Structural and Multidisciplinary Optimization

, Volume 59, Issue 1, pp 201–228 | Cite as

Sensitivity analysis of a two-plate coupled system in the statistical energy analysis (SEA) framework

  • Vinayak H. Patil
  • Dhanesh N. ManikEmail author
Research Paper


The main objective of this paper is to perform design sensitivity analysis of two right angle coupled plates, connected by various joint connections, to determine an optimum coupling loss factor (CLF) using optimization in the statistical energy analysis (SEA) framework. The theoretical analysis of obtaining such optimum CLFs can be used during the design stage of a dynamic system to specify the right type of joint. First- and second-order sensitivity analysis using theoretical equations of CLFs of two right angle plates in the SEA framework, coupled to form welded, riveted, and bolted connections, is presented in the audible frequency range. These sensitivities were determined using both analytic (direct differentiation) and finite difference methods; the sensitivities computed by the analytic method agree well with the finite difference method, indicating that the direct differentiation method can be directly used to predict variation in the CLF and the corresponding response of coupled plates joined by various joint connections. The sensitivity analysis also gives a feasible region in terms of frequency range for the determination of optimum values of CLF by selecting the right type of joint at the design stage based on its stiffness. The study presented in this paper will be very useful at the drawing board stage of designing vibro-acoustic systems to reduce vibration or noise of such systems by giving a definite direction for the modification of design parameters, thus eliminating expensive experimentation; it will be helpful in arriving at the optimum values of CLF that would eventually reduce the vibro-acoustic response of dynamic systems with a large number of subsystems connected by welded, riveted, and bolted joints.


Statistical energy analysis Optimization Sensitivity analysis Coupled plates Joints 



