M 12 – V. 7.1 ©
Table of contents
4
3. REDUCTION METHODS .........................................................................................43
3.1 Introduction.......................................................................................................................43
3.2. Substructuring methods ..................................................................................................44
3.3 Projection methods ..........................................................................................................49
4. STABILITY ANALYSIS AND COMPUTATION OF CRITICAL SPEEDS .....................................51
4.1 Introduction.......................................................................................................................51
4.2 Stability and critical speeds ............................................................................................51
4.3 Orthogonality properties of the homogeneous system [L1] ........................................55
4.4 Determining eigenvalues and eigenvectors...................................................................60
4.5. Direct computation of the critical velocities ..................................................................69
4.6 Classification of the eigenvectors ..................................................................................70
4.7. Sensitivity analysis [K2,K3] .............................................................................................73
4.8. Statistical analysis............................................................................................................76
5. HARMONIC RESPONSE COMPUTATION ....................................................................77
5.1. Introduction.......................................................................................................................77
5.2. Computing the harmonic response in the linear case ..................................................77
5.3. Computation of the response in the non-linear case ....................................................81
A.5 Annex to chapter 5 ...........................................................................................................92
6. TRANSIENT ANALYSIS ...........................................................................................93
6.1 Introduction.......................................................................................................................93
6.2 Excitation processes........................................................................................................94
6.3 Initial state .........................................................................................................................95
6.4 Resolution methods adapted to the linear case ............................................................97
6.4.1 Direct integration of the complete set of equations....................................................97
6.4.2 Projection on a real basis ........................................................................................104
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