### Solving boundary value problems with moving boundaries using the method of change of variables in the functional equation

#### V. L. Litvinov^{1}

Annotation | The method of analytical solution of wave equation with the conditions, assigned on the moving boundaries, is described. With the aid of the change of variables in the functional equation the original boundary-value problem is brought to the difference equation with one fixed bias, which can be solved using the Laplace integral transform. The expression for amplitude of oscillation corresponding to n-th dynamic mode is obtained for the first kind boundary conditions. As an example, the torsional vibrations of a beam of variable length considered. Study the resonance properties brought to the numerical solution. |
---|---|

Keywords | wave equation, variations of systems with moving boundaries, laws of boundary moving |

^{1}Senior lecturer of dept. of general – theoretical disciplines, Syzran Branch of Samara State Technical University, Syzran, vladlitvinov@rambler.ru.

**Citation**: V. L. Litvinov, "[Solving boundary value problems with moving boundaries using the method of change of variables in the functional equation]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,15:3 (2013) 112–119 (In Russian)