Vibrations in engineering and technology

Sivak Roman - Doctor of Technical Sciences, Associate Professor, Vinnytsia National Agrarian University (3 Sonyachna Street, Vinnytsia, Ukraine, 21008, e-mail: sivak_r_i@ukr.net).

It is suggested to use smoothing cubic spline functions to approximate the current functions. The structure of the selected functional provides the minimum curvature of the spline and the smallest deviation of the spline from the function smoothed at the nodes. The necessary correlation between these requirements is provided by the choice of weights. The algorithm for approximating the current function is implemented by moving from a grid created by current lines and auxiliary lines to a rectangular grid. To reduce the effect of random errors of experimental information on the current line, a smoothing algorithm with a given accuracy was used. The current function is interpolated from the physical grid to the calculated one. The flow velocities were approximated to calculate the strain rates. To estimate the accuracy of the calculations, it is proposed to use the deviation from the incompatibility condition.

The main disadvantage is that their behavior around a point determines their behavior as a whole. In this regard, other approaches to the approximation free of this deficiency have been developed in recent years. One such approach that has proven itself well in both theoretical and practical applications is the use of so-called splines. Splines are called functions that are glued together from different pieces of polynomials by a fixed system. The simplest example is broken. Splines naturally occur in many mechanical problems. For example, the spline shape has an elastic beam with point loads. Among the splines, polynomial splines glued together from pieces of polynomials play the most important role. The development of the theory of such splines and their popularization were facilitated by I. Schoenberg's work. Polynomial splines are beginning to be used in many application problems related to function approximation.

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