# Multiple Sine Tones Fatigue Analysis

When there is no underlying random vibration but there are a sufficient number of simultaneously occurring sine tones, it can be considered random vibration.

## Damage Calculation

Damage calculation due to vibration from multiple sine tones is a similar procedure to regular random vibration fatigue (Refer to Random Response Fatigue Analysis).The difference caused by absence of contribution from stress PSD to the spectral moments calculation is considered, and only the contribution from the multiple simultaneous sine tones exists.

The moments are calculated as:(1)
${m}_{n}=\frac{1}{2}\sum _{i=1}^{L}{f}_{i}^{n}{A}_{i}^{2}$
Where,
$n$
Moment order.
${f}_{i}$
Sine-tone frequency values defined on the HARMO continuation line on FATLOAD.
$L$
Number of frequencies of sine tones.
${A}_{i}$
Stress amplitude due to sine tones at the i-th frequency defined on the HARMO continuation line on FATLOAD.

Subsequent calculation of number of cycles is similar to random fatigue. Refer to Random Response Fatigue Analysis.

## Input

A frequency response analysis is the underlying subcase for vibration fatigue due to multiple sine tones. In a particular FATEVNT entry, a FATLOAD entry referencing frequency response analysis should be specified.

The FATLOAD data referencing the frequency response analysis should also list frequencies (in Hz) and their amplitude factors in the HARMO continuation line.

As an example, consider SUBCASE 20 is a frequency response analysis subcase. The following setup showcases how fatigue from multiple sine tones is activated:
FATLOAD,200,,20
+,HARMO,1.0,0.1,15.0,1.0,20.0,1.1
FATEVNT,1000,200

Where the three sine tone frequency values are 1.0, 15.0, and 20.0; their corresponding amplitude factors are 0.1, 1.0, and 1.1, respectively.

## Output

General fatigue output for Damage and Life are supported. The damage output is multiplied by exposed time T defined on the FATSEQ Bulk Data Entry and reported.