Werner Exinger wrote:
Yes, seems to be not that easy. Alan suggested to solve for F(), too and use the derivative of F in the solve block. But I am not quite sure, how.
If F(t,s) were not a function of s, then it would be straightforward (if a little tedious to develop!). Split F into the sum of F1 and F2 by expanding the cos(phio(t-tau)) term; differentate each of these terms wrt time to create functions for dF1/dt and dF2/dt which could be solved simultaneously with the dtheta/dt etc.
Unfortunately, F(t,s) is a function of s, so this doesn't quite work. I thought one possibility might be to use an average of F over s, but then noticed something strange - in the definition of pp the integrals over s go from zero to ul. However, for values of s less than mu^2/4g phio is imaginary! This doesn't feel right to me.
I guess I would need to look at the derivation of these equations in detail to have a chance of resolving this.
If it helps, the paper where I have extracted the formulae is attached if you have the time/interest to examine. Equation 21 is the formula for the Dynamic Pressure pp(t,y). My formulation is slightly different as the paper assumes a flat gate shape and adjusts for curvature using an area coefficient cg in deriving the moment M(t). I have integrated the pressure over the curved surface to obtain the vertical force Fv(t) and then the moment M(t). This slight difference does not affect the the math approach. The integrals in s use an upper limit of infinity, whereas I have used ul = 100 - sensitivty seemed to indicate this value of ul was adequate.
I would be interested in your opinion if I have handled the evaluation of the last 2 integrals in equation 21 correctly. The last integral over dtau has the phase function cos(phio(s)), which is problematic as s is undefined in this integral. I evaluated this integral symbolically and then inserted the result in the second integral over ds.Is this "kosher" ?.
I agree with you that phio(s) is imaginary for small values of s. Being a phase function this is probably ok as it results in a change in the spatial pressure from positive to negative.
Much obliged for your interest. I will soon be getting a chance to do some tests on the dam gate that exhibited unstable behaviour earlier this year hence my interest to try to simulate the problem.
I managed to find another paper that took a different approach to solving Equation 21. I will send my Mathcad sheet to you shortly out of interest to close out the problem.
I have a new problem with a new bug to fix! Vibration tests we have performed on a cardan shaft indicate it is exhibiting symptoms of a parametric instability. I am looking to solve several differential equations using a solve block. I have copied a previous odesolve method you provided some time ago but it is giving an errror I cannot seem to clear. I'm sure it will be trivial. If you can assist I would appreciate it.
Thanks again for your de-bugging expertise. I can't believe I missed the error with "t" in lieu of "tau". I mucked around for hours trying to source the problem!That's what a fresh pair of eyes does. With your modification I have the sheet working (attached) the method to plot results is clunky but it does the job.I will send through a copy of the Laplace transform sheet under a reply in the other discussion in case others haave an interest in the result.
Thanks again and have a great Xmas if we do not chat in the interim.
Ross Emslie wrote:
... the method to plot results is clunky ...
There is no need to define K and G etc. Just transpose A and B in the return vector, for example. Also, no need for F at all; your definition of t works perfectly well - see attached.
There always seems to be one more bug to fix, although most of the time its me!
I have adapted your sheet to now include coupled 2nd order equations and it doesn't seeem to like it. The equations have been input as an expansion of the following matricies.It seems to solve OK when one of he second order terms is removed. from other discussions I have seen it appraes Mathcad can solve such coiupled systems, however, have I done something that is not allowed?
My sheet is attached.
Always best to get a single equation for each of the derivatives. You should check that I've rearranged things correctly. See attached for working version.