Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry, Volume 8

41 Reduced Order Models for Systems with Disparate Spatial and Temporal Scales 455 5. Maier, D., Hager, C., Hetzler, H., Fillot, N., Vergne, P., Dureisseix, D., Seemann, W.: A nonlinear model order reduction approach to the elastohydrodynamic problem. Tribol. Int. 82, 484–492 (2015) 6. Kudryavtsev, M., Rudnyi, E., Korvink, J., Hohlfeld, D., Bechtold, T.: Computationally efficient and stable order reduction methods for a large-scale model of mems piezoelectric energy harvester. Microelectron. Reliab. 55(5), 747–757 (2015) 7. Benner, P., Feng, L.: Model order reduction for coupled problems. Appl. Comput. Math. Int. J. 14(1), 3–22 (2015) 8. Foias, C., Jolly, M., Kevrekidis, I., Sell, G., Titi, E.: On the computation of inertial manifolds. Phys. Lett. A131(7), 433–436 (1988) 9. Pesheck, E., Pierre, C., Shaw, S.: A new galerkin-based approach for accurate non-linear normal modes through invariant manifolds. J. Sound Vib. 249(5), 971–993 (2002) 10. Feldmann, P., Freund, R.W.: Efficient linear circuit analysis by padé approximation via the lanczos process. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 14(5), 639–649 (1995) 11. Rahrovani, S., Vakilzadeh, M.K., Abrahamsson, T.: Modal dominancy analysis based on modal contribution to frequency response function H2-norm. Mech. Syst. Signal Process. 48(1), 218–231 (2014) 12. Vakilzadeh, M.K., Rahrovani, S., Abrahamsson, T.: Modal reduction based on accurate input-output relation preservation. In: Topics in Modal Analysis, vol. 7, pp. 333–342. Springer, New York (2014) 13. Glover, K.: All optimal hankel-norm approximations of linear multivariable systems and their L; 1-error bounds . Int. J. Control. 39(6), 1115–1193 (1984) 14. Zhou, H., Su, X., Song, Y.-D., Yan, Q.: Hankel-norm model reduction for delayed fuzzy systems. In: IEEE 2015 27th Chinese Control and Decision Conference (CCDC), pp. 964–968 (2015) 15. Phillips, J.R., Daniel, L., Silveira, L.M.: Guaranteed passive balancing transformations for model order reduction. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 22(8), 1027–1041 (2003) 16. Baur, U., Benner, P., Feng, L.: Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Arch. Comput. Meth. Eng. 21(4), 331–358 (2014) 17. Kerschen, G., Golinval, J.-C., Vakakis, A.F., Bergman, L.A.: The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlinear Dyn. 41(1–3), 147–169 (2005) 18. Rathinam, M., Petzold, L.R.: A new look at proper orthogonal decomposition. SIAM J. Numer. Anal. 41(5), 1893–1925 (2003) 19. Willcox, K., Peraire, J.: Balanced model reduction via the proper orthogonal decomposition. AIAA J. 40(11), 2323–2330 (2002) 20. Benner, P., Breiten, T.: Two-sided projection methods for nonlinear model order reduction. SIAM J. Sci. Comput. 37(2), B239–B260 (2015) 21. Georgiou, I.: Advanced proper orthogonal decomposition tools: using reduced order models to identify normal modes of vibration and slow invariant manifolds in the dynamics of planar nonlinear rods. Nonlinear Dyn. 41(1–3), 69–110 (2005) 22. Ghasemi, M., Yang, Y., Gildin, E., Efendiev, Y., Calo, V., et al.: Fast multiscale reservoir simulations using pod-deim model reduction. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, Richardson, TX (2015) 23. Shaw, S., Pierre, C.: Non-linear normal modes and invariant manifolds. J. Sound Vib. 150(1), 170–173 (1991) 24. Pesheck, E., Pierre, C., Shaw, S.W.: Modal reduction of a nonlinear rotating beam through nonlinear normal modes*. J. Vib. Acoust. 124(2), 229–236 (2002) 25. Kerschen, G., Peeters, M., Golinval, J.-C., Vakakis, A.F.: Nonlinear normal modes, part i: a useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23(1), 170–194 (2009) 26. Grolet, A., Thouverez, F.: Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and groebner bases. Mech. Syst. Signal Process. 52, 529–547 (2015) 27. Mohammadali, M., Ahmadian, H.: Efficient model order reduction of structural dynamic systems with local nonlinearities under periodic motion. Shock. Vib. 2014 (2014) 28. Blanc, F., Touzé, C., Mercier, J.-F., Ege, K., Ben-Dhia, A.-S.B.: On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems. Mech. Syst. Signal Process. 36(2), 520–539 (2013) 29. Wang, Y., Palacios, R., Wynn, A.: A method for normal-mode-based model reduction in nonlinear dynamics of slender structures. Comput. Struct. 159, 26–40 (2015) 30. Amabili, M., Sarkar, A., Paıdoussis, M.: Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method. J. Fluids Struct. 18(2), 227–250 (2003) 31. Smith, T.R., Moehlis, J., Holmes, P.: Low-dimensional modelling of turbulence using the proper orthogonal decomposition: a tutorial. Nonlinear Dyn. 41(1–3), 275–307 (2005) 32. Kerschen, G., Feeny, B., Golinval, J.-C.: On the exploitation of chaos to build reduced-order models. Comput. Methods Appl. Mech. Eng. 192(13), 1785–1795 (2003) 33. Vakakis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, vol. 156. Springer Science & Business Media, Berlin (2008) 34. Kuether, R.J., Deaner, B.J., Hollkamp, J.J., Allen, M.S.: Evaluation of geometrically nonlinear reduced-order models with nonlinear normal modes. AIAA J. 53(11), 3273–3285 (2015) 35. Wang X, Construction of frequency-energy plots for nonlinear dynamical systems from time-series data, Thesis, partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering, Graduate College of the University of Illinois, Urbana-Champaign (2010). 36. Peter, S., Grundler, A., Reuss, P., Gaul, L., Leine, R.I.: Towards finite element model updating based on nonlinear normal modes. In: Nonlinear Dynamics, vol. 1, pp. 209–217. Springer, Berlin (2016) 37. Vakakis, A.F., Manevitch, L.I., Mikhlin, Y.V., Pilipchuk, V.N., Zevin, A.A.: Normal Modes and Localization in Nonlinear Systems. Springer, Berlin (1996) 38. Segala, D.B., and Chelidze, D. Robust and dynamically consistent model order reduction for nonlinear dynamic systems. J. Dyn. Syst. Meas. Control. 137(2), 021011 (2015) 39. Chelidze, D.: Identifying robust subspaces for dynamically consistent reduced-order models. In: Nonlinear Dynamics, vol. 2, pp. 123–130. Springer, Berlin (2014)

RkJQdWJsaXNoZXIy MTMzNzEzMQ==