Nonlinear Dynamics

, Volume 88, Issue 1, pp 223–237 | Cite as

An effective numerical method for calculating nonlinear dynamics of structures with dry friction: application to predict the vibration response of blades with underplatform dampers

  • Dayi Zhang
  • Jianwei Fu
  • Qicheng Zhang
  • Jie Hong
Original Paper


This paper describes an efficient method to predict the nonlinear steady-state response of a complex structure with multi-scattered friction contacts. The contact friction force is equivalent to additional stiffness and damping based on optimal approximation theory, and as a consequence, the computation is simplified greatly by the linearization for a nonlinear system. In order to obtain accurate pressure distribution on the contact interfaces, the dynamic contact normal pressure is obtained by the equivalent static analysis which is validated for most engineering cases. Considering the complex procedure to determine the transformation between two different contact states, the differential forms of friction force are given to solve the tangential force accurately under the complex movement of interfaces. The approaches developed in this paper are particularly suitable to solve the dynamic response of large-scale structures with local contact nonlinearities. The entire procedure to calculate the steady-state response of a finite element model with a large number of degrees of freedom is demonstrated taking the blades with underplatform dampers as an example. The method is proved to be accurate and efficient; in particular, it does not suffer convergence problem in the allowable range of precision error, which exhibits remarkable potential engineering application values.


Dry friction Equivalent stiffness and damping Underplatform damper Nonlinear dynamics 



This work was financially supported by the National Natural Science Foundation of China, the Grant Nos. 51475021 and 51575022.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Energy and Power EngineeringBeihang UniversityBeijingPeople’s Republic of China
  2. 2.Collaborative Innovation Center of Advanced Aero-EngineBeijingPeople’s Republic of China

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