Research On Nonlinear Dynamic Modelling And Response Prediction Methods

A strongly nonlinear system often has multiple solutions under harmonic excitation.However,measuring all of these multiple responses is challenging in structural dynamics because often one solution is unstable and difficult to obtain.In this thesis,we solved the challenging problem and systematically established the fixed frequency test,the fixed frequency simulation and nonlinear parameter identification methods of the weakly nonlinear system and strongly nonlinear system.These method was demonstrated in a strongly nonlinear support structure,a three degrees of freedom system with weakly nonlinearities and a strongly nonlinear roto-bearing system.The main research achievements are summarized briefly as follows:(1)Fixed frequency test method.A fixed frequency test method is proposed to measure the multivalued response curves synchronously and continuously,including the amplitude and phase.The force drop-out phenomena in fixed frequency tests are exploited in the experimental testing of strongly nonlinear systems.The input voltage of the electrodynamic shaker is used as a natural continuation parameter in the fixed frequency tests.Based on these two findings,an experimental measurement method for multivalued response curves for strongly nonlinear systems is proposed.This method uses the force drop-out phenomenon of electrodynamic shaker in fixed frequency tests to automatically and passively control the variation of excitation amplitude.With the input voltage as the continuation parameter the multivalued response curves through the force drop-out are measured.(2)Fixed frequency simulation method.Based on the harmonic balance method,the continuation calculation method with the forcing frequency fixed are studied,which is used for fixed frequency simulation,reconstruction of constant force continuation and construction of the multivalued response surface.In order to improve the efficiency of the fixed frequency simulation,the analytic Jacobian matrix is proposed.The concept,description and construction method of the multivalued response surface of a strongly nonlinear system are proposed.The multivalued response surface of strongly nonlinear structure(including amplitude surface and phase surface)is reconstructed based on fixed frequency continuation.A conversion method from the fixed frequency continuation to the constant force continuation is established.The multivalued response curves obtained from the fixed frequency continuation can be used to reconstruct the constant force continuation results,which can be used not only in simulation but also in experiments.(3)Nonlinear parameter identification of a weakly nonlinear system.A novel strategy to characterize and identify weakly nonlinearities in MDOF systems based on reconstructingconstant response tests from fixed frequency tests is developed in this paper.According to the equivalent linearization theory,the functional characterization and parameter identification of the weakly nonlinearities are achived.Based on the single-valued function relationship between excitation and response in weakly nonlinear systems,a method for reconstructing a constant response test is proposed.Using the open-loop fixed frequency test results,the nonlinear stiffness is identified through the reconstruction of the constant displacement tests and the nonlinear stiffness is identified through the reconstruction of the constant velocity tests.This approach is mathematically simple and suitable for structures with weak nonlinearities.It is demonstrated on a framed structure with unknown weak nonlinearities,and the nonlinear stiffness and damping parameters of the structure are identified and validated.The results demonstrate the feasibility and effectiveness of the approach,and also show the potential for practical applications in engineering.(4)Nonlinear parameter identification of of a strongly nonlinear rotor-bearing system.A novel strategy to to identify nonlinearities in a strongly nonlinear rotor-bearing system is developed.The highlight of this strategy is the fixed frequency test method which is demonstrated in a strongly nonlinear rotor-bearing system.And the multivalued response amplitude and phase curves of the strongly nonlinear rotor-bearing system can be measured synchronously and continuously in a non-rotating state.A reconstruction method of constant response tests is also proposed for a strongly nonlinear system from fixed frequency test data.A rotor-bearing system with a strongly nonlinear support is used to demonstrate the method,and the nonlinear support stiffness parameters are identified and validated in a non-rotating state.The identified nonlinear rotor-bearing model also could predict the jump phenomena in the acceleration or deceleration process.The results demonstrate the feasibility and effectiveness of the approach,and also show the potential for practical applications in engineering.