In this article I am not going to lament as an old grandmother “they plundered everything, ghouls !!”, because I’m not interested in who does it and whether it does. I am not interested in the favorite temka of motorists, “zadolbali these pits and potholes!”, I personally have no reason to go around them: in matters of choice of vehicles, I prefer to relay the opinion of Andrei Rubanov from his book “Iodine” (e mast hev yaschitayu), in a peaceful same time there is a bike and a bus. I don’t have any claims to our repair services, which, as they say in your Internet users, put a bituminous mixture on rain and snow, contrary to the opinion of these same Internet sites. I am a simple pedestrian, and yet the current state of affairs suits me.
By the way, I am not a mathematician at all, but only a student a la an applied mathematician. If someone doesn’t know, these are dudes and ladies (may office plankton forgive me), who, due to the duty of their professions, have to convert mathematical algorithms of famous and widely known theorists into algorithms. These lap algorithms, in turn, work first in applied research, and then go into applied software, if suddenly, at the behest of fate, the market desires to purchase the achievements of an applied mathematician, steeped in Fortran-Matron-impregnated sorts.
So historically, it happened that on the student bench I had to periodically solve problems for which no other better off and, I suppose, a more reasonable homosapiens did not undertake. And so, on the debt of my student path, I was introduced to one task from the field of road-building structures. The topic was "hopeless." “Oh, it’s a new one,” I thought, and took up the decision purely in exchange for getting practical skills, for free. The results of the work I was a little surprised. But about everything in order, due to the style of Giktatimes "nauchpop for sysadmins who are tired of the day and pogromisms starting to go bald";)
In the far-distant galaxy, i.e., in a remote distance from the Moscow hipsters Permsky Krai, in the summer of 2014, two people, taking with them equipment, a wheelbarrow and a bit of free time, drove around the local autoban, hmm, more precisely, automobile roads of the fourth class. In some places they got on the side of the road, set up equipment, sculpted sensors to the top layer of asphalt, and when another treasure of domestic and not very domestic auto industry flew past, they measured the movement of the canvas. Then they filmed about 100 control measurements. And all this experimental goodness lay and collected dust on the hard of some ancient pissies ajn until December 2016, it lay and waited for me, just like Snow White in a famous fairy tale.
Well, then - no fairy tale and no kisses =) There was a conversation on the topic
“we have goods, you have a merchant” “the data is and we should use them; you feel, young, rosette is ripe - it's time for her to go to the shelves of the great science of strength of materials, you see what we are going to do in the process. ” They outlined the following task: to check the possibility of using the captured control measurements to determine at least some patient characteristics - the road.
What kind of characteristics can we talk about? I now wonder, can you imagine that the roads can hurt or ache? You and I, readers, seem to be quite modern people, some of us are even intelligent and, oh, horror, formed in defiance of the programs of the Ministry of Education. “Animzm,” educated intellectuals will say to me, recalling Vysotsky. But by a strange coincidence, educated intellectuals do not always have a technical education. From the point of view of the technician, every construction has its own life cycle, which even the managers know and guess. In the life cycle certainly includes such a parameter as the lifetime. Technique and design gradually come into disrepair, wearing out and breaking down. No exception and highways. What can be taken as a parameter for the upcoming fever of our patient - I don’t really know even now. But over time, I have indirect data.
First of all, I came, I saw, I convinced one of those two comrades to let me copy some of the results to my flash drive and think about what can be done with this. Since I am an applied mathematician, or, as they say, strong, I decided to make a mathematical model of a layered road construction as a strong one — I used the finite element method apparatus. In CalculiX created a finite element mesh,
Fig. Uno Schematic description of the object under studyassuming that the plane-deformed case is enough for the task, and in Scilab I inserted the code of Newmark's method to solve the equation of motion of the object in question in dynamics. If anyone does not know what is higher for words such new - google, I do not mind =)
So, I set a model problem, and began to compare the results of the full-scale experiment of 2014 and the experiment of computational 2017. By the way, what can be compared exactly? Above, I wrote that on the roads we measured the movements of the canvas. But displacement is such a bjaka, which on the one hand speaks little to the uninitiated, and for initiates most often causes headaches. If you look at the graph of such a signal,
Fig. Dos. One of hundreds of experimental displacement curves.then you can see a bunch of sinusoids dying away into the sunset, summing up with each other. There is no ideal reference sinusoidal signal from the chamber of measures and weights, which was told at secret gatherings of radio engineering circles (if there are still dedicated individuals in nature who remember these).
