| [ ],{ } |
matrix, vector |
| - |
conjugate |
| [b] |
input shape matrix for model with N DOFs and
NA inputs (see section 2.1). { jTb},{ jTb} modal input matrix of the jth normal / complex mode |
| [c] |
sensor output shape matrix, model with N DOFs and NS
outputs (see section 2.1). {cj},{cj} modal output matrix of the jth normal / complex mode |
| [E]NS × NA |
correction matrix for high frequency modes (see section 2.6) |
| [F]NS × NA |
correction matrix for low frequency modes (see section 2.6) |
| 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 2.2) |
| {q}N × 1 |
degree of freedom of a finite element model |
| s |
Laplace variable (s=i for the Fourier transform) |
| [Rj] |
={cj}{jTb} residue matrix
of the jth complex mode (see section 2.6) |
| [Tj] |
={cj}{jTb} residue matrix
of the jth normal mode (used for proportionally
damped models) (see section 2.6) |
| {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]) |
[ (s)] |
dynamic compliance matrix (force to displacement transfer function) |
| p, |
design parameters of a FE model (see section 6.3.1) |
| D M,D C,D K |
additive modifications of the mass, damping and
stiffness matrices (see section 6.3.1) |
| [G] |
non-diagonal modal damping matrix (see section 2.3) |
 j |
complex pole (see section 2.5) |
| []N × NM |
real or normal modes of the undamped system(NM £ N) |
| [\ W2 \ ] |
modal stiffness (diagonal matrix of modal frequencies squared) matrices (see section 2.2) |
[ ]N × NM |
NM complex modes of a first order symmetric structural
model (see section 2.5) |
| []N × NM |
NM complex modes of damped structural model (see section 2.5) |
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