Floating Frame of Reference formulation for modeling flexible multi-body systems in premise operational conditions

Abstract

The Floating Frame of Reference (FFR) formulation is a well-established and reliable method for modeling flexible multi-body systems. The FFR formulation has been adopted for dynamic systems that are characterized by large rotations with relatively small deformations. Many scientific papers have pointed out these characteristics with the scrutiny of the simulation results and comparisons with other modeling techniques. However, the FFR is still enclosed in the theoretical aspects and simulation work and faces difficulties when being applied to practical systems. The crucial point in these difficulties centers on coordinate reduction and the associated mapping between nodal and modal coordinates. The process of selecting the necessary modes may be theoretically simple, but the situation is different when applied in a real operational environment. The strategy developed in this work combines the Operational Modal Analysis, specifically the Frequency Domain Decomposition (FDD) approach, and the FFR formulation to build a suitable model of practical multi-body systems. The output model has been validated experimentally. The results show that the proposed FFR-FDD method can be efficiently used to construct multi-body models for those systems that work in premise operational conditions.

Keywords

Floating Frame of Reference coordinate reduction modal identification Operational Modal Analysis

Get full access to this article

View all access options for this article.

References

Brincker

(2014) Some elements of operational modal analysis. Shock and Vibration 2014: 1–11.

Brincker

Ventura

(2015) Introduction to Operational Modal Analysis, Chichester: John Wiley & Sons, Ltd.

Brincker R, Ventura CE and Andersen P (2001a) Damping estimation by frequency domain decomposition. In: 19th international modal analysis conference (IMAC), Kissimmee, Florida, USA, 5-8 February 2001, pp.698–703. Berlin, Germany: Society for Experimental Mechanics (SEM) – VDE-Verl.

Brincker

Zhang

Andersen

(2001b) Modal identification of output-only systems using frequency domain decomposition. Smart Materials and Structures 10(3): 441–445.

Ghahari

Abazarsa

Ghannad

, et al.(2012) Response-only modal identification of structures using strong motion data. Earthquake Engineering & Structural Dynamics 42(8): 1221–1242.

Holm-Jørgensen

Nielsen

(2009) A component mode synthesis algorithm for multibody dynamics of wind turbines. Journal of Sound and Vibration 326(3–5): 753–767.

Holzwarth P and Eberhard P (2015) Interface reduction for CMS methods and alternative model order reduction. IFAC-PapersOnLine 48(1): 254–259.

Korkealaakso

Mikkola

Rantalainen

, et al.(2009a) Description of joint constraints in the floating frame of reference formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 223(2): 133–145.

Korkealaakso

Mikkola

Rantalainen

, et al.(2009b) Description of joint constraints in the floating frame of reference formulation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 223(2): 133–145.

10.

Megahed S and Nada A (2003) Dynamic modeling of a flexible cantilever beam an experimental technique. In: Proceedings of the ASME Design Engineering Technical Conference, 19th Biennial Conference on Mechanical Vibration and Noise (ed AA Shabana), Chicago, Illinois, USA, 2-6 September 2003, pp.449–456. New York, NY: American Society of Mechanical Engineers (ASME).

11.

Nada A (2007) Flexible robotic manipulators: modeling, simulation and control with experimentation. PhD Thesis, Mechanical Design and Production Engineering, Cairo University, Egypt.

12.

Nada

Al-Shahrani

(2017) Dynamic modelling and experimental validation of small-size wind turbine using flexible multibody approach. International Journal of Dynamics and Control 5(3): 721–732.

13.

Nada AA, Hussein BA, Megahed SM, et al. (2009) Floating frame of reference and absolute nodal coordinate formulations in the large deformation analysis of robotic manipulators: a comparative experimental and numerical study. In: Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C (eds A Shabana, K Anderson and G Flowers), San Diego, California, USA, 30 August-2 September 2009, pp.889–900. New York, NY: American Society of Mechanical Engineers (ASME).

14.

Nada

Hussein

Megahed

, et al.(2010) Use of the floating frame of reference formulation in large deformation analysis: Experimental and numerical validation. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 224(1): 45–58.

15.

Nowakowski C, Fehr J, Fischer M, et al. (2012) Model order reduction in elastic multibody systems using the floating frame of reference formulation. In: IFAC Proceedings Volumes, 45(2): 40–48.

16.

Omar

Tounsi

, et al.(2010) An optimized rational fraction polynomial approach for modal parameters estimation from FRF measurements. Journal of Mechanical Science and Technology 24(3): 831–842.

17.

Reynders

(2012) System identification methods for (operational) modal analysis: Review and comparison. Archives of Computational Methods in Engineering 19(1): 51–124.

18.

Richardson MH and Formenti DL (1982) Parameter estimation from frequency response measurements using rational fraction polynomials. In: Proceedings of the International Modal Analysis Conference & Exhibit (eds PB Juhl and R Eisenstadt), Orlando, Florida, USA, 8–10 November 1982, pp.167–181. Schenectady, New York: Union College.

19.

Shabana

(2013) Dynamics of Multibody Systems, Volume 9781107042, Cambridge: Cambridge University Press.

20.

Shabana

(2015) Definition of ANCF finite elements. Journal of Computational and Nonlinear Dynamics 10(5): 054506.

21.

Sugiyama

Shabana

Omar

, et al.(2006) Development of nonlinear elastic leaf spring model for multibody vehicle systems. Computer Methods in Applied Mechanics and Engineering 195(50–51): 6925–6941.

22.

Wasfy

Noor

(2003) Computational strategies for flexible multibody systems. Applied Mechanics Reviews 56(6): 553.

23.

Yin

Živanović

(2012) Displacement modal identification method of elastic system under operational condition. Nonlinear Dynamics 70(2): 1407–1420.

24.

Ziegler

Humer

Pechstein

, et al.(2016a) Generalized component mode synthesis for the spatial motion of flexible bodies with large rotations about one axis. Journal of Computational and Nonlinear Dynamics 11(4): 041018.

25.

Ziegler

Humer

Pechstein

, et al.(2016b) Generalized component mode synthesis for the spatial motion of flexible bodies with large rotations about one axis 1. Journal of Computational and Nonlinear Dynamics 11(4): 041018.