*PIEZOELECTRIC DAMPING

Required and mutually exclusive parameters

BETA

Use this parameter to indicate that four $β_{i} (i = 1, 4)$ factors will be read from the data line to create Rayleigh stiffness proportional damping for the displacement, piezoelectric coupling, and dielectric parts of the damping operator in the following procedures:

COMPLEX FREQUENCY
MATRIX GENERATE
SUBSTRUCTURE GENERATE
STEADY STATE DYNAMICS, DIRECT
STEADY STATE DYNAMICS, SUBSPACE PROJECTION
STEADY STATE DYNAMICS that allows nondiagonal damping

STRUCTURAL

Use this parameter to indicate that four $s_{i} (i = 1, 4)$ factors will be read from the data line to create stiffness proportional structural damping for the displacement, piezoelectric coupling, and dielectric parts of the damping operator in the following procedures:

COMPLEX FREQUENCY
MATRIX GENERATE
SUBSTRUCTURE GENERATE
STEADY STATE DYNAMICS, DIRECT
STEADY STATE DYNAMICS, SUBSPACE PROJECTION
STEADY STATE DYNAMICS that allows nondiagonal damping

Data lines to define temperature-dependent stiffness proportional Rayleigh damping

First line

$β_{1}$ . Damping coefficient for the displacement part of the damping operator. (Units of T.)
$β_{2}$ . Damping coefficient for the dielectric part of the damping operator. (Units of T.)
$β_{3}$ . Damping coefficient for the piezoelectric coupling (displacement/dielectric) part of the damping operator. (Units of T.)
$β_{4}$ . Damping coefficient for the piezoelectric coupling (dielectric/displacement) part of the damping operator. (Units of T.)
Temperature.

Repeat this data line as often as necessary.

Data lines to define temperature-dependent stiffness proportional structural damping

First line

$s_{1}$ . Damping coefficient for the displacement part of the damping operator.
$s_{2}$ . Damping coefficient for the dielectric part of the damping operator.
$s_{3}$ . Damping coefficient for the piezoelectric coupling (displacement/dielectric) part of the damping operator.
$s_{4}$ . Damping coefficient for the piezoelectric coupling (dielectric/displacement) part of the damping operator.
Temperature.

Repeat this data line as often as necessary.