# Sine-Sweep on Random Fatigue Analysis

Sine-sweep on random vibration is a superposition of swept sinusoidal vibration on random vibration. It is considered as a series of single sine tones on top of random vibration.

This is useful when the sine-sweep test rig is on a moving vehicle. An example application is to determine fatigue damage at resonance frequencies across a sweep frequency range when the structure is also undergoing a background random vibration. For instance, calculation of fatigue damage at possible resonance frequencies of sinusoidally vibrating parts inside a car driving down a bumpy road.

## Damage Calculation

Damage calculation due to sine-sweep on random vibration is a similar procedure to regular random vibration fatigue (Refer to Random Response Fatigue Analysis), with some noted differences.

The vibration is considered as a series of single sine tones on top of random
vibration. During sine-sweep, consider the time duration `T`, as
the time that is spent moving from one frequency to another. Numerically,
`T` is determined by sweep rate (`SR`) on a
FATLOAD Bulk Data Entry and DF (or
NF) on the `SWEEP` continuation line on a
FATPARM Bulk Data Entry.

`T`, which is spent sweeping across a particular frequency. For each

`T`, the spectral moments can be calculated as:

- $n$
- Moment order.
- ${f}_{k}$
- Frequency values for random vibration.
- ${G}_{k}$
- Stress PSD response value at frequency ${f}_{k}$ .
- $N$
- Number of frequencies in stress PSD.
- $A$
- Stress amplitude due to the single sine tone assumed during the time
duration
`T`.

Fatigue damage is calculated based on the calculated moments, similar to Random Response Fatigue Analysis.

The total damage per sweep due to the swept sine tone on random vibration is the summation of damages during each time duration.

$D={D}_{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}(\text{during}\text{\hspace{0.17em}}t={t}_{1})+{D}_{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}(\text{during}\text{\hspace{0.17em}}t={t}_{2})+{D}_{3}\text{\hspace{0.17em}}\text{\hspace{0.17em}}(\text{during}\text{\hspace{0.17em}}t-{t}_{3})$ and so on across the entire sweep.

## Input

A random response analysis and a frequency response analysis are underlying subcases for sine-sweep on random fatigue. In a particular FATEVNT entry, a FATLOAD referencing the random response analysis and another FATLOAD referencing a frequency response analysis should be specified to activate sine-sweep on random fatigue.

The FATLOAD data referencing the frequency response analysis
should also contain the `SWEEP` continuation line along with the
sweep rate (`SR`) and the sweep rate unit
(`SRUNIT`).

```
FATLOAD,100,,10
FATLOAD,200,,20
+,SWEEP,1.5,OCTPM
FATEVNT,1000,100,200
```

Where the sweep rate is 1.5 and the sweep rate unit is set to octaves per minute (OCTPM).

## Output

General fatigue output for Damage and Life are supported. The damage output is
multiplied by the number of sweeps `N` defined on the
FATSEQ Bulk Data Entry and reported.