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1.4  Typesetting conventions and scientific notations

The following typesetting conventions are used in this manual


courierblue monospace font : Matlab function names, variables
feplotlight blue monospace font: SDT function names
commandpink : strings and SDT Commands
varitalic pink: part of command strings that have to be replaced by their value
% comment green: comments in script examples
ItalicsMATLAB Toolbox names, mathematical notations, and new terms when they are defined
Boldkey names, menu names and items
Small printcomments
(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


CMSComponent Mode Synthesis (see section 6.3.3)
COMACCoordinate Modal Assurance Criterion (see ii_mac)
DOF,DOFsdegree(s) of freedom (see section 7.5)
FEfinite element
MACModal Assurance Criterion (see ii_mac)
MMIFMultivariate Mode Indicator Function (see ii_mmif)
POCPseudo-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 × NAcorrection matrix for high frequency modes (see section 5.6)
[F]NS × NAcorrection matrix for low frequency modes (see section 5.6)
M,C,Kmass, damping and stiffness matrices
N,NMnumbers of degrees of freedom, modes
NS,NAnumbers of sensors, actuators
{p}NM × 1principal coordinate (degree of freedom of a normal mode model) (see section 5.2)
{q}N × 1degree of freedom of a finite element model
sLaplace 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 × 1inputs (coefficients describing the time/frequency content of applied forces)
{y(s)}NS × 1outputs (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)
pdesign parameters of a FE model (see section 6.4.2)
Δ MCKadditive modifications of the mass, damping and stiffness matrices (see section 6.4.2)
[Γ]non-diagonal modal damping matrix (see section 5.3)
λjcomplex pole (see section 5.5)
[φ]N × NMreal or normal modes of the undamped system(NMN)
[\ Ω2 \ ]modal stiffness (diagonal matrix of modal frequencies squared) matrices (see section 5.2)
[θ]N × NMNM complex modes of a first order symmetric structural model (see section 5.5)
[ψ]N × NMNM complex modes of damped structural model (see section 5.5)

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