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 = 1 2 ∑ i=1 L f i n A i 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGTbWaaSbaaSqaaiaad6gaaeqaaO Gaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmaaaadaaeWbqaaiaadAga daqhaaWcbaGaamyAaaqaaiaad6gaaaGccaWGbbWaa0baaSqaaiaadM gaaeaacaaIYaaaaaqaaiaadMgacqGH9aqpcaaIXaaabaGaamitaaqd cqGHris5aaaa@41B9@
Where,
n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaaaa@36E9@
Moment order.
f i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGMbWaaSbaaSqaaiaadMgaaeqaaa aa@33BD@
Sine-tone frequency values defined on the HARMO continuation line on FATLOAD.
L MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C5@
Number of frequencies of sine tones.
A i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGbbWaaSbaaSqaaiaadMgaaeqaaa aa@3398@
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.