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#74020 - 10/25/19 02:55 AM Sign of phase angle in harmonic analysis
Lido (TCS) Offline
Member

Registered: 03/23/05
Posts: 38
Loc: livorno - italy
I see in the user's manual that harmonic forces/displacements have the formula F(t) = A * cos(wt + phi) or F(t) = A * cos(wt - phi).

Tested by results, the correct formula (used by software) is with minus sign.

F(t) = A * cos(wt - phi)

I don't know why this choice, and I don't want to discuss (If someone knows... please explain me)

But important... please , I think it can be considered by Intergraph to change pages 709 and 719 of the user's manual, where the formula is with plus sign referring to phase angle. It can lead the user to error in applying correct phasing.
All formulas with minus is better...


Edited by Lido (TCS) (10/25/19 03:03 AM)
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TCS Eng.

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#74026 - 10/25/19 12:59 PM Re: Sign of phase angle in harmonic analysis [Re: Lido (TCS)]
Richard Ay Offline
Member

Registered: 12/13/99
Posts: 5995
Loc: Houston, Texas, USA
Damping 'delays' response. When I put a displacement at the end of a cantilever, the maximum load near the anchor occurs after the start of the load. This supports the equation cos(wt+phi), not cos(wt-phi).

Could you provide more information to support your conclusion above?
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Richard Ay
Hexagon PPM (CAS)
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#74279 - 12/10/19 10:28 AM Re: Sign of phase angle in harmonic analysis [Re: Richard Ay]
Lido (TCS) Offline
Member

Registered: 03/23/05
Posts: 38
Loc: livorno - italy
I have not understand your reply...i'm speaking about phase sign in the formula by Caesar manual, not damping...

the test for looking at the sign of phase for a rotating displacement is quite simple.

1) created a simple system, starting at node 10

2) applied the following harmonic displacements at node 10:

frequency 50Hz
displacement 0.5", dir. Y, phase 0
displacement 0.5", dir. Z, phase +90

3) run harmonic analysis with the following displacements results at node 10


CASE 2 (OCC) 50.0000 Hz 0.00
CASE 3 (OCC) 50.0000 Hz 80.00
CASE 4 (OCC) 50.0000 Hz 180.00
CASE 5 (OCC) 50.0000 Hz 280.24
CASE 6 (OCC) 50.0000 Hz 340.00

Node Load DX in. DY in. DZ in. RX deg. RY deg. RZ deg.


10 2(OCC) 0.0000 0.4982 -0.0299 -0.0000 0.0000 0.0000
10 3(OCC) -0.0000 0.1160 0.4854 -0.0000 -0.0000 0.0000
10 4(OCC) -0.0000 -0.4982 0.0299 0.0000 -0.0000 -0.0000
10 5(OCC) 0.0000 0.0591 -0.4956 0.0000 0.0000 -0.0000
10 6(OCC) 0.0000 0.4579 -0.1985 -0.0000 0.0000 0.0000

my interpretation is that at 0 (omega t) the combined displacement is in direction +Y, at 90 is in direction +Z, at 180 in direction -Y, at 270 in direction -Z (360 in direction +Y again)
therefore I've simulated at counterclock wise rotation around X axys (CCW looking to -X).

therefore the displacement in Z direction must have the form A*cos(wt - phi).
the correct sign in the formula for the phasing angle is MINUS.
When the user insert a +90 phase angle in the input dialog of harmonic analysis of CII, the wave applied by the software is A*cos(wt - 90) ... not A*cos(wt + 90) as, I think, all users can imagine (because it is the normal formula)


Attachments
phase.png




Edited by Lido (TCS) (12/10/19 10:54 AM)
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TCS Eng.

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