Numerical methods for parametric model reduction in the simulation of disk brake squeal

Akay, 2002, Acoustics of friction, J. Acoust. Soc. Am. (USA), 111, 1525, 10.1121/1.1456514

2000, Software, Environments and Tools

Campbell, 1995, Linearization of DAE's along trajectories, Z. Angew. Math. Phys. (Switzerland), 46, 70, 10.1007/BF00952257

Davis, 2006, Direct methods for sparse linear systems, Vol. 2 of Fundamentals of Algorithms, 10.1137/1.9780898718881

Dowson, 1998, History of Tribology

Ericsson, 1980, The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems, Math. Comput. (USA), 35, 1251

Fan, 2004, Normwise scaling of second order polynomial matrices, SIAM J. Matrix Anal. Appl., 26, 252, 10.1137/S0895479803434914

Gohberg, 1982, Matrix Polynomials

Golub, 2009, Matrices, Moments and Quadrature with Applications, 10.1515/9781400833887

Golub, 1996, Matrix Computations, 3rd ed.

N. Gräbner S. M. Quraishi C. Schröder V. Mehrmann U. von Wagner New numerical methods for the complex eigenvalue analysis of disk brake squeal Proceedings of Eurobrake Conference Lille, France 2014

N. Gräbner . Tiedemann U. Von Wagner N. Hoffmann Nonlinearities in friction brake NVH - experimental and numerical studies, Technical Paper 2014-01-2511, SAE, 2014

1996, Dynamics with Friction: Modeling, Analysis and Experiment, Series on stability, Vibration and control of systems

2001, Dynamics with Friction: Modeling, Analysis and Experiment, Series on Stability, Vibration and Control of Systems, Vol. 7, Part II

Hahn, 1967, Stability of Motion, 10.1007/978-3-642-50085-5

Hammarling, 2013, An algorithm for the complete solution of quadratic eigenvalue problems, ACM Trans. Math. Softw., 39, 1, 10.1145/2450153.2450156

Hartman, 1960, A lemma in the theory of structural stability of differential equations, Proceedings of the American Mathematical Society, 11, 610, 10.1090/S0002-9939-1960-0121542-7

Higham, 2008, Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems, International Journal of Numerical Methods in Engineering, 73, 344, 10.1002/nme.2076

Higham, 2002, Accuracy and Stability of Numerical Algorithms, second ed., 10.1137/1.9780898718027

Higham, 2006/07, Symmetric linearizations for matrix polynomials, SIAM J. Matrix Anal. Appl., 29, 143, 10.1137/050646202

D. Hochlenert U. von Wagner How do nonlinearities inuence brake squeal? Proceedings of 29th SAE brake colloquium 179 186 2011

INTES, Stuttgart, PERMAS Product Description, Version 14 2012

INTES, Stuttgart, PERMAS Example Manual, 2014. Version 14.00.147, INTES publication no. 550 2014

Kannan, 2014, Detecting the causes of ill-conditioning in structural finite element models, Comput. Struct., 133, 79, 10.1016/j.compstruc.2013.11.014

Kerschen, 2005, The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: An overview, Nonlinear Dyn. (Netherlands), 41, 141

Kinkaid, 2003, Automotive disc brake squeal, J. Sound Vib. (UK), 267, 105, 10.1016/S0022-460X(02)01573-0

Knothe, 2008, Finite Elemente, Eine Einführung für Ingenieure, 4th ed.

Lancaster, 2002, Lambda Matrices and Vibrating Systems

Lehoucq, 1996, ARPACK Software Package

G. Liles Analysis of disc brake squeal using finite element methods, Technical Paper 891150, SAE 1989

Mackey, 2006, Structured polynomial eigenvalue problems: Good vibrations from good linearizations, SIAM J. Matrix Anal. Appl., 28, 1029, 10.1137/050628362

Mackey, 2010, Jordan structures of alternating matrix polynomials, Linear Algebra Appl., 432, 867, 10.1016/j.laa.2009.10.002

2014, MATLAB version R2014b

Mehrmann, 2011, Nonlinear eigenvalue and frequency response problems in industrial practice, Journal of Mathematics in Industry, 1

Mehrmann, 2005, Nonlinear eigenvalue problems: A challenge for modern eigenvalue Methods, GAMM-Mitteilungen, 27, 121, 10.1002/gamm.201490007

Ouyang, 2005, Numerical analysis of automotive disc brake squeal: A review, Int. J. of Vehicle Noise and Vibration, 1, 207, 10.1504/IJVNV.2005.007524

Rabinovicz, 1965, Friction and Wear of Materials

Rao, 1996, Rotor Dynamics

Sethna, 2006, Statistical Mechanics: Entropy, Order Parameters and Complexity

Spelsberg-Korspeter, 2012, Complex eigenvalue analysis and brake squeal: Traps, shortcomings and their removal, SAE Int. J. Passeng. Cars - Mech. Syst., 5, 1211, 10.4271/2012-01-1814

Stewart, 1990, Matrix Perturbation Theory

Tisseur, 2001, The quadratic eigenvalue problem, SIAM Rev. (USA), 43, 235, 10.1137/S0036144500381988

Trefethen, 2005, The Behavior of Nonnormal Matrices and Operators

Schaft, 2014, Port-Hamiltonian Systems Theory: An Introductory Overview, Vol.1 of: Foundations and Trends in Systems and Control, 10.1561/9781601987877

Sluis, 1969/1970, Condition numbers and equilibration of matrices, Numer. Math., 14, 14, 10.1007/BF02165096

Varga, 2004, Geršgorin and His Circles, 10.1007/978-3-642-17798-9

Veselić, 2011, Damped Osciallations of Linear Systems - A Mathematical Introduction, 10.1007/978-3-642-21335-9

Volkwein, 2013, Proper Orthogonal Decomposition: Theory and Reduced-Order Modelling