Contents Functions PDF Index |

The following typesetting conventions are used in this manual

courier | blue monospace font : Matlab function names, variables |

feplot | light blue monospace font: SDT function names |

command | pink : strings and SDT Commands |

var | italic pink: part of command strings that have to be replaced by their value |

% comment | green: comments in script examples |

Italics | MATLAB Toolbox names, mathematical notations, and new terms when they are defined |

Bold | key names, menu names and items |

Small print | comments |

(1,2) | the element of indices 1, 2 of a matrix |

(1,:) | the first row of a matrix |

(1,3:end) | elements 3 to whatever is consistent of the first row of a matrix |

Programming rules are detailed under section 7.17. Conventions used to specify string commands used by user interface functions are detailed under commode.

Usual abbreviations are

CMS | Component Mode Synthesis (see section 6.3.3) |

COMAC | Coordinate Modal Assurance Criterion (see ii_mac) |

DOF,DOFs | degree(s) of freedom (see section 7.5) |

FE | finite element |

MAC | Modal Assurance Criterion (see ii_mac) |

MMIF | Multivariate Mode Indicator Function (see ii_mmif) |

POC | Pseudo-orthogonality check (see ii_mac) |

For mathematical notations, an effort was made to comply with the notations of the International Modal Analysis Conference (IMAC) which can be found in Ref. [1]. In particular one has

[ ],{ } | matrix, vector |

conjugate | |

[b] | input shape matrix for model with N DOFs and
NA inputs (see section 5.1). {φ_{j}^{T}b},{ψ_{j}^{T}b} modal input matrix of the j^{th} normal / complex mode |

[c] | sensor output shape matrix, model with N DOFs and NS
outputs (see section 5.1). {cφ_{j}},{cψ_{j}} modal output matrix of the j^{th} normal / complex mode |

[E]_{NS × NA} | correction matrix for high frequency modes (see section 5.6) |

[F]_{NS × NA} | correction matrix for low frequency modes (see section 5.6) |

M,C,K | mass, damping and stiffness matrices |

N,NM | numbers of degrees of freedom, modes |

NS,NA | numbers of sensors, actuators |

{p}_{NM × 1} | principal coordinate (degree of freedom of a normal mode model) (see section 5.2) |

{q}_{N × 1} | degree of freedom of a finite element model |

s | Laplace variable (s=iω for the Fourier transform) |

[R_{j}] | ={cψ_{j}}{ψ_{j}^{T}b} residue matrix
of the j^{th} complex mode (see section 5.6) |

[T_{j}] | ={cφ_{j}}{φ_{j}^{T}b} residue matrix of the j^{th} normal mode (used for proportionally damped models) (see section 5.6) |

{u(s)}_{NA × 1} | inputs (coefficients describing the time/frequency content of applied forces) |

{y(s)}_{NS × 1} | outputs (measurements, displacements, strains, stresses, etc.) |

[Z(s)] | dynamic stiffness matrix (equal to [Ms^{2}+Cs+K]) |

[α(s)] | dynamic compliance matrix (force to displacement transfer function) |

p,α | design parameters of a FE model (see section 6.4.2) |

Δ M,Δ C,Δ K | additive modifications of the mass, damping and stiffness matrices (see section 6.4.2) |

[Γ] | non-diagonal modal damping matrix (see section 5.3) |

λ_{j} | complex pole (see section 5.5) |

[φ]_{N × NM} | real or normal modes of the undamped system(NM ≤ N) |

[^{\} Ω^{2} _{\} ] | modal stiffness (diagonal matrix of modal frequencies squared) matrices (see section 5.2) |

[θ]_{N × NM} | NM complex modes of a first order symmetric structural model (see section 5.5) |

[ψ]_{N × NM} | NM complex modes of damped structural model (see section 5.5) |

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