But not everything is so simple. Once upon a time, there was someone Fourier, who, I think, for fun / dispute, was able to split the sines and cosines of the curves of the character and curvilinearity of his own wife’s forms, it’s hard to imagine other reasons for creating the Fourier method =) in vain, since it has now become possible to create a unique capacious digital portrait of such a complex technical object as a real woman (8), as well as many other technical objects. This, of course, is about the amplitude-frequency response, which de facto can be considered a photo of the muzzle in the passport of any technology. When I write any - it means any. Since our wave-particle microcosm continually sausages and oscillates, these vibrations are present everywhere and in everything. Each object of the meso and macroworld is unique, unique and consists of a non-coinciding set of atoms. The uniqueness of the form gives rise to the uniqueness of macro-movements, which means that the amplitudes of the sinusoids will change in the decomposition of the function in a Fourier series, which means that the uniqueness will also be displayed on the spectrum.
When building a highway instead of asphalt concrete, pour clean concrete - the signal spectrum will change. Do not sleep with layers of sand and gravel - the spectrum will change. Soak the sand in the pavement layers, which will increase its density - the spectrum will change. Any change in the constants of road construction materials and the thickness of the road construction layers will affect the shape of the spectrum. The same applies to any other technical objects: bridges, panel houses, ladies' shoes, your boss chair, and even your own skull (the latter are engaged in biomechanics).
Why am I leading this lengthy conversation? To the end =) I promised to tell you in the heading why, in my opinion, our roads are “guano”. I will cite at last that very long-awaited spectrum, which has calmed to all readers of the eyes.
Fig. Traz One of the experimental spectra
Fig. Quatro. One of the numerical spectra superimposed on one of the experimentalAnd now we recall the high school course and the textbook of physics.
As we see, the frequency range from 0 to 40 Hz is the main one. Let us introduce the assumption that during the movement of motor vehicles the pavement works in a resonant mode. Let's check this statement. We will determine the frequency of exposure to the moving load web, [1 / c]:
where V is the speed of the vehicle, km / h, S is the wheelbase, m.
Then, in the particular case, when the speed of the ATC movement is 60 km / h and the wheelbase is 1.8 m, the frequency of the impact load on the roadway is 9.26 Hz. In the graph of Fig. 4, it is noticeable that the amplitude at a frequency of ~ 10 Hz has a minimum, while at frequencies above and below 10 Hz, the amplitudes of the oscillations increase sharply. This fact suggests that it is possible to select the recommended speed of the ATC flow along the roadway, separating from the resonant modes ...
Wait a minute how ... Resonance? Resonance ... Resonance !!! Here you can attach spoilers vidos Takomsky bridge or pictures from a physics textbook or books of Perelman with walking soldiers. My guess is that our painfully native loam, on which the road structure is built, plays a cruel joke with the life of the canvases. Engineering practice shows that structures operating in resonance are destroyed earlier. A simulation indicates that it is the loam that makes the main contribution to the low-frequency region (0-40Hz). Change our loam to tougher bases - the low-frequency region will move to the right to higher frequencies, the cars will not roll on the canvas at resonance.
Stupid idea, of course, pinable. There are road mechanics and problems with frost heaving of soils, and difficult problems with phase transitions, and chipping of the surface of asphalt concrete. And this article is more of a humorous nature, but I am responsible for the accuracy of computational calculations - yet I am an applied mathematics student, after all.