Uncertainty propagation of frequency response of viscoelastic damping structures using a modified high-dimensional adaptive sparse grid collocation method

References

• B. C. Nakra, Vibration control in machines and structures using viscoelastic damping, J. Sound Vib., vol. 211, no. 3, pp. 449–465, 1998. DOI: 10.1006/jsvi.1997.1317.
   Web of Science ®Google Scholar
• D. I. G. Jones, Handbook of Viscoelastic Vibration Damping, Wiley, Chichester, 2001.
   Google Scholar
• M. D. Rao, Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes, J. Sound Vib., vol. 262, no. 3, pp. 457–474, 2003. DOI: 10.1016/S0022-460X(03)00106-8.
   Web of Science ®Google Scholar
• K. Akoussan, H. Boudaoud, E. M. Daya, and E. Carrera, Vibration modeling of multilayer composite structures with viscoelastic layers, Mech. Adv. Mater. Struct., vol. 22, no. 1–2, pp. 136–149, 2015. DOI: 10.1080/15376494.2014.907951.
   Web of Science ®Google Scholar
• K. G. Lougou, H. Boudaoud, E. M. Daya, and L. Azrar, Vibration modeling of large repetitive sandwich structures with viscoelastic core, Mech. Adv. Mater. Struct., vol. 23, no. 4, pp. 458–466, 2016. DOI: 10.1080/15376494.2014.984095.
   Web of Science ®Google Scholar
• K. Akoussan, H. Boudaoud, E. M. Daya, Y. Koutsawa, and E. Carrera, Numerical method for nonlinear complex eigenvalues problems depending on two parameters: Application to three-layered viscoelastic composite structures, Mech. Adv. Mater. Struct., vol. 25, no. 15–16, pp. 1361–1373, 2018. DOI: 10.1080/15376494.2017.1286418.
   Web of Science ®Google Scholar
• S. H. Alavi, and H. Eipakchi, An analytical approach for free vibrations analysis of viscoelastic circular and annular plates using FSDT, Mech. Adv. Mater. Struct., vol. 27, no. 3, pp. 250–264, 2020. DOI: 10.1080/15376494.2018.1472348.
   Web of Science ®Google Scholar
• F. Abdoun, L. Azrar, E. M. Daya, and M. Potier-Ferry, Forced harmonic response of viscoelastic structures by an asymptotic numerical method, Comput. Struct., vol. 87, no. 1–2, pp. 91–100, 2009. DOI: 10.1016/j.compstruc.2008.08.006.
   Web of Science ®Google Scholar
• J. D. Chazo, B. Nennig, and P. D. Emmanuel, Harmonic response computation of poroelastic multilayered structures using ZPST shell elements, Comput. Struct., vol. 121, pp. 99–107, 2013. DOI: 10.1016/j.compstruc.2013.02.013.
   Web of Science ®Google Scholar
• L. Li, Y. J. Hu, and X. L. Wang, Harmonic response calculation of viscoelastic structures using classical normal modes: An iterative method, Comput. Struct., vol. 133, pp. 39–50, 2014. DOI: 10.1016/j.compstruc.2013.11.009.
   Web of Science ®Google Scholar
• L. Rouleau, J. F. Deue, and A. Legay, A comparison of model reduction techniques based on modal projection for structures with frequency-dependent damping, Mech. Syst. Signal Process., vol. 90, pp. 110–125, 2017. DOI: 10.1016/j.ymssp.2016.12.013.
   Web of Science ®Google Scholar
• X. Xie, H. Zheng, S. Jonckheere, A. van de Walle, B. Pluymers, and W. Desmet, Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping, Comput. Methods Appl. Mech. Eng., vol. 332, pp. 363–381, 2018. DOI: 10.1016/j.cma.2017.12.023.
   Web of Science ®Google Scholar
• W. P. Hernandez, D. A. Castello, and T. G. Ritto, Uncertainty propagation analysis in laminated structures with viscoelastic core, Comput. Struct., vol. 164, pp. 23–37, 2016. DOI: 10.1016/j.compstruc.2015.10.006.
   Web of Science ®Google Scholar
• J. Xu, and J. Li, Stochastic dynamic response and reliability assessment of controlled structures with fractional derivative model of viscoelastic dampers, Mech. Syst. Signal Process., vol. 72–73, pp. 865–896, 2016. DOI: 10.1016/j.ymssp.2015.11.016.
   Web of Science ®Google Scholar
• R. Capillon, C. Desceliers, and C. Soize, Uncertainty quantification in computational linear structural dynamics for viscoelastic composite structures, Comput. Methods Appl. Mech. Eng., vol. 305, pp. 154–172, 2016. DOI: 10.1016/j.cma.2016.03.012.
   Web of Science ®Google Scholar
• M. Guedri, A. M. G. de Lima, N. Bouhaddi, and D. A. Rade, Robust design of viscoelastic structures based on stochastic finite element models, Mech. Syst. Signal Process., vol. 24, no. 1, pp. 59–77, 2010. DOI: 10.1016/j.ymssp.2009.03.010.
   Web of Science ®Google Scholar
• F. Druesne, M. Hamdaoui, P. Lardeur, and E. M. Daya, Variability of dynamic responses of frequency dependent visco-elastic sandwich beams with material and physical properties modeled by spatial random fields, Compos. Struct., vol. 152, pp. 316–323, 2016. DOI: 10.1016/j.compstruct.2016.05.026.
