Good morning to all

This post is a continuation of my previous post:
Plot of functions having big range on Y axis - No plot when trying to plot functions having big range
(you can consult for more infos).

I'm testing the combination of more transfer matrix (representing a stepped beam: I can give more technical details
if someone is interested....).

When I tried a three-pieces stepped beam the calculations still runs after hours....for comparison, I tested
a 32-pieces configuration in MathCAD, ending calculation in 1h and half...I used the same sequence of calculation
I adopted in MathCAD but I suspect that I have to change "strategy" in SMath: has any one a suggestion?

More in general: it's possible to freeze results of a SMath sheet, and start from the last completed calculation
for the new calculations?

I attach the files

Many thanks in advance for whatever the suggestion. Do not hesitate to ask for me if you need further detail (or you are simply curious...).

Best Regards

FabioФайл не найден.Файл не найден.

Hello

My PC calculated the TMMT.sm file in 21 seconds, and the ThreeHollowBeams_SteppedBeam,sm file in 32 minutes.

The last 2 lines of the last calculation are the ones that take the longest to execute.

The graphs of the functions do not appear.

Operating System: Windows 11 Pro

Processor: 12th Gen Intel(R) Core(TM) i7-12650H 2.30 GHz
Installed RAM: 32.0 GB (31.8 GB usable)

Best Regards

Carlos

ConfigPCFabbro.docx (28 КиБ) скачан 21 раз(а).Thanks CBG, thanks Jean

For CBG: about visualizing the plot, I had some suggestions following my previous post.
In fact you gave me matter to think it over. The configuration of my PC is attachedConfigPCFabbro.docx (28 КиБ) скачан 21 раз(а)..

At a first sight I'd say that the weak point is in RAM, not in the SO (Windows10 Pro), nor in processor (8 cores!)
What do you think about?

More, do you think that SMath is "running better" with a lot of RAM or with a fast processor?

I'm not an expert but I remember well that NASTRAN (until 2005 version at least) was more performant with fast processors than with a lot of RAM....

More it's not possible to make "parallel" calculations (maybe my PC is not at the edge but still it has 8 processors......)?


For Jean: thanks for your feedback (in line with my doubts). To progress in my calculations it should be useful to understand what is "dominating":
RAM (or processor) capabilities OR solvers capabilities? Unfortunately I cannot, for now, make a sure statement as the MathCAD reference times (I quoted
in my post) are also linked to a different PC (than the one where SMath is presently running)....and I do not remember nor the model nor the configuration....

On the other side, I think there has been a misunderstanding about SMath "freezing": I think you mean that calculation does not end after long time...it's the case. BUT it's also true that every time SMath recalculates the sheet since the very beginning. My question was: it's not possible to complete calculations in two steps; i.e. until a certain point (line), save, and, then, restart calculation from that point (line)? For example I could calculate the sheet until the first of the last 2 lines. Then, restart the sheet ONLY to calculate last line and plot.

By the way, I could completely change of strategy. Until now my strategy was: plot the function, see where roots are approximatively, find the the roots more "precisely". BUT I could do other way: sweep with big steps the range of Omega I'm interested; see btw which steps, the function change of sign; iteratively search the root...

Best Regards

Fabio

... here is the transit Solver 30405.
Please confirm it works ... Jean.

TMMT plot_roots.sm (113 КиБ) скачан 26 раз(а).

Hi JEAN,

I tried to run your last sheet (TMMT plot roots.sm) BUT a new bug (unknown until now) jumps out
for ALL my sheets involving TMMT algorithm (so, your sheet included....) : could you give me a hint
to solve it?

I'm very surprised and a bit upset: it's not matter of scientific calculation but debugging....

To be noticed that the bug involves SMath sheets previously working correctly (even if something was
signaled, randomly, in the past, for the same function BUT without any effect on calculations)

Many Thanks

Fabio

.....sorry JEAN to bother you...but I've solved the issue I hinted before...apparently I have ticked (and forgot) the option "Pause" in "Calculation/On Error"...
sorry..I'll check TMMT plot roots.sm asap and let you know

Wrote

All accurate roots, min/max Golden ratio.

Doctored version ... NO red region.
Does it work ? Jean

TMMT plot_roots.sm (134 КиБ) скачан 25 раз(а).

It works indeed!! Do you think that it could work as well and sufficiently fast for multiple transfer matrix? I'll try and let you know..THANKS again!

Hi JEAN, could you check (in the meanwhile I'll do also) that the attached version of your SM file,
is running correctly and sufficiently fastTMMT plot_roots V1.sm (150 КиБ) скачан 22 раз(а).?

Modification are highlighted in pink.

THANKS!!!

Wrote

It works indeed!!
Do you think that it could work as well and sufficiently fast for multiple transfer matrix ? I'll try and let you know..THANKS again!

I don't quite understand multiple transfer matrix ?
Do you mean a matrix system that would plot more waves ?
Or plot more wrt to different initial parameters ?
Plot/Solve all the maths in < 40 s !!!

Wrote

Modification are highlighted in pink.

It complains from the very beginning D,d not defined

Sorry JEAN,

I discovered in the meanwhile some flaws that I corrected: I can confirm no "complains" now.

BUT after more than 3h, SMath is stuck on detZ function....

What I ask you is to try to run the "modified version" here attached...Please stop
calculation after 1h running, particularly if, in this timeframe, the roots have not been calculated
: no need to make you also waste energy!

TMMT plot_roots V2.sm (147 КиБ) скачан 28 раз(а).

Let me know : I think that I'm at the last tests before switching to MathCAD (for this problem at least - bending frequencies
of inhomogeneous stepwise beams) and, possibly, adding RAM to my PC (16 Gb is not sufficient in my opinion).

Thanks you very much for your support

Fabio

Greetings,

To accelerate your function call, insert the definition of detZ() into a line call (shown below; note the black vertical bar = 'line(▮)' )







You will notice drastic acceleration in detZ() definition; I would repeat this technique for any function that references another function within its own definition (ie., Z(x) and f(x)).


May this be of Good Help;
⚜ Kenny Lemens, P.E. ᵂᴵ

Thanks JEAN, thanks KENNY,

For KENNY: I'm trying just now your suggestion: a first result is that, in fact, DetZ() is passed away in 50' ...could you be so kind to give me a short hint on how the modification act ? Please,
keep in mind I'm nor a informatic expert nor a mathematicians but only an aeronautical/mechanical engineer with some basis of numerical calculation...

For JEAN, thanks again for all your efforts...about what you call "Clean roots", please take into consideration that complex results (with small
imaginary part, let's say < 5% of real part) are acceptable: it probably means that the vibration has components on both normal axis...
More, these methods are used mainly in preliminary dynamic&vibration verification (hence 5% error is more than good). By the way in one of the
original version of the my SMath file (ThreeHollowBeams_SteppedBeam) the calculation ended after 1h & 50' on solve (......) with the error message:
"No real roots"...I do not think it's matter of units (it worked in previous SMath files...). But on the other side, I do not know how could I ask to have even
complex roots...
Plus, do not consider negative axis and max the first 5 roots (lowest frequencies are always the most 'tedious' and a modal basis made by first 5 modes/frequencies
is more than adequate if we should want to consider an "answer" of the structure): this should limit the values (even if, to be honest with you, when I studied the same
cases in MathCAD, values of 10e18 were not uncommon).

Keep in touch

All done correct in few minutes vs hours.
Quick plot 10 min ... X_Y less greedy.
No imaginary roots encountered.
For 12 Decimals roots ... Dichotomy.
Explore from command line, or meshed data XY.
Jean.

TMMT plot_roots V2 part doctored.sm (126 КиБ) скачан 28 раз(а).

Greetings,

Fabbro, to the best of my knowledge, the line() function bypasses some of the Symbolic calculations, so it has the effect of just creating a definition, whereas before SMath was attempting to define and symbolically process (and simplify/combine) ALL of the preceding equations into the current equation.

May this be of Good Help;
⚜ Kenny Lemens, P.E. ᵂᴵ

I deleted most of non associated to document.
Every demand is greedy ... plots, solve, export.
At the point of Export, copy/paste in new sheet
for total independence, inspection.
Cheers ... Jean.

TMMT plot_roots V2 part doctored.sm (145 КиБ) скачан 23 раз(а).

Hi JEAN,

thank you very much!! Really kind of you!! Me also I'm doing some test by myself with cross check
with respect to the expected results....yes, I'm doing a benchmark with respect to the following article
Response Analysis of Ladder Beams Under Inertial mOVING lOAD.pdf (788 КиБ) скачан 28 раз(а). - See fig.2 and Table 1 (first example).

And it seems to me that not considering the units of measure has an impact on the expected results

In Mathcad and in the first, very manual, examples, the first frequency was got (around 5Hz); for the other frequencies
the method - that I baptized TMMT - revealed "stiffer" and stiffer (higher frequencies)...if you want to know something
more on this method please ask, it's nothing secret or new...simply forgotten...but I think TMMT has a distinct advantage
and it's "sold" elsewhere as particularly accurate for high frequencies...so, maybe, there is something wrong in the reference
article (that uses a much more complicated method in my opinion).

BUT all your work is really useful for me as I'm trying to "implant" many of your line in my original file (preserving units)
and results are promising. I'll keep you informed and exchange files.

Best Regards

Fabio