Obliczanie Sił Krytycznych dla Sprężystych Prętów Niepryzmatycznych Metoda Interpolacji Częściowej - Życzkowski, M. (Engineering Transactions, 1956)
The existing tables of critical forces for the most common perfectly elastic non-prismatic bars, prepared chiefly by Dinnik, are not accurate. The subject of this paper is to present a method for obtaining 5 or 6 figure tables with small intervals of the argument (the taper k).The values of the critical forces can be obtained in an accurate manner by solving transcendental equations of the type (3.20) involving Bessel's functions. Such an equation determines a composite function expressing the dependency of the stability coefficient on- the taper. Equations of the type (3.20) appearing in various domains of theoretical physics have already been considered by several investigators, J. Mac Mahon developed a method based on the expansion of a function in a power series convergent in a certain neighbourhood of the point k = 1 (a prismatic bar), thus computing the values of the first several derivatives of the sought function, at the point k = l. A. Kalähne proposed a method based on the knowledge of the zeros of B e s s e l functions Jp(x) and Yp(x). This method enables us to solve the equation considered for certain values of k non-uniformly scattered over the interval 0