Abstract
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.
Highlights
The dynamic responses of structures with various nonlinear characteristics have become an important research field that is able to improve the design of future engineering structures
E-energy balance method (EBM) is tested and validated for three different test cases: a oneDoF system with frictional contact, a two-DoF system interacting with a moving belt and a full-scale joint beam with contact interface
The paper is organised as follows: the general nonlinear dynamic equations for a forced system and autonomous system are given in Sect. 2; the method to compute damped nonlinear normal mode (dNNM) is explained in Sect. 3; the energy balance method (E-EBM) is introduced and explained in Sect. 4; the results from three test cases are investigated in Sects. 5–6; the benefits and the limitations of this E-EBM are critically discussed in Sect. 7 followed by the conclusions
Summary
The dynamic responses of structures with various nonlinear characteristics have become an important research field that is able to improve the design of future engineering structures. Backbone curves are sometimes seen as the collection of resonance points for a varying value of the excitation force Based on these considerations, an analytical method named energy balance method (EBM) has been attempted by Hill [8] to predict where the resonant solution of the forced response crosses the underlying nonlinear mode. An analytical method named energy balance method (EBM) has been attempted by Hill [8] to predict where the resonant solution of the forced response crosses the underlying nonlinear mode Before this EBM, similar energy transfer analysis has been described in [5,13,29]. A novel extended energy balance method (E-EBM) is described in this work and used to predict the resonance in systems with non-conservative nonlinearities. The paper is organised as follows: the general nonlinear dynamic equations for a forced system and autonomous system are given in Sect. 2; the method to compute dNNMs is explained in Sect. 3; the E-EBM is introduced and explained in Sect. 4; the results from three test cases are investigated in Sects. 5–6; the benefits and the limitations of this E-EBM are critically discussed in Sect. 7 followed by the conclusions
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