Hi Dave,
I have to perform a Harmonic analysis of a piping system connected to a reciprocating Pump. I am trying to simulate the forced mechanical response of the system by imposing on it all the necessary shaking forces.
As mentioned in CAESAR user guide, I have calculated Harmonic shaking force using formula F=0.5*DP*A (where “DP” is the Peak-to-Peak pressure pulsation at that point and “A” is the area of the pipe section) and I am applying that harmonic shaking forces along the pipe axis (and so for each bend there are two separate loads applied with different directions and same value of amplitude and phase) at every geometric discontinuity of the system such as elbows, tees & capped ends (As described in API 688).
I have calculated phase angle (as mentioned in CAESAR user guide) between shaking forces at every bend using formula Phase angle= 360*f*(L/c), where “L” is the distance between the starting point (First elbow) and the respective concerned point, “c” is the speed of the sound of the fluid inside pipes and “f” is the frequency of the pressure pulsation.
Please confirm whether my understanding is correct or not in order to perform harmonic analysis of a piping system connected to a reciprocating pump.
I would like to let you know why I have a confusion in calculating shaking forces and phase angle with above formulas:
If you refer Caesar II manual help file there are another formulas for calculating shaking force and phase angle. Those are populated in Harmonic force and harmonic displacement tabs when we use F1 for respective fields. Those are as below:
The form of the harmonic forcing function is:
F(t) = A*cosine(wt-f)
where "F(t)" is the force as a function of time. "A" is the maximum amplitude of the dynamic force. "w" is the frequency of the excitation (in radians per second), and "f" is the phase angle (in radians).
f(degrees) = 180tw/p
where t is given in seconds and w is given in radians per second.
The phase angle is usually entered as either zero or 90. Use the phase specification when defining eccentric loads on rotating equipment.
Pl’s clarify.
If anyone has opinion on this, pl's let me know.

Our documentation is inconsistent in terms used. While at one place "f" is frequency, elsewhere it is phase angle. But within any one topic, the terms are used consistently.
A few points on your post:
1 - "I am applying that harmonic shaking forces along the pipe axis (and so for each bend there are two separate loads applied with different directions and same value of amplitude and phase) at every geometric discontinuity of the system" -- I don't think you should have two loads on each bend. I would place a single sinusoidal load on each run between discontinuities. The magnitude of these loads would be dependent on the phase shift between the two discontinuities.
2 - Yes, I agree that the phase shift or phase angle, in degrees, would be set by 360*(frequency of the pulsation)*(L/c)
3 - As you note, our documentation later presents the equation F(t)=A*cosine(wt-f). Here A is amplitude - this is identical to the 0.5*DP you referenced earlier. And here, "f" is now phase angle and this equation is using radians. You then show the equation to convert this f to degrees.
4 - you state that phase angle is usually entered as either 0 or 90. This is not correct when we are calculating the delta P between discontinuities.

So each run between discontinuities will have a harmonic force. If you wish to excite several runs in the same analysis, you will have to also consider the phase shift between the different loads using the same phase shift equation - in degrees.

Since your dynamic model is probably off due to uncertainties in mass and stiffness, we recommend sweeping through a range of excitation frequencies centered around your (true) excitation frequency.

I would focus my attention on loading the runs that produce the largest delta P (based on phase shift) and the runs that may produce the largest response. You can learn about the latter by simply extracting natural frequencies and mode shapes that are near your forcing frequencies. Modes where runs move axially will probably be excited.