# Dynamic study of viscoelastic rotor: a comparative study using analytical and finite element model considering higher-order system

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## Abstract

In the past, many researchers developed rotor models using either lump system or finite element approach, where material damping played a crucial role in dynamic behaviour. Such damping in any rotating structure triggers instability at the supercritical range. In most of the literatures, material damping has been incorporated either by frequency-independent hysteretic damping or frequency-dependent viscous damping, but these models are insufficient to estimate the dynamic characteristics of the system. The motivation for using general viscoelastic model arises from a need to capture the influence of both types of damping. Such type of modelling is done through operator-based constitutive relationship. The numerator and denominator of material modulus are a polynomial of differential time operator, and polynomial coefficients are known as a viscoelastic parameter. The operator-based constitutive relationship is further utilized to bring down higher-order equations of motion by using two different techniques, i.e. (a) analytical approach and (b) finite element approach.The shaft damping is tackled in such a manner that the dissipation effects can be considered through all coordinates. The significance of both approaches is explained with the help of stability and response analysis at various disc positions.

## Keywords

Analytical model Finite element model Viscoelastic rotor Effective mass Effective diametral mass moment of inertia Stability analysis## References

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