   Web of Science ®Google Scholar
• V. A. C. Silva, A. M. G. de Lima, N. Bouhaddi, and H. B. Lacerda, Uncertainty propagation and experimental verification of nonlinear viscoelastic sandwich beams, Mech. Syst. Signal Process., vol. 132, pp. 654–669, 2019. DOI: 10.1016/j.ymssp.2019.07.022.
   Web of Science ®Google Scholar
• R. Y. Rubinstein, and D. P. Kroese, Simulation and the Monte Carlo Method, Wiley, Hoboken, NJ, 2016.
   Google Scholar
• A. Manan, and J. E. Cooper, Prediction of uncertain frequency response function bounds using polynomial chaos expansion, J. Sound Vib., vol. 329, no. 16, pp. 3348–3358, 2010. DOI: 10.1016/j.jsv.2010.01.008.
   Web of Science ®Google Scholar
• V. Yaghoubi, S. Rahrovani, H. Nahvi, and S. Marelli, Reduced order surrogate modeling technique for linear dynamic systems, Mech. Syst. Signal Process., vol. 111, pp. 172–193, 2018. DOI: 10.1016/j.ymssp.2018.02.020.
   Web of Science ®Google Scholar
• E. Pagnacco, E. Sarrouy, R. Sampaio, and E. Souza de Crusis, Polynomial chaos for modeling multimodal dynamical systems-investigations on a single degree of freedom system, Proceeding of XX Congress on Numerical Methods and Their Applications., vol. XXXII, pp. 705–727, 2013.
   Google Scholar
• E. Jacquelin, S. Adhikari, J. J. Sinou, and M. I. Friswell, Polynomial chaos expansion and steady-state response of a class of random dynamical systems, J. Eng. Mech., vol. 141, no. 4, pp. 4014145, 2015. DOI: 10.1061/(ASCE)EM.1943-7889.0000856.
   Web of Science ®Google Scholar
• E. Jacquelin, S. Adhikari, J. J. Sinou, and M. I. Friswell, Polynomial chaos expansion in structural dynamics: Accelerating the convergence of the first two statistical moment sequences, J. Sound Vib., vol. 356, pp. 144–154, 2015. DOI: 10.1016/j.jsv.2015.06.039.
   Web of Science ®Google Scholar
• V. Yaghoubi, S. Marelli, B. Sudret, and T. Abrahamsson, Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation, Probabilist. Eng. Mech., vol. 48, pp. 39–58, 2017. DOI: 10.1016/j.probengmech.2017.04.003.
   Web of Science ®Google Scholar
• X. Ma, and N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations, J. Comput. Phys., vol. 228, no. 8, pp. 3084–3113, 2009. DOI: 10.1016/j.jcp.2009.01.006.
   Web of Science ®Google Scholar
• I. M. Sobol, Theorems and examples on high dimensional model representation, Reliab. Eng. Syst. Safe., vol. 79, no. 2, pp. 187–193, 2003. DOI: 10.1016/S0951-8320(02)00229-6.
   Web of Science ®Google Scholar
• X. Ma, and N. Zabaras, An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations, J. Comput. Phys., vol. 229, no. 10, pp. 3884–3915, 2010. DOI: 10.1016/j.jcp.2010.01.033.
   Web of Science ®Google Scholar
• C. Xu, S. Lin, and Y. Z. Yang, Optimal design of viscoelastic damping structures using layerwise finite element analysis and multi-objective genetic algorithm, Comput. Struct., vol. 157, pp. 1–8, 2015. DOI: 10.1016/j.compstruc.2015.05.005.
   Web of Science ®Google Scholar
• C. Xu, M. Z. Wu, and M. Hamdaoui, Mixed integer multi-objective optimization of composite structures with frequency-dependent interleaved viscoelastic damping layers, Comput. Struct., vol. 172, pp. 81–92, 2016. DOI: 10.1016/j.compstruc.2016.05.006.
   Web of Science ®Google Scholar
• S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Dokl Akad Nauk SSSR, vol. 148, no. 5, pp. 1042–1045, 1963.
   Google Scholar
• D. B. Xiu, and J. S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput., vol. 27, no. 3, pp. 1118–1139, 2005. DOI: 10.1137/040615201.
   Web of Science ®Google Scholar
• A. Klimke, and B. Wohlmuth, Algorithm 847: Spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB, ACM Trans. Math. Softw., vol. 31, no. 4, pp. 561–579, 2005. DOI: 10.1145/1114268.1114275.
   Web of Science ®Google Scholar
• H. Xu, and S. Rahman, A generalized dimension-reduction method for multidimensional integration in stochastic mechanics, Int. J. Numer. Meth. Eng., vol. 61, no. 12, pp. 1992–2019, 2004. DOI: 10.1002/nme.1135.
   Web of Science ®Google Scholar
• H. Rabitz, O. F. Aliş, J. Shorter, and K. Shim, Efficient input—output model representations, Comput. Phys. Commun., vol. 117, no. 1–2, pp. 11–20, 1999. DOI: 10.1016/S0010-4655(98)00152-0.
   Web of Science ®Google Scholar