  1. Burkewitz B, Cohen L, Baran F (1994) Application of large scale SEA model to ship noise problem. NOISE-CON’94:697-701.Google Scholar
  2. Campbell B, Abrishan M, Stokes W (1993) Structural acoustic analysis for the prediction of vehicle body acoustic sensitivities. SAE pPaper nNo. 93197.Google Scholar
  3. Chavan AT, Manik DN (2010) Sensitivity analysis of vibro-acoustic systems in statistical energy analysis framework. Struct Multidisc Optim 40:283–306MathSciNetCrossRefGoogle Scholar
  4. Choi KK, Shim I, Wang S (1997) Design sensitivity analysis of structure-induced noise and vibration. J Vib Acoust 119:173–179CrossRefGoogle Scholar
  5. Cordioli JA, Gerges SNY, Pererira AK, Carmo M, Grandi C (2004) Vibro-acoustic modeling of aircrafts using statistical energy analysis. SAE paper.Google Scholar
  6. Cremer L, Heckl M, Ungar E (1973) Structure-borne sound. Spring, BerlinCrossRefGoogle Scholar
  7. Cunefare KA, Koopman GH (1992) Acoustic design sensitivity for structural radiators. J Vib Acoust 114:179–186CrossRefGoogle Scholar
  8. DeJong RG (2002) Optimization of noise control designs using SEA. Proceedings of the Second International AutoSEA Users Conference, Detroit-Troy Marriot-Troy, Michigan, USA.Google Scholar
  9. Fritze D, Marburg S, Hardtke HJ (2005) FEM-BEM coupling and structural-acoustic sensitivity analysis for shell geometries. Comput StructComputer Struct 83:143–154CrossRefGoogle Scholar
  10. Hambric SA (1995) Approximate techniques for broadband acoustic radiated noise design optimization problems. J Vib Acoust 117:136–144CrossRefGoogle Scholar
  11. Hynna P, Klinge P, Vuoksinen J (1995) Prediction of structure-borne sound transmission in large welded ship structures using statistical energy analysis. J Sound Vib 180:583–584CrossRefGoogle Scholar
  12. Jensen JO, Janssen JH (1997) Calculation of structure born noise transmission in ships using statistical energy analysis approach. Proceedings in International Symposium on Ship Board Acoustic.Google Scholar
  13. Kaminsky C, Unglenieks R (1997) Statistical energy analysis of noise and vibration from an automotive engine. SAE paper.Google Scholar
  14. Kane JH, Mauo S, Everstine GC (1991) A boundary element formulation for acoustic shape sensitivity analysis. J Acoust Soc Am 90:561–573CrossRefGoogle Scholar
  15. Kim NH, Dong J, Choi KK, Vlahopoulos N, Ma Z-D, Castanier M, Pierre C (2003) Design sensitivity analysis for sequential structural-acoustic problems. J Sound Vib 263:569–591CrossRefGoogle Scholar
  16. Kim NH, Dong J, Choi KK (2004) Energy flow analysis and design sensitivity of structural problems at high frequencies. J Sound Vib 269:213–250Google Scholar
  17. Koo BU (1997) Shape design sensitivity analysis of acoustic problems using a boundary element method. Comput StructComputer Struct 65:713–719CrossRefGoogle Scholar
  18. Lu LKH (1987) Optimum damping selection by statistical energy analysis. Statistical energy analysis winter annual meeting, Boston, MA., pp 9–14.Google Scholar
  19. Lyon RH, DeJong RG (1995) Theory and applications of statistical energy analysis, 2nd edn. Butterworth-Heinemann, LondonGoogle Scholar
  20. Ma ZD, Hagiwara I (1991a) Sensitivity analysis methods for coupled acoustic-structural systems part I. Modal sensitivities. AIAAJ 29:1787–1795zbMATHGoogle Scholar
  21. Ma ZD, Hagiwara I (1991b) Sensitivity analysis methods for coupled acoustic-structural systems part II. Direct frequency response and its sensitivities. AIAAJ 29:1795–1801CrossRefGoogle Scholar
  22. Miller VR, Faulkner LL (1983) Prediction of aircraft interior noise using the statistical energy analysis. J Vib Acoust Stress Reliab Des 105:512–518CrossRefGoogle Scholar
  23. Patil VH, Manik DN (2015) Determination of coupling loss factor (CLF) for right angled plates. 22nd International Conference on Sound and Vibration, Milan, Italy, July 12-16, 2015.Google Scholar
  24. Powell RE. (1995) Design sensitivity analysis of statistical energy analysis models. SAE paper.Google Scholar
  25. Radcliffe CJ, Huang XL (1997) Putting statistics into the statistical energy analysis of automotive vehicles. J Vib Acoust 119:629–634CrossRefGoogle Scholar
  26. Rodrigo GA, Klein M, Borello G (1994) Vibro-acoustic analysis of manned space craft using SEA. NOISE-CON’94.Google Scholar
  27. Salagame RR, Belegundu AD, Koopman GH (1995) Analytical sensitivity of acoustic power radiated from plates. J Vib Acoust 117:43–48CrossRefGoogle Scholar
  28. Scarpa F (2000) Parametric sensitivity analysis of coupled acoustic-structural systems. J Vib Acoust 122:109–115CrossRefGoogle Scholar
  29. Smith DC, Bernhard RJ (1992) Computation of acoustic shape design sensitivity using boundary element method. J Vib Acoust 114:127–132CrossRefGoogle Scholar
  30. Steel JA (1996) The prediction of structural vibration transmission through a motor vehicle using statistical energy analysis. J Vib Acoust 197:691–703Google Scholar
  31. Walsh SJ, Simpson G, Lalor N (1990) A computer system to predict internal noise in motor cars using ststistical energy analysis. Proceedings of inter-noise 90, Gothenburg, Sweden, pp 961-964.Google Scholar
  32. Wang S, Choi KK, Kulkarni H (1994) Acousical optimization of vehicle passenger space. SAE paper no. 941075.Google Scholar
  33. Zhang ZD, Raveendra ST (2003) Sound power sensitivity analysis and design optimization using BEM. SAE paper.Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Cummins, India, LtdPumeIndia
  2. 2.IIT Bombay MumbaiMumbaiIndia

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