Abstract
Continuum topology optimization is an effective way to reduce vibration and noise of vibro-acoustic coupling system. However, the high computation time required for calculating the vibro-acoustic responses during topology optimization is a major obstacle for practical applications. In this paper, a novel symmetric method of vibro-acoustic system matrix is proposed, and a new model reduction method is developed based on Craig–Bampton mode synthesis method to compute dynamic responses with adequate efficiency and accuracy for topology optimization. The comparison results show that the proposed method substantially reduces the degrees of freedom (DOFs) and calculation time. The response values and eigenfrequencies calculated by the model reduction method are exactly the same as those of the full model. Furthermore, the bidirectional evolutionary structural optimization (BESO) algorithm is applied to solve the problem of minimizing the response of a single frequency and a certain range of frequency excitation at a specified target point. The results show that the optimization algorithm converges fast, the iterative process is robust and the response values of different coupling systems can be reduced to a higher extend, which indicates the applicability of the optimization algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akl, W., El, S.A., Al, M.K., et al.: Topology optimization of a plate coupled with acoustic cavity. Int. J. Solids Struct. 46, 2060–2074 (2009)
Vicente, W.M., Picelli, R., Pavanello, R., et al.: Topology optimization of frequency responses of fluid–structure interaction systems. Finite Elem. Anal. Des. 98, 1–13 (2015)
Chen, L.L., Liu, L.C., Zhao, W.C., et al.: 2D Acoustic design sensitivity analysis based on adjoint variable method using different types of boundary elements. Acoust Aust 44, 343–357 (2016)
Xu, Z.S., Huang, Q.B., Zhao, Z.G.: Topology optimization of composite material plate with respect to sound radiation. Eng. Anal. Boundary Elem. 35, 61–67 (2011)
Yoon, G.H., Jensen, J.S., Sigmund, O.: Topology optimization of acoustic structure interaction problems using a mixed finite element formulation. Int. J. Numer. Meth. Eng. 70, 1049–1075 (2007)
Chu, D.N., Xie, Y.M., Hira, A., et al.: Evolutionary structural optimization for problems with stiffness constraints. Finite Elem. Anal. Des. 1996(21), 239–251 (1996)
Jensen, J.S.: Topology optimization of dynamics problems with PADE approximants. Int. J. Numer. Meth. Eng. 72, 1605–1630 (2010)
Allaire, G., Michailidis, G.: Modal basis approaches in shape and topology optimization of frequency response problems. Int. J. Numer. Methods Eng. 113, 1258–1299 (2018)
Kang, Z., Zhang, X., Jiang, S., et al.: On topology optimization of damping layer in shell structures under harmonic excitations. Struct. Multidiscipl. Optim. 46, 51–67 (2012)
Choi, W.S., Park, G.J.: Structural optimization using equivalent static loads at all time intervals. Comput. Methods Appl. Mech. Eng. 191, 2105–2122 (2002)
Zhao, J., Wang, C.: Dynamic response topology optimization in the time domain using model reduction method. Struct. Multidiscipl. Optim. 53, 101–114 (2016)
Lee, H.A., Park, G.J.: Nonlinear dynamic response topology optimization using the equivalent static loads method. Comput. Methods Appl. Mech. Eng. 283, 956–970 (2015)
Teng, X.Y., Jiang, X.D., Sun, Y.X., et al.: Structural topology optimization using equivalent static load and mode tracking. J. Vib. Eng. 3, 349–356 (2017)
Craig, J.R.R., Bampton, M.C.: Coupling of subcomponents for dynamic analyses. AIAA J. 6, 1313–1319 (1968)
Kim, J.G., Lee, P.S.: An enhanced Craig–Bampton method. Int. J. Numer. Methods Eng. 103, 79–93 (2015)
Go, M.S., Lim, J.H., Kim, J.G., Hwang, K.R.: A family of craig–bampton methods considering residual mode compensation. Appl. Math. Comput. 369, 1–15 (2020)
Herrmann, J., Maess, M., Gaul, L.: Substructuring including interface reduction for the efficient vibro-acoustic simulation of fluid-filled piping systems. Mech. Syst. Signal Process. 24, 153–163 (2010)
Maess, M., Gaul, L.: Substructuring and model reduction of pipe components interacting with acoustic fluids. Mech. Syst. Signal Process. 20, 45–64 (2006)
Kim, S.M., Kim, J.G., Chae, S.W., et al.: A strongly coupled model reduction of vibro-acoustic interaction. Comput. Methods Appl. Mech. Eng. 347, 495–516 (2019)
Morand, H.J.P., Roger, O.: Fluid Structure Interaction-Applied Numerical Methods. Wiley, Paris (1995)
Sandberg, G., Wernberg, P.A., Davidsson, P.: Fundamentals of Fluid–Structure Interaction, vol. 505. Springer, Vienna (2008)
Du, J.B., Wang, X.C.: Fluid–structure coupling dynamic characteristic analysis for rotationally periodic liquidfilled vessel (I). J. Tsinghua 39, 108–111 (1999)
Du, J.B., Wang, X.C.: Fluid–structure coupling dynamic characteristic analysis for rotationally periodic liquid-filled vessel (II). J. Tsinghua 39, 112–116 (1999)
Huang, X., Xie, Y.M.: Convergent and mesh independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem. Anal. Des. 43, 1039–1049 (2007)
Acknowledgements
This study is supported by the Chinese National Natural Science Fund (No. 11602300).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, X., Wang, D. & Liu, B. Efficient Acoustic Topology Optimization Using Vibro-Acoustic Coupled Craig–Bampton Mode Synthesis. Acoust Aust 48, 407–418 (2020). https://doi.org/10.1007/s40857-020-00194-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40857-020-00194-2