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.

Damage is estimated for each time duration T, which is spent sweeping across a particular frequency. For each T, the spectral moments can be calculated as:(1)
m n = ∑ k = 1 N f k n G k δ f + 1 2 f A 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGTbWaaSbaaSqaaiaad6gaaeqaaO Gaeyypa0ZaaabCaeaacaWGMbWaa0baaSqaaiaadUgaaeaacaWGUbaa aOGaam4ramaaBaaaleaacaWGRbaabeaakiabes7aKjaadAgaaSqaai aadUgacqGH9aqpcaaIXaaabaGaamOtaaqdcqGHris5aOGaey4kaSYa aSaaaeaacaaIXaaabaGaaGOmaaaacaWGMbGaamyqamaaCaaaleqaba GaaGOmaaaaaaa@4733@
Where,
f k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGMbWaaSbaaSqaaiaadUgaaeqaaa aa@33BF@
Frequency values for random vibration.
G k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGhbWaaSbaaSqaaiaadUgaaeqaaa aa@33A0@
Stress PSD response value at frequency f k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGMbWaaSbaaSqaaiaadUgaaeqaaa aa@33BF@ .
N MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaaaa@36C7@
Number of frequencies in stress PSD.
A MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGa caGaaeqabaqaaeaadaaakeaacaWGbbaaaa@327E@
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).

As an example, consider SUBCASE 10 is a random analysis subcase, and SUBCASE 20 is a frequency response analysis subcase. The following setup showcases how sine-sweep on random fatigue is activated:
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.