Geodesic
On the mathematical model of the process of impulsive vibration driving process and its stability
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 2, pp. 152-163

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A mathematical model of the functioning of the impulse pile driver consists of models of the operation of the impulse pile driver itself, a model of the interaction of the pile element with the soil in a form of the friction force of the side surface and frontal resistance, which are phenomenological. The process of operation of the impulse pile driver is described using the Maxwell — Fejer series, and its optimality in terms of the asymmetry coefficient has been rigorously proven. At the same time, when using optimal ratios in the design, tolerances are mandatory, which are inevitable in the production of elements. These imperfections disrupt the shape of the optimal pulse. A problem arises of studying the dependence of the impulse on deviations in parameters and estimating admissible values of these deviations. For this, a software implementation of the mathematical model of the process of functioning of the impulse pile driver was used, which formed a basis of a numerical experiment. The article presents the characteristic results of the experiment and their analysis.
Keywords: mathematical modeling, pile-driving vibration loader, impulse driver, asymmetry coefficient. 
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     author = {A. V. Zhurba and S. D. Baboshin and T. I. Kostina and P. Raynaud de Fitte},
     title = {On the mathematical model of the process of impulsive vibration driving process and its stability},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {152--163},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_2_a2/}
}
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A. V. Zhurba; S. D. Baboshin; T. I. Kostina; P. Raynaud de Fitte. On the mathematical model of the process of impulsive vibration driving process and its stability. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 2, pp. 152-163. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_2_a2/