An extended energy balance method for resonance prediction in forced response of systems with non-conservative nonlinearities using damped nonlinear normal mode
Damped nonlinear normal modes; Force–amplitude responses; Frictional contact; Energy balance method; Engineering structures; Forced response analysis; Full-scale structures; Non conservative systems; Nonlinear modal analysis; Nonlinear normal modes; Self-excited vibrations; Control and Systems Engineering; Aerospace Engineering; Ocean Engineering; Mechanical Engineering; Applied Mathematics; Electrical and Electronic Engineering
Abstract :
[en] The dynamic analysis of systems with nonlinearities has become an important topic in many engineering fields. Apart from the forced response analyses, nonlinear modal analysis has been successfully extended to such non-conservative systems thanks to the definition of damped nonlinear normal modes. The energy balance method is a tool that permits to directly predict resonances for a conservative system with nonlinearities from its nonlinear modes. In this work, the energy balance method is extended to systems with non-conservative nonlinearities using the concept of the damped nonlinear normal mode and its application in a full-scale engineering structure. This extended method consists of a balance between the energy loss from the internal damping, the energy transferred from the external excitation and the energy exchanged with the non-conservative nonlinear force. The method assumes that the solution of the forced response at resonance bears resemblance to that of the damped nonlinear normal mode. A simplistic model and full-scale structure with dissipative nonlinearities and a simplistic model showing self-excited vibration are tested using the method. In each test case, resonances are predicted efficiently and the computed force–amplitude curves show a great agreement with the forced responses. In addition, the self-excited solutions and isolas in forced responses can be effectively detected and identified. The accuracy and limitations of the method have been critically discussed in this work.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Sun, Yekai ; Department of Mechanical Engineering, Imperial College London, London, United Kingdom
Vizzaccaro, Alessandra; Department of Mechanical Engineering, Imperial College London, London, United Kingdom
Yuan, Jie; Department of Mechanical Engineering, Imperial College London, London, United Kingdom
Salles, Loïc ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M) ; Department of Mechanical Engineering, Imperial College London, London, United Kingdom
Language :
English
Title :
An extended energy balance method for resonance prediction in forced response of systems with non-conservative nonlinearities using damped nonlinear normal mode
CSC - China Scholarship Council EPSRC - Engineering and Physical Sciences Research Council
Funding text :
We thank Mattia Cenedese (ETH Zürich, Switzerland), Dr. Xing Wang (Sun Yat-sen University, China) and Dr. Ludovic Renson (Imperial College London, UK) for useful discussions.Yekai Sun is grateful to China Scholarship Council (File NO. 201708060239) for providing the financial support for this project. Dr. Jie Yuan acknowledges financial support from EPSRC (SYSDYMATS Project WP3). Dr. Loïc Salles thanks Rolls-Royce plc and the EPSRC for the support under the Prosperity Partnership Grant “Cornerstone: Mechanical Engineering Science to Enable Aero Propulsion Futures”, Grant Ref: EP/R004951/1. Acknowledgements
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