastic oscillator and its frequency response. J Vib Eng Technol 6(1):1–6. https://doi.org/10.1007/s42417-018-0005-8

    Article  Google Scholar 

  23. Ojha RK, Dwivedy SK (2020) Dynamic analysis of a three-layered sandwich plate with composite layers and leptadenia pyrotechnica rheological elastomer -based viscoelastic core. J Vib Eng Technol 8:541–553. https://doi.org/10.1007/s42417-019-00129-w

    Article  Google Scholar 

  24. Madeira JFA, AraujoSoares ALCMM (2016) Multiobjective optimization of constrained layer damping treatments in composite plate structures. Mech Compos Mater St 24(5):427–436. https://doi.org/10.1080/15376494.2016.1190427

    Article  Google Scholar 

  25. Luis NF, Madeira JFA, Araujo AL et al (2017) Active vibration attenuation in viscoelastic laminated composite panels using multiobjective optimization. Compos Part B-Eng 128:53–66. https://doi.org/10.1016/j.compositesb.2017.07.002

    Article  Google Scholar 

  26. Xu YK, Gao WG, Yu YH et al (2017) Dynamic optimization of constrained layer damping structure for the headstock of machine tools with modal strain energy method. Shock Vib 10:1–13. https://doi.org/10.1155/2017/2736545

    Article  Google Scholar 

  27. Liu S, Xu Y, Shi X et al (2018) Distribution optimization of constrained damping materials covering on typical panels under random vibration. J Vib Acoust 23(3):370–377. https://doi.org/10.20855/ijav.2018.23.31266

    Article  Google Scholar 

  28. Liu QM, Ruan D, Huang XD (2018) Topology optimization of viscoelastic materials on damping and frequency of macrostructures. Comput Method Appl M 337:305–323. https://doi.org/10.1016/j.cma.2018.03.044

    Article  MathSciNet  MATH  Google Scholar 

  29. Delgado G, Hamdaoui M (2019) Topology optimization of frequency dependent viscoelastic structures via a level-set method. Appl Math Comput 347:522–541. https://doi.org/10.1016/j.amc.2018.11.014

    Article  MathSciNet  MATH  Google Scholar 

  30. Fang ZP, Yao L, Tian S et al (2020) Microstructural topology optimization of constrained layer damping on plates for maximum modal loss factor of macrostructures. Shock Vib 2020:1–13. https://doi.org/10.1155/2020/8837610

    Article  Google Scholar 

  31. Sainsbury MG, Zhang QJ (1999) The Galerkin element method applied to the vibration of damped sandwich beams. Comput Struct 71(3):239–256. https://doi.org/10.1016/S0045-7949(98)00242-9

    Article  Google Scholar 

  32. Zhang QJ, Sainsbury MG (2000) The Galerkin element method applied to the vibration of rectangular damped sandwich plates. Comput Struct 74(6):717–730. https://doi.org/10.1016/S0045-7949(99)00068-1

    Article  Google Scholar 

  33. Baz AM, Ro JJ (1995) Vibration control of plates with active constrained layer damping. Smart Mater Struct 5(3):272–280. https://doi.org/10.1088/0964-1726/5/3/005

    Article  Google Scholar 

  34. Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip O 34(2):91–110. https://doi.org/10.1007/s00158-007-0167-6

    Article  MathSciNet  MATH  Google Scholar 

  35. Bendsoe MP, Sigmund O (2004) Topology optimization theory, methods, and applications. Springer

    MATH  Google Scholar 

  36. Bendsoe MP (1989) Optimal shape design as a material distribution problem. Struct Optimization 1:193–202. https://doi.org/10.1007/BF01650949

    Article  Google Scholar 

  37. Mlejnek HP, Schirrmacher R (1993) An engineer’s approach to optimal material distribution and shape finding. Comput Method Appl M 106(1/2):1–26. https://doi.org/10.1016/0045-7825(93)90182-W

    Article  MATH  Google Scholar 

  38. Rietz A (2001) Sufficiency of a finite exponent in SIMP (power law) methods. Struct Multidiscip O 21(2):159–163. https://doi.org/10.1007/s001580050180

    Article  Google Scholar 

  39. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip O 22(2):116–124. https://doi.org/10.1007/s001580100129

    Article  Google Scholar 

  40. Tortorelli DA, Michaleris P (1994) Design sensitivity analysis: overview and review. Inverse Prob Eng 1(1):71–105. https://doi.org/10.1080/174159794088027573

    Article  Google Scholar 

  41. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip O 33(4):401–424. https://doi.org/10.1007/s00158-006-0087-x

    Article  MathSciNet  Google Scholar 

  42. Sainsbury MG, Masti RS (2007) Vibration damping of cylindrical shells using strain-energy-based distribution of an add-on viscoelastic treatment. Finite Elem Anal Des 43(3):175–192. https://doi.org/10.1016/j.finel.2006.09.003

    Article  Google Scholar 

  43. Du JZ, Meng FW, Guo YH et al (2020) Fail-safe topology optimization of continuum structures with fundamental frequency constraints based on the ICM method. Acta Mech Sinica 36:1065–1077. https://doi.org/10.1007/s10409-020-00988-7

    Article  MathSciNet  Google Scholar 

  44. Correia VMF, Soares CMM, Soares CAM (2003) Buckling optimization of composite laminated adaptive structures. Compos Struct 62(3/4):315–321. https://doi.org/10.1016/j.compstruct.2003.09.030

    Article  Google Scholar 

  45. Moita JMS, Correia VMF, Martins PG et al (2006) Optimal design in vibration control of adaptive structures using a simulated annealing algorithm. Compos Struct 75(1/4):79–87. https://doi.org/10.1016/j.compstruct.2006.04.062

    Article  Google Scholar 

  46. Ma ZD, Kikuchi N, Hagiwara I (1993) Structural topology and shape optimization for a frequency response problem. Comput Mech 13(3):157–174. https://doi.org/10.1007/BF00370133

    Article  MathSciNet  MATH  Google Scholar 

  47. Svanberg K (2007) MMA and GCMMA. In: the homepage of krister svanberg. Department of mathematics at KTH royal institute of technology. http://www.math.kth.se/~krille/gcmma07.pdf. (Accessed 1 Jan 2021).

  48. Chen SX, Ye SH (1986) A guide-weight criterion method for the optimal design of antenna structures. Eng Optimiz 10(3):199–216. https://doi.org/10.1080/03052158608902537

    Article  Google Scholar 

  49. Liu X, Li D, Wang J et al (2011) Solving topology optimization problems by the Guide-Weight method. Front Mech Eng-PRC 6:136–150. https://doi.org/10.1007/s11465-010-0126-6

    Article  Google Scholar 

  50. Jiao HY, Li Y, Yang LY (2019) An improved guide-weight method without the sensitivity analysis. IEEE Access 7:109208–109215. https://doi.org/10.1109/ACCESS.2019.2933853

    Article  Google Scholar 

  51. Abdulhadi F (1969) Transverse vibrations of laminated plates with viscoelastic layer damping. Shock Vib Bull 40:90–104

    Google Scholar 

  52. Li EQ (2007) Dynamics analysis of passive constrained layer damping structure by the distributed parameter transfer function method. Chinese National University of Defense Technology

    Google Scholar 

Download references

Acknowledgements

This work was supported by Natural Science Foundation of Shaanxi Province (2020JM-200) and China Scholarship Council (201506965015). The authors are grateful to the anonymous reviewers for their valuable suggestions for improving the manuscript.

Author information

Authors and Affiliations

  1. School of Mechano-Electronic Engineering, Xidian University, Xi’an, 710071, People’s Republic of China

    Mingtao Cui, Jie Wang, Pengjie Li & Min Pan

  2. Shaanxi Key Laboratory of Space Extreme Detection, Xi’an, 710071, People’s Republic of China

    Mingtao Cui

  3. Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 2K6, Canada

    Mingtao Cui

Authors
  1. Mingtao Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pengjie Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Min Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mingtao Cui.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cui, M., Wang, J., Li, P. et al. Topology Optimization of Plates with Constrained Layer Damping Treatments Using a Modified Guide-Weight Method. J. Vib. Eng. Technol. 10, 19–36 (2022). https://doi.org/10.1007/s42417-021-00361-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42417-021-00361-3

Keywords

Search

Navigation