Abstract
Objective
The present work proposes a new Euler–Bernoulli shaft element for structurally damped and viscoelastic rotors in a spinning frame. The Maxwell–Wiechert linear viscoelastic material model, having one elastic branch and several parallel Maxwell branches, is used. This model introduces additional internal displacement variables between elastic and viscous elements in the Maxwell branches. Here, the stress depends not only on the elastic strain and elastic strain rate but also on additional fictitious strains and their rates.
Methods
In the present work, it is assumed that these additional strains can be derived from continuous fictitious displacement variables in the same way as the elastic strains are derived from the actual displacement variables. These continuous fictitious displacements in turn are interpolated from their nodal values using the conventional beam shape functions. Therefore, in addition to the standard degrees of freedom, extra degrees of freedom are defined at the nodes.
Simulation
The viscoelastic shaft element is then used in time-domain analysis of rotors with structural damping or frequency-dependent damping. Parameters of the Maxwell–Wiechert model are so selected that they appropriately represent structural damping of a mild steel rotor and frequency-dependent storage modulus and loss coefficient of a typical viscoelastic rotor. Both stability and time response analyses are performed.
Conclusion
The results obtained through dynamic analysis of two different rotor models using both structurally damped mild steel and a typical viscoelastic material PPC as shaft material are similar to those available in the literature and justify the methods applied.
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References
Liu F, Li-Q Chen (2008) Complex modal analysis for vibration of damped continua. Adv Vib Eng 7(3):283–291
Bhangale RK, Ganesan N (2007) Vibration and damping behavior of a viscoelastic functionally graded sandwich plate. Adv Vib Eng 6(4):333–341
Ramachandra Reddy BN, Roja Rani P, Badari Narayana K (2007) Visco-elastic damping with composite constraining layers. Adv Vib Eng 6(4):321–332
Gounaris GD, Nikolakopoulos PG, Papadopoulos CA (2014) Hysteretic damping and stress evaluation of rotor-bearing systems in the resonance zone. J Vib Eng Technol 2(2):171–189
Nakra BC, Chawla DR (1971) Shock response of a three-layer sandwich beam with viscoelastic core. J Aeronaut Soc India 23(3):135–139
Dutt JK, Roy H (2011) Viscoelastic modeling of rotor-shaft systems using an operator-based approach. J Mech Eng Sci 225(1):73–87
Genta G, Bassani D, Delprete C (1996) DYNROT: a finite element code for rotordynamic analysis based on complex co-ordinates. Eng Comput 13(6):86–109
Bagley RL, Torvik BJ (1983) Fractional calculus—a different approach to finite element analysis of viscoelastic damped structures. AIAA J 21(5):741–748
Friswell MI, Dutt JK, Adhikari S, Lees AW (2010) Time domain analysis of a viscoelastic rotor using internal variable models. Int J Mech Sci 52(10):1319–1324
Roy H, Dutt JK, Datta PK (2013) Dynamic behavior of stepped multilayered viscoelastic beams—a finite element approach. Adv Vib Eng 12(1):75–88
Roy H, Dutt JK, Chandraker S (2014) Modeling of multilayered viscoelastic rotors—an operator based approach. J Vib Eng Technol 2(6):485–494
Golla DF, Hughes PC (1985) Dynamics of viscoelastic structures—a time domain finite element formulation. J Appl Mech 52:897–906
McTavish DJ, Hughes PC (1993) Modeling of linear viscoelastic space structures. J Vib Acoust 115:103–110
Adhikari S (2001) Eigenrelations for non-viscously damped systems. AIAA J 39:1624–1630
Adhikari S (2002) Dynamics of non-viscously damped linear systems. J Eng Mech 128:328–339
Wagner N, Adhikari S (2003) Symmetric state-space formulation for a class of non-viscously damped systems. AIAA J 41:951–956
Adhikari S, Wagner N (2003) Analysis of a symmetric non-viscously damped linear dynamic system. J Appl Mech 70:885–893
Adhikari S (2005) Qualitative dynamic characteristics of a non-viscously damped oscillator. Proc R Soc Lond Ser A 461:2269–2288
Adhikari S (2008) Dynamic response characteristics of a non-viscously damped oscillator. J Appl Mech 75:011003:1–12
Genta G, Amati N (2010) Hysteretic damping in rotordynamics: an equivalent formulation. J Sound Vib 329:4772–4784
Nelson HD, McVaugh JM (1976) The dynamics of rotor-bearing systems using finite elements. ASME J Eng Industry 98(2):593–600
Genta G (2009) Vibration dynamics and control. Springer, New York
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Ganguly, S., Nandi, A. & Neogy, S. A State Space Viscoelastic Shaft Finite Element for Stability and Response Analysis of Rotors with Structural and Frequency Dependent Damping. J. Vib. Eng. Technol. 6, 1–18 (2018). https://doi.org/10.1007/s42417-018-0006-7
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DOI: https://doi.org/10.1007/s42417-018-0006-7