Post on 18-Jan-2018
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System Defintion: R7, R8, R9
• System R8 = Cantilever beam = slide 2• System R9 = Full Machine = slide 3• System R7 = All except machine mass/spring – see
slide 4
R8-Problem Studied. Absorber on fixed mount
L=29” a=21”
1”
Concentrated mass 18.0 kg=39.7 lbm
12”Bar propertiesRho=0.282 lbm/inch^3E=2.9E7 psi(Bar mass =62.5kg)
FappliedSomewhereAlong beam
R9-Problem Studied – Composite system including machine represented by M1, K1
M1
L=29” a=21”
1”
Concentrated mass 18.0 kg=39.7 lbm
12”Bar propertiesRho=0.282 lbm/inch^3E=2.9E7 psi(Bar mass =62.5kg)
FappliedK1
R7-Problem Studied
L=29” a=21”
1”
Concentrated mass 18.0 kg=39.7 lbm
12”Bar propertiesRho=0.282 lbm/inch^3E=2.9E7 psi(Bar mass =62.5kg)
Fapplied Massless rolling support allows displacement in lateral direction, but enforces slope of absorber perpendicular to the base as signifified by red right-angle symbol
R7-Driving Point Transfer Fn at Base. Note vertical axis is 100*Hv =100*V/F in metric unitsSlope to left suggests M=66kg. Total mass is 62.5kg
M =1/[w*Hv]= 1/[2*pi*10.5*0.00023)=66 kg
M =1/[w*Hv]= 1/[2*pi*1.4*0.001729]=66 kg
R7 FIT 5-40hz => M= 60.3kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:5.0-40.0hz. Best fit:M=60.3, K=2.12E+6 .
R7 10-38hz => M= 57.9kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:10.0-38.0hz. Best fit:M=57.9, K=2.04E+6 .
R7 15-36hz => M= 55.3kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:15.0-35.9hz. Best fit:M=55.3, K=1.94E+6 .
R7 20-34hz => M= 52.3kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:20.0-33.9hz. Best fit:M=52.3, K=1.84E+6 .
R7 25-32hz => M= 52.3kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:25.0-31.9hz. Best fit:M=52.3, K=1.84E+6 .
R7 28-30.7hz => M= 52.3kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:28.0-30.7hz. Best fit:M=52.3, K=1.84E+6 .
R7 29.5-30.1hz => M= 52.3kg
Comparison of FE results vs SDOF best fit
0.0000001
0.000001
0.00001
0.0001
0.001
5 10 15 20 25 30 35 40
Freq (hz)
|H|=
|Vel
ocity
/For
ce|
H=V/FSDOF Fit of HWeightWindow
Interval:29.5-30.1hz. Best fit:M=52.3, K=1.84E+6 .
R9 Full System
R9 - Bode 5-40hz
R7 Bode 5-40hz
R8 Bode 1-300hz
R8-Impact/Monitor 4.2” from base (loc = 1)
R8-Impact/Monitor 12.6” from base (loc = 5)
R8-Impact/Monitor 21” from base = at loc of concentrated mass. (loc=9)
R8-Impact monitor 29” from base = at end of absorber (loc=11)