# *AMPLITUDE

 Define an amplitude curve. This option allows arbitrary time (or frequency in an Abaqus/Standard analysis) variations of load, displacement, and other prescribed variable magnitudes to be given throughout a step.
 Related Topics In Other Guides Amplitude Curves

ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/CAE

TypeModel or history data

LevelModelStep

Abaqus/CAEAmplitude toolset; bubble loading is not supported. Similar functionality is available in the Interaction module.

## Required parameters

NAME

Set this parameter equal to a label that will be used to refer to the amplitude curve.

## Optional parameters

DEFINITION

Set DEFINITION=TABULAR (default) to give the amplitude-time (or amplitude-frequency) definition in tabular form.

Set DEFINITION=EQUALLY SPACED, PERIODIC, MODULATED, DECAY, SMOOTH STEP, SOLUTION DEPENDENT, or BUBBLE to define the amplitude according to the definitions given in Amplitude Curves.

Set DEFINITION=USER to define the amplitude via user subroutines UAMP and VUAMP.

Set DEFINITION=ACTUATOR to define the amplitude via co-simulation with a logical modeling program.

INPUT

Set this parameter equal to the name of the alternate input file containing the data lines for this option. See Input Syntax Rules for the syntax of such file names. If this parameter is omitted, it is assumed that the data follow the keyword line.

This parameter cannot be used if DEFINITION=USER or DEFINITION=ACTUATOR.

SCALEX

Set this parameter equal to the value by which the time values are to be scaled. The default is 1.

This parameter cannot be used if DEFINITION=SOLUTION DEPENDENT, BUBBLE, USER, or ACTUATOR.

SCALEY

Set this parameter equal to the value by which the amplitude values are to be scaled. The default is 1.

This parameter cannot be used if DEFINITION=SOLUTION DEPENDENT, BUBBLE, or USER.

SHIFTX

Set this parameter equal to the value by which the time values are to be shifted. The default is 0.

This parameter cannot be used if DEFINITION=SOLUTION DEPENDENT, BUBBLE, USER, or ACTUATOR.

SHIFTY

Set this parameter equal to the value by which the amplitude values are to be shifted. The default is 0.

This parameter cannot be used if DEFINITION=SOLUTION DEPENDENT, BUBBLE, or USER.

TIME

Set TIME=STEP TIME (default) for step time. If the step in which the amplitude is referenced is in the frequency domain, STEP TIME corresponds to frequency.

Set TIME=TOTAL TIME for total time accumulated over all non-perturbation analysis steps.

See Conventions for a discussion of these time measures.

VALUE

Set VALUE=RELATIVE (default) for relative magnitude definition.

Set VALUE=ABSOLUTE for direct input of absolute magnitudes. In this case the data line values in the load option are ignored. Because the values given in the field definition are ignored, the absolute amplitude value will be used to define both the temperature and the gradient. For this reason, VALUE=ABSOLUTE should not be used when temperatures or predefined field variables are specified for nodes connected to beam and shell elements whose section definition includes TEMPERATURE=GRADIENTS (default).

## Required parameter for DEFINITION=EQUALLY SPACED

FIXED INTERVAL

Set this parameter equal to the fixed time (or frequency) interval at which the amplitude data will be given.

## Optional parameter for DEFINITION=EQUALLY SPACED

BEGIN

Set this parameter equal to the time (or lowest frequency) at which the first amplitude is given. The default is BEGIN=0.0.

## Optional parameter for DEFINITION=TABULAR or DEFINITION=EQUALLY SPACED

SMOOTH

Set this parameter equal to the fraction of the time interval before and after each time point during which the piecewise linear time variation is to be replaced by a smooth quadratic time variation in any case when time derivatives of the amplitude definition are required. The defaults are SMOOTH=0.25 in Abaqus/Standard and SMOOTH=0.0 in Abaqus/Explicit. The allowable range is 0.0 $<$SMOOTH$≤$ 0.5. A value of 0.05 is suggested for amplitude definitions that contain large time intervals to avoid severe deviation from the specified definition. This parameter is applicable only when time derivatives are needed (for displacement or velocity boundary conditions in a direct integration dynamic analysis) and is ignored for all other uses of this option.

## Optional parameters for DEFINITION=USER

PROPERTIES

Set this parameter equal to the number of properties being entered. The properties are available for use in user subroutines UAMP and VUAMP. They can be defined on the data lines or directly within the user subroutine. The default is PROPERTIES=0.

VARIABLES

Set this parameter equal to the number of solution-dependent state variables that must be stored with this amplitude definition. Its value must be greater than 0. The default is VARIABLES=1.

## Data lines for DEFINITION=TABULAR or DEFINITION=SMOOTH STEP with four data points (eight entries) per line

First line
1. Time or frequency.

2. Amplitude value (relative or absolute) at the first point.

3. Time or frequency.

4. Amplitude value (relative or absolute) at the second point.

5. Etc., up to four pairs per line.

Repeat this data line as often as necessary. Each line (except the last one) must have exactly four time/magnitude or frequency/magnitude data pairs.

## Data lines for DEFINITION=TABULAR or DEFINITION=SMOOTH STEP with one data pair (two entries) per line

First line
1. Time or frequency.

2. Amplitude value (relative or absolute) at the first point.

Repeat this data line as often as necessary. Each line must have exactly one time/magnitude or frequency/magnitude data pair.

## Data lines for DEFINITION=EQUALLY SPACED with eight values per line

First line
1. Amplitude value at the time or frequency given on the BEGIN parameter.

2. Amplitude value at the next point.

3. Etc., up to eight values per line.

Repeat this data line as often as necessary. Each line (except the last one) must have exactly eight amplitude values.

## Data lines for DEFINITION=EQUALLY SPACED with one value per line

First line
1. Amplitude value at the time or frequency given on the BEGIN parameter.

Repeat this data line as often as necessary. Each line must have exactly one amplitude value.

## Data lines to define periodic data (DEFINITION=PERIODIC)

First line
1. N, the number of terms in the Fourier series.

2. $ω$, the circular frequency, in radians per time.

3. $t0$, the starting time.

4. $A0$, the constant term in the Fourier series.

Second line
1. $A1$, the first coefficient of the cosine terms.

2. $B1$, the first coefficient of the sine terms.

3. $A2$, the second coefficient of the cosine terms.

4. $B2$, the second coefficient of the sine terms.

5. Etc., up to eight values per line.

Repeat this data line as often as necessary. Each line (except the last one) must have exactly eight entries, to a total of 2N entries.

## Data line to define modulated data (DEFINITION=MODULATED)

First (and only) line
1. $A0$.

2. A.

3. $t0$.

4. $ω1$.

5. $ω2$.

## Data line to define exponential decay (DEFINITION=DECAY)

First (and only) line
1. $A0$, the constant term.

2. A, the coefficient of the exponential function.

3. $t0$, the start time of the exponential function.

4. $td$, the decay time of the exponential function.

## Data line to define a solution-dependent amplitude (DEFINITION=SOLUTION DEPENDENT)

First (and only) line
1. Initial amplitude value (default = 1.0).

2. Minimum amplitude value (default = 0.1).

3. Maximum amplitude value (default = 1000.).

First line
1. Charge material constant, K.

2. Charge material constant, k.

3. Charge material constant, A.

4. Charge material constant, B.

5. Adiabatic charge constant, $Kc$.

6. Ratio of specific heats for gas, $γ$.

7. Density of charge material, $ρc$.

8. Mass of charge material, $mc$.

9. Depth magnitude of charge material, $dI$.

Second line
1. Fluid mass density, $ρf$.

2. Sound speed in fluid, $cf$.

3. X-direction cosine of fluid surface normal.

4. Y-direction cosine of fluid surface normal.

5. Z-direction cosine of fluid surface normal.

Third line
1. Acceleration due to gravity, g.

2. Atmospheric pressure, $pa⁢t⁢m$.

3. Wave effect parameter, $η$. Set to 1.0 for wave effects in the fluid and gas; set to 0.0 to neglect these effects. The default is 1.0.

4. Flow drag coefficient, $CD$. The default is 0.0.

5. Flow drag exponent, $ED$ ($ED≥0$). The default is 2.0.

Fourth line
1. Time duration, $Tfinal$.

2. Maximum number of time steps for the bubble simulation, $Nsteps$. The bubble amplitude simulation ceases when the number of steps reaches $Nsteps$ or the time duration, $Tfinal$, is reached. The default is 1500.

3. Relative step size control parameter, $Ωrel$. The default is 1 × 10−11.

4. Absolute step size control parameter, $Xabs$. The default is 1 × 10−11.

5. Step size control exponent, $β$. The step size, $Δ⁢t$, is decreased or increased according to the error estimate: $(Ωrel⁢|x|+Xabs)β≤Δ⁢t⁢|d⁢xd⁢t|β$. The default is 0.2.

## Data lines to define user amplitude properties when PROPERTIES is specified with DEFINITION=USER

First line
1. Enter the amplitude properties, eight per line.

Repeat this data line as often as necessary to define all amplitude properties.