Abstract
Recent developments on the optimization of passive damping for vibration reduction in sandwich structures are presented in this paper, showing the importance of appropriate finite element models associated with gradient based optimizers for computationally efficient damping maximization programs. A new finite element model for anisotropic laminated plate structures with viscoelastic core and laminated anisotropic face layers has been formulated, using a mixed layerwise approach. The complex modulus approach is used for the viscoelastic material behavior, and the dynamic problem is solved in the frequency domain. Constrained optimization is conducted for the maximization of modal loss factors, using gradient based optimization associated with the developed model, and single and multiobjective optimization based on genetic algorithms using an alternative ABAQUS finite element model. The model has been applied successfully and comparative optimal design applications in sandwich structures are presented and discussed.
Similar content being viewed by others
References
ABAQUS (2005) Analysis user’s manual version 6.5. Hibbit, Karlsson and Sorensen, Pawtucket
Alvelid M (2008) Optimal position and shape of applied damping material. J Sound Vib 310:947–965
Araújo AL, Mota Soares CM, Herskovits J, Pedersen P (2002) Development of a finite element model for the identification of mechanical and piezoelectric properties through gradient optimisation and experimental vibration data. Compos Struct 58:307–318
Araújo AL, Lopes HMR, Vaz MAP, Mota Soares CM, Herskovits J, Pedersen P (2006) Parameter estimation in active plate structures. Comput Struct 84:1471–1479
Araújo AL, Mota Soares CM, Mota Soares CA (2008) Optimal design of active, passive, and hybrid sandwich structures. In: Lindner DK (ed) Modeling, signal processing, and control for smart structures, proc. of SPIE, vol 6926. SPIE, Bellingham, p 69260T
Araújo AL, Mota Soares CM, Mota Soares CA (2009) Finite element model for hybrid active-passive damping analysis of anisotropic laminated sandwich structures. J Sandw Struct Mater doi:10.1177/1099636208104534
Baz A, Ro J (1995) Optimum design and control of active constrained layer damping. J Mech Eng Des 117:135–144
Boudaoud H, Belouettar S, Daya EM, Potier-Ferry M (2008) A shell finite element for active-passive vibration control of composite structures with piezoelectric and viscoelastic layers. Mech Adv Mater Struct 15:208–219
Canelas A, Roche JR, Herskovits J (2009) The inverse electromagnetic shaping problem. Struct Multidiscipl Optim doi:10.1007/s00158-008-0285-9
DiTaranto RA (1965) Theory of vibratory bending for elastic and viscoelastic layered finite-length beams. ASME J Appl Mech 32:881–886
Douglas BE, Yang JCS (1978) Transverse compressional damping in the vibratory response of elastic-viscoelastic beams. AIAA J 16:925–930
Goel T, Vaidyanathan R, Haftka RT, Shyy W, Queipo NV, Tucker K (2007) Response surface approximation of pareto optimal front in a multi-objective optimization. Comput Methods Appl Mech Eng 196:879–893
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Boston
Haftka RT, Gurdal Z (1992) Elements of structural optimization. Kluwer, Dordrecht
Herskovits J (1986) A two-stage feasible directions algorithm for nonlinear constrained optimization. Math Program 36:19–38
Herskovits J (1998) A feasible directions interior point technique for nonlinear optimization. J Optim Theory Appl 99:121–146
Herskovits J, Mazorche JR (2009) A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics. Struct Multidiscipl Optim 37:435–446
Herskovits J, Mappa P, Goulart E, Mota Soares CM (2005) Mathematical programming models and algorithms for engineering design optimization. Comput Methods Appl Mech Eng 194:3244–3268
Lifshitz JM, Leibowitz M (1987) Optimal sandwich beam design for maximum viscoelastic damping. Int J Solids Struct 23:1027–1034
Marcelin JL, Trompette P, Smati A (1992) Optimal constrained layer damping with partial coverage. Finite Elem Anal Des 12:273–280
Marcelin JL, Shakhesi S, Pourroy F (1995) Optimal constrained layer damping of beams: experimental numerical studies. Shock Vib 2:445–450
Mead DJ, Markus S (1969) The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions. AIAA J 10:163–175
Moreira RAS, Rodrigues JD (2006) A layerwise model for thin soft core sandwich plates. Comput Struct 84:1256–1263
Moreira RAS, Rodrigues JD, Ferreira AJM (2006) A generalized layerwise finite element for multi-layer damping treatments. Comput Mech 37:426–444
Nagendra S, Justin D, Gurdal Z, Haftka RT, Watson LT (1996) Improved genetic algorithm for the design of stiffened composite panels. Comput Struct 58:543–555
Nashif AD, Jones DIG, Henderson JP (1985) Vibration damping. Wiley, New York
Nokes DS, Nelson FC (1968) Constrained layer damping with partial coverage. Shock Vib Bull 38:5–10
Rao DK (1978) Frequency and loss factors of sandwich beams under various boundary conditions. Int J Mech Eng Sci 20:271–278
Rao MD, He S (1993) Dynamic analysis and design of laminated composite beams with multiple damping layers. AIAA J 31:736–745
Sorensen DC (1995) Implicitly restarted arnoldi/lanczos methods for large scale eigenvalue calculations. Tech. Rep. Technical Report TR95-13, Department of Computational and Applied Mathematics, Rice University, Houston, Texas
Sun CT, Lu YP (1995) Vibration damping of structural elements. Prentice Hall PTR, Englewood Cliffs
Yan MJ, Dowell EH (1972) Governing equations of vibrating constrained-layer damping sandwich plates and beams. ASME J Appl Mech 39:1041–1046
Yang G, Reinstein LE, Pai S, Carroll DL (1998) A new genetic algorithm technique in optimization of permanent 125-i prostate implants. Med Phys 25:2308–2315
Author information
Authors and Affiliations
Corresponding author
Additional information
Some parts of this paper were presented at EngOpt 2008, International Conference on Engineering Optimization, held at Rio de Janeiro, Brazil.
Rights and permissions
About this article
Cite this article
Araújo, A.L., Martins, P., Mota Soares, C.M. et al. Damping optimization of viscoelastic laminated sandwich composite structures. Struct Multidisc Optim 39, 569 (2009). https://doi.org/10.1007/s00158-009-0390-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00158-009-0390-4