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Computer methods for calculating tuple solutions of polynomial matrix equations

Dorożyński J., Nedashkovskyy M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2020

Vol. 68, nr 2

235--243

Schemes are presented for calculating tuples of solutions of matrix polynomial equations using continued fractions. Despite the fact that the simplest matrix equations were solved in the second half of the 19th century, and the problem of multiplier decomposition was then deeply analysed, many tasks in this area have not yet been solved. Therefore, the construction of computer schemes for calculating the sequences of solutions is proposed in this work. The second-order matrix equations can be solved by a matrix chain function or iterative method. The results of the numerical experiment using the MatLab package for a given number of iterations are presented. A similar calculation is done for a symmetric square matrix equation of the 2nd order. Also, for the discrete (time) Riccati equation, as its analytical solution cannot be performed yet, we propose constructing its own special scheme of development of the solution in the matrix continued fraction. Next, matrix equations of the n-th order, matrix polynomial equations of the order of non-canonical form, and finally, the conditions for the termination of the iterative process in solving matrix equations by branched continued fractions and the criteria of convergence of matrix branching chain fractions to solutions are discussed.

Impact Tests of UHSS Steel Welded Joints Using the Drop - Tower Impact Drop Method

Dorożyński J., Nowacki J., Sajek A.

Advances in Materials Science

2019

Vol. 19, nr 3(61)

19--31

The article characterizes the impact test method using Drop-Tower Impact Test with the registration of the value of force and energy of breaking. Based on sources, the possibilities and scope of the current application of this method were determined and the current state of knowledge on the results of these tests was reviewed. In order to determine the possibility of using the method in impact tests of high strength steel joints, investigations of hybrid PTA - GMA welding conditions on impact strength of joints of MART S1300QL steel were carried out. In particular, the influence of t8/5 cooling time on the impact strength of welded joints by the Drop - Tower Impact Test method was determined. It has been shown that the use of dropping machine with computer-based registration of breaking force and energy values was possible in the case of impact strength testing of UHSS welded joints and enabled precise analysis of the energy distribution dynamics absorbed by the tested.