Construction of nