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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). {φjTb},{ψjTb} modal input matrix of the jth normal / complex mode |
| [c] | sensor output shape matrix, model with N DOFs and NS outputs (see section 5.1). {cφj},{cψj} modal output matrix of the jth 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) |
| [Rj] | ={cψj}{ψjTb} residue matrix of the jth complex mode (see section 5.6) |
| [Tj] | ={cφj}{φjTb} residue matrix of the jth 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 [Ms2+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) |
| λj | complex pole (see section 5.5) |
| [φ]N × NM | real or normal modes of the undamped system(NM ≤ N) |
| [\ Ω2 \ ] | 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) |
