Estimation of self-sustained vibration for a finite element brake model based on the shooting method with a reduced basis approximation of initial conditions

Abstract The objective of this paper is to discuss and propose an original nonlinear method for the estimation of nonlinear vibrations for mechanical systems subject to friction-induced noise and vibration. To fulfill such an objective the computation of nonlinear dynamic steady-state solutions of autonomous non-smooth contact systems prone to mono-instability is performed by developing an extension of the shooting method. This adaptation consists in using a reduced basis in the iterative process of this nonlinear method in order to seek the unknown initial conditions that verify condition of periodicity of the nonlinear solution of the problem. Efficiency of the proposed approach is illustrated through numerical examples for the prediction of self-sustained vibrations of a railway braking system.

[1]  Jean-Jacques Sinou,et al.  Periodic and quasi-periodic solutions for multi-instabilities involved in brake squeal , 2009 .

[2]  J. Sinou,et al.  Self-excited vibrations of a non-smooth contact dynamical system with planar friction based on the shooting method , 2018, International Journal of Mechanical Sciences.

[3]  Paul Bannister,et al.  Uncertainty quantification of squeal instability via surrogate modelling , 2015 .

[4]  Jean-Jacques Sinou,et al.  Parametric study of the mode coupling instability for a simple system with planar or rectilinear friction , 2016 .

[5]  Xavier Lorang,et al.  Study of nonlinear behaviors and modal reductions for friction destabilized systems. Application to an elastic layer , 2012 .

[6]  Svetozar Margenov,et al.  Numerical computation of periodic responses of nonlinear large-scale systems by shooting method , 2014, Comput. Math. Appl..

[7]  Oliver M. O’Reilly,et al.  Automotive disc brake squeal , 2003 .

[8]  Jean-Jacques Sinou,et al.  Non Smooth Contact Dynamics Approach for Mechanical Systems Subjected to Friction-Induced Vibration , 2019, Lubricants.

[9]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[10]  Gaëtan Kerschen,et al.  Numerical computation of nonlinear normal modes in mechanical engineering , 2016 .

[11]  P. J. Berndt,et al.  Experimental and theoretical investigation of brake squeal with disc brakes installed in rail vehicles , 1986 .

[12]  Vincent Acary,et al.  Energy conservation and dissipation properties of time‐integration methods for nonsmooth elastodynamics with contact , 2014, 1410.2499.

[13]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[14]  Xavier Lorang,et al.  A global strategy based on experiments and simulations for squeal prediction on industrial railway brakes , 2013 .

[15]  P. E. Gautier,et al.  TGV disc brake squeal , 2006 .

[16]  Pedro Ribeiro,et al.  Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods , 2004 .

[17]  Matthew S. Allen,et al.  A numerical approach to directly compute nonlinear normal modes of geometrically nonlinear finite element models , 2014 .

[18]  Jean-Jacques Sinou,et al.  A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal , 2009 .

[19]  S. Nacivet,et al.  Modal Amplitude Stability Analysis and its application to brake squeal , 2017 .

[20]  Annalisa Fregolent,et al.  Instability scenarios between elastic media under frictional contact , 2013 .

[21]  Huajiang Ouyang,et al.  Numerical analysis of automotive disc brake squeal: a review , 2005 .

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

[23]  Wen-Bin Shangguan,et al.  A unified approach for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties , 2017 .

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

[25]  Jean-Jacques Sinou,et al.  Performances of some reduced bases for the stability analysis of a disc/pads system in sliding contact , 2011 .

[26]  Sebastian Oberst,et al.  Impact of an irregular friction formulation on dynamics of a minimal model for brake squeal , 2018, Mechanical Systems and Signal Processing.

[27]  Fengxia Wang,et al.  Bifurcations of nonlinear normal modes via the configuration domain and the time domain shooting methods , 2015, Commun. Nonlinear Sci. Numer. Simul..

[28]  Joseph C. Slater,et al.  A numerical method for determining nonlinear normal modes , 1996 .

[29]  Raouf A. Ibrahim,et al.  Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling , 1994 .

[30]  Gerhard Müller,et al.  Uncertainty quantification applied to the mode coupling phenomenon , 2017 .

[31]  R. F. Nunes,et al.  Improvement in the predictivity of squeal simulations: Uncertainty and robustness , 2014 .

[32]  L. Gaul,et al.  A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations , 2002 .