# 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.

## 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:

- ${f}_{k}$
- 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`.

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

D = D1 during T1 + D2 during T2 + D3 during T3, 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.