Skip to main content
SpringerLink
Log in

An FEM-based method to evaluate and optimize vibration power flow through a beam-to-plate connection

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Power flow is an important measure in vibratory energy propagation path analysis. For one-dimensional structural elements, i.e., bars or beams, power flow is obtained using a relationship involving degrees of freedom (DOF) of interest, and the respective internal forces. Several published works on vibration analysis involving the finite element method (FEM) and its optimization describe measures of interest only in terms of DOF (such as displacement and mean square velocity). However, in scenarios involving the coupling of different structures, these measures are inadequate. For example, minimizing only dynamical displacements at specific points in a structure could result in the internal forces at those points becoming unacceptably large. In such cases, minimizing power flow is preferable over minimizing displacements. In this manuscript, using FEM and a gradient-based optimization method, the authors propose a technique to evaluate and optimize vibratory power flow specifically in cases involving beam–plate coupling. The total power flow at the connection point is defined as a function of the global displacement vector, and it is evaluated for a given frequency by harmonic analysis; the relevant sensitivities are obtained using elementary matrices and the adjoint method. Geometrical parameters of the beam are used as design variables. A description of the methodology and two examples of its application to beam–plate structures are presented.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Bendsøe MP, Sigmund O (2004) Topology optimization: theory, methods and applications. Springer, New York

  2. Cho S, Park CY, Park YH, Hong SY (2006) Topology design optimization of structures at high frequencies using power flow analysis. J Sound Vib 298(12):206–220

    Article  Google Scholar 

  3. Cieślik J (2004) Vibration energy flow in rectangular plates. J Theor Appl Mech 42:195–212

    Google Scholar 

  4. Diaz A, Haddow A, Ma L (2005) Design of band-gap grid structures. Struct Multidiscip Optim 29(6):418–431

    Article  Google Scholar 

  5. Du J, Olhoff N (2007) Minimization of sound radiation from vibrating bi-material structures using topology optimization. Struct Multidiscip Optim 33(4–5):305–321

    Article  Google Scholar 

  6. Gavric L, Pavic G (1993) A finite element method for computation of structural intensity by the normal mode approach. J Sound Vib 164(1):29–43

    Article  MATH  Google Scholar 

  7. Jensen JS, Pedersen N (2005) Sensitivity analysis and topology optimization in structural dynamics. DCAMM Report

  8. Jensen JS, Sigmund O (2003) Systematic design of phononic bandgap materials and structures by topology optimization. Philos Trans R Soc Lond Ser A Math Phys Eng Sci 361(1806):1001–1019

    Article  MathSciNet  MATH  Google Scholar 

  9. Jensen JS, Sigmund O (2005) Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide. J Opt Soc Am B 22(6):1191–1198

    Article  Google Scholar 

  10. Kim NH, Dong J, Choi KK (2004) Energy flow analysis and design sensitivity of structural problems at high frequencies. J Sound Vib 269(12):213–250

    Article  Google Scholar 

  11. Li K, Li S, Zhao D (2010) Investigation on vibration energy flow characteristics in coupled plates by visualization techinques. J Mar Sci Technol 18(6):907–914

    Google Scholar 

  12. Liu L, Hussein MI (2011) Wave motion in periodic flexural beams and characterization of the transition between bragg scattering and local resonance. ASME. J Appl Mech 79(1):011003-1–011003-17. doi:10.1115/1.4004592

    Google Scholar 

  13. Martins P, Lenzi A (2015) Vibrational power flow analysis to hermetic compressor housing through a discharge tube made of polymeric material. In: Proceedings of the XVII international symposium on dynamic problems of mechanics, Natal

  14. Mead D (1999) Passive vibration control. Wiley, New York

  15. Niu B, Olhoff N (2014) Minimization of vibration power transmission from rotating machinery to a flexible supporting plate. Int J Struct Stab Dyn 14(3):1350068-1–1350068-28

    Article  Google Scholar 

  16. Olhoff N, Du J (2009) On topological design optimization of structures against vibration and noise emission. In: Sandberg G, Ohayon R (eds) Computational aspects of structural acoustics and vibration, CISM international centre for mechanical sciences, vol 505. Springer, Vienna, pp 217–276

  17. Przemieniecki J (1985) Theory of matrix structural analysis. Dover, New York

  18. Silva OM, Guesser TM, Fiorentin TA, Lenzi A (2015) Shape optimization of compressor supporting plate based on vibration modes. Noise Control Eng J 63(1):49–58

    Article  Google Scholar 

  19. Sorokin S, Nielsen J, Olhoff N (2001a) Analysis and optimization of energy flows in structures composed of beam elements—part II: examples and discussion. Struct Multidiscip Optim 22(1):12–23

    Article  Google Scholar 

  20. Sorokin S, Nielsen J, Olhoff N (2001b) Analysis and optimization of energy flows in structures composed of beam elements—part I: problem formulation and solution technique. Struct Multidiscip Optim 22(1):3–11

    Article  Google Scholar 

  21. Sorokin S, Olhoff N, Ershova O (2008) Analysis of the energy transmission in spatial piping systems with heavy internal fluid loading. J Sound Vib 310(45):1141–1166

    Article  Google Scholar 

  22. Svanberg K (1987) The method of moving asymptotesa new method for structural optimization. Int J Numer Methods Eng 24(2):359–373

    Article  MathSciNet  MATH  Google Scholar 

  23. Weisser T, Foltte E, Bouhaddi N, Gonidou LO (2015) A power flow mode approach dedicated to structural interface dynamic characterization. J Sound Vib 334:202–218

    Article  Google Scholar 

  24. Xing JT, Price WG (1999) A powerflow analysis based on continuum dynamics. Proc R Soc Lond Ser A Math Phys Eng Sci 455(1982):401–436

    Article  MathSciNet  MATH  Google Scholar 

  25. Yang X, Li Y (2013) Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment. Struct Multidiscip Optim 47(3):399–408

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhang X, Kang Z, Li M (2014) Topology optimization of electrode coverage of piezoelectric thin-walled structures with cgvf control for minimizing sound radiation. Struct Multidiscip Optim 50(5):799–814

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by CAPES (Brazil) and IDMEC, Polo IST (Portugal). The authors are grateful to Prof. Krister Svanberg from Royal Institute of Technology, Stockholm, for providing his Matlab version of MMA, and to Prof. Luiz Augusto Saeger from Federal University of Santa Catarina, Brazil, for his valuable support on mathematical issues.

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Federal University of Santa Catarina, Florianópolis, SC, Brazil

    Olavo M. Silva, Roberto Jordan & Arcanjo Lenzi

  2. LAETA, IDMEC, Instituto Superior Tecnico, University of Lisbon, Lisbon, Portugal

    Miguel M. Neves

Authors
  1. Olavo M. Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miguel M. Neves
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roberto Jordan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arcanjo Lenzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olavo M. Silva.

Additional information

Technical Editor: Fernando Alves Rochinha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Silva, O.M., Neves, M.M., Jordan, R. et al. An FEM-based method to evaluate and optimize vibration power flow through a beam-to-plate connection. J Braz. Soc. Mech. Sci. Eng. 39, 413–426 (2017). https://doi.org/10.1007/s40430-015-0360-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-015-0360-2

Keywords

Search

Navigation