# Notation

SymbolDefinition
$t$Time
$T$Period
$\mathbf{M}$Mass matrix
$\mathbf{Μ}_{e}$Element mass matrix
$\mathbf{K}$Stiffness matrix
$\mathbf{Κ}_{e}$Element stiffness matrix
$\mathbf{K}_{g}$Geometric stiffness
$\mathbf{K}_{g,e}$Element geometric stiffness
$\mathbf{C}$Damping matrix
$\mathbf{u}$Displacement vector
$\mathbf{a}$Acceleration vector
$\phi$Mode shape
$\lambda$Eigenvalue or buckling load factor
$\mathbf{\Lambda}$Diagonal eigenvalue matrix
$\widetilde{m}$Modal mass
$\widetilde{k}$Modal stiffness
${\widetilde{k}}_{g}$Modal geometric stiffness
$f,\mathbf{f}$Force or force vector
$f$Frequency
$\omega$Angular frequency
$\Gamma$Participation factor
$\mu$Effective mass
$a$Dynamic amplification
$\alpha,\beta$Rayleigh damping coefficients
$\xi, \zeta$Damping ratio

In general:

• scalar quantities are denoted by italics e.g. mass $m$ or mass $M$

• vector quantities are denoted by lower case upright characters e.g. displacements $\mathbf{u}$

• matrix quantities are denoted by upper case, upright characters e.g. stiffness $\mathbf{K}$