Время науки - The Times of Science

Ермолицкая А. Д. Ermolitskaya A. D. 2025 11 The partial solutions of equations  ( ) and  ( ) satisfy the conditions: By varying the boundary conditions in the systems of equations (32) and (33) it is possible to obtain solutions under different fixation conditions: both ends are pinched; both ends are supported; one end is pinched and the other is supported. Here is an example of the calculation of forced vibrations of a steel rod using the Wolfram Mathematica symbolic algebra package.The rod has a rectangular cross- section with a height of 10 mm and a width of 5 mm and a length of 1 metre. The rod is subjected to a distributed load and a concentrated mass, the left end is supported. Let us assume a distributed load of the form ( , ) = 48.3 15.2 5 + 23.1 15.2 5 . (36) We apply the concentrated mass equal to = 100 kg to the centre of the rod. Let us take the coefficient of internal friction equal to 0 = 0.3 and the coefficient of resistance of the medium = 0.5 . We take the constants to be equal, respectively: 2 = 0.03, 4 = 0.04, 2 = 0.07, 4 = 0.05 (37) The system (10) will take the form: Let us apply the Laplace operator method. As a result, the previous system will become equal: