Amplitudes

Amplitudes represent scale factors that allow time (or frequency) variations of load, displacement, and other prescribed variables throughout a step. You can assign arbitrary schemes to vary the amplitude throughout a step.

Default amplitudes are available for some loads and other features. Amplitudes might be ramp functions (vary linearly over the duration of a step) or step functions (maintain a constant magnitude over the duration of a step). The amplitude type depends on the applied feature. For example, a default amplitude for a displacement is a ramp function in which the amplitude varies linearly from zero to one throughout the step.

Many problems require a more elaborate amplitude definition. For example, a simulation combining both thermal and mechanical loads might require two amplitude curves to account for the differences in thermal and mechanical variation within the same step.

Amplitudes are stand-alone simulation features. Load feature definitions reference pre-existing amplitudes; therefore, you can reuse the same amplitude for multiple features.

Amplitudes can use two measures of time: step time and total time. Both types track time during general analysis steps; perturbation steps are ignored. Step time is measured from the beginning of each step. Amplitudes defined using step time end at the completion of the step; amplitude time values that exceed the time of the step are ignored. Total time starts at zero and accumulates over all general analysis steps. Amplitudes using total time vary according to the defined values through all general analysis steps.

The 3DEXPERIENCE platform supports tabular, periodic, and smooth step amplitudes.

This page discusses:

Tabular Amplitudes
Periodic Amplitudes
Smooth Step Amplitudes

Tabular Amplitudes

A tabular amplitude curve is defined by a table of values at convenient points on a time scale.

In addition to time, frequency, and magnitude information, you can specify a smoothing factor in which the linear time variation is replaced by a smooth quadratic time variation. The scale factor you specify is the factor that is then multiplied by the value of the feature (for example, the magnitude of a pressure load).

A tabular amplitude curve is interpolated linearly between the specified values.

Periodic Amplitudes

A periodic amplitude curve is defined by a Fourier series and repeats over a specified period of time.

You can specify the circular frequency, starting time, initial amplitude, and Fourier constants. For periodic amplitudes, a repeating amplitude curve is established for a specific time period to allow the load magnitude to vary throughout the step.

When the step time equals or exceeds the starting time, a periodic amplitude is defined according to the following formula:

a = A_{0} + \sum_{n = 1}^{N} [A_{n} \cos n ω (t - t_{0}) + B_{n} \sin n ω (t - t_{0})],

where $A_{0}$ is the initial amplitude, $n$ is the table row (incremented from 1 to $N$ ), $ω$ is the circular frequency, $t$ is the step time, and $t_{0}$ is the starting time for the series.

Smooth Step Amplitudes

A tabular amplitude curve is defined by a table of values at convenient points on a time scale.

A smooth amplitude curve varies smoothly between values defined at convenient points on a time scale.

You can specify time, frequency, and magnitude information to create the curve. The scale factor you specify is the factor that is then multiplied by the value of the feature (for example, the magnitude of a pressure load).

A smooth amplitude curve is interpolated between the specified values according to the following formula:

a = A_{i} + (A_{i + 1} - A_{i}) ξ^{3} (10 - 15 ξ + 6 ξ^{2}),

where $(t_{i}, A_{i})$ represents one data point, $(t_{i + 1}, A_{i + 1})$ represents the subsequent data point, and $ξ = (t - t_{i}) / (t_{i + 1} - t_{i})$ .

The curve is created such that its first and second derivatives are zero at each specified time point.