Substructures’ coupling with nonlinear connecting elements

The analysis of complex structures is often very challenging since reliable data can only be obtained if the underlying model represents properly the real case. Thus, nonlinearities should be considered if their effect can significantly affect the results. In many cases, the relevant nonlinearity is concentrated on the junction between the components of the system (bolted joints, contacts, etc.). In this work, modal substructuring methods are used to get the behaviour of complex linear systems which are coupled through a nonlinear interface. This can be modelled as an additional substructure to be included in the substructuring process. The dynamic behaviour of the nonlinear connecting substructure is evaluated through the computation of its nonlinear normal modes. The proposed method is applied to lumped parameter systems connected by cubic springs as nonlinear elements. Two scenarios are analysed: the former considering a single nonlinear connection and the latter accounting for multipoint nonlinear connection, being more representative of real cases.

[1]  Aldo Sestieri,et al.  Using distributed modifications to change the dynamic behaviour of structures , 1999 .

[2]  Aldo Sestieri,et al.  COUPLING THEORETICAL DATA AND TRANSLATIONAL FRFS TO PERFORM DISTRIBUTED STRUCTURAL MODIFICATION , 2001 .

[3]  Mehmet Imregun,et al.  COUPLING OF NON-LINEAR SUBSTRUCTURES USING VARIABLE MODAL PARAMETERS , 2000 .

[4]  G. Kerschen,et al.  Dynamic testing of nonlinear vibrating structures using nonlinear normal modes , 2011 .

[5]  Joseph J. Hollkamp,et al.  Reduced-order models for nonlinear response prediction: Implicit condensation and expansion , 2008 .

[6]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[7]  Gaëtan Kerschen,et al.  Nonlinear Normal Modes of a Full-Scale Aircraft , 2011 .

[8]  H. Nevzat Özgüven,et al.  Nonlinear Structural Modification and Nonlinear Coupling , 2014 .

[9]  Gaëtan Kerschen,et al.  Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques , 2009 .

[10]  C. Pierre,et al.  Characteristic Constraint Modes for Component Mode Synthesis , 2001 .

[11]  Morteza Karamooz Mahdiabadi,et al.  Nonlinear Substructuring Using Fixed Interface Nonlinear Normal Modes , 2017 .

[12]  R. M. Rosenberg,et al.  The Normal Modes of Nonlinear n-Degree-of-Freedom Systems , 1962 .

[13]  Gaëtan Kerschen,et al.  Numerical computation of nonlinear normal modes in a modal derivative subspace , 2018 .

[14]  Matthew S. Allen,et al.  Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities , 2013 .

[15]  Jörg Wallaschek,et al.  On the computation of the slow dynamics of nonlinear modes of mechanical systems , 2020, ArXiv.

[16]  D. Rixen,et al.  General Framework for Dynamic Substructuring: History, Review and Classification of Techniques , 2008 .

[17]  W. Hurty.  Dynamic Analysis of Structural Systems Using Component Modes , 1965 .

[18]  Annalisa Fregolent,et al.  Decoupling procedures in the general framework of Frequency Based Substructuring , 2009 .

[19]  S. Rubin.  Improved Component-Mode Representation for Structural Dynamic Analysis , 1975 .

[20]  H. Nevzat Özgüven,et al.  Structural modifications using frequency response functions , 1990 .

[21]  Malte Krack,et al.  Harmonic Balance for Nonlinear Vibration Problems , 2020, Mathematical Engineering.

[22]  Matthew S. Allen,et al.  Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction , 2017 .

[23]  Aldo Sestieri,et al.  Predicting the effect of distributed structural modifications by alternative techniques , 2001 .

[24]  Robert J. Kuether,et al.  Structural Modification of Nonlinear FEA Subcomponents Using Nonlinear Normal Modes , 2014 .

[25]  Alexander F. Vakakis,et al.  Nonlinear normal modes, Part I: A useful framework for the structural dynamicist , 2009 .