Sign of phase angle in harmonic analysis

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...

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?

thank you Richard , but I have not understand your reply...i'm speaking about phase sign in the formula by Caesar manual, not damping.

the test I made 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:

0.5", dir. Y, phase 0
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 (selected near 90)
CASE 4 (OCC) 50.0000 Hz 180.00
CASE 5 (OCC) 50.0000 Hz 280.24 (selected near 270)
CASE 6 (OCC) 50.0000 Hz 340.00 (selected near 360)

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

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 (time, angle) the 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).

the displacement in Z direction applied to the system have the form A*cos(wt - phi).
therefore the sign in the formula that should be presented in the CaesarII manual to the user is MINUS phasing angle.

Lido,

System damping delays response - the maximum response at a node occurs after the maximum applied force or applied displacement. This was Rich's focus in his response to you - relating input to response.

Your topic is CAESAR II dynamic input (not response) where we are interested in establishing a relationship between two or more harmonic force vectors. This phase angle establishes that relationship.

I do not know which version of CAESAR II you are using - pages 709 & 719 of the current User Guide have nothing to do with phase angles. Looking at page 722 of the User Guide (C2 2019 / Version 11), I see A*cos(wt+phi). Phase angle also appears on pages 725 & 728. These equations show A*cos(wt-phi).

I will agree that there is no reason for there to be both a (wt+phi) and a (wt-phi). The first reference (+phi, page 722) is used in the definition of the applied harmonic frequencies. But here, phi is not used - just the frequencies (w) are collected. The other two occurrences are correct (-phi, pages 725 & 728).

I will ask that the User Guide be updated to remove that (+phi) from page 722.

thank you Dave, you have centered the issue.

user should consider -phi (negative sign in the formula) applying phase angle in harmonic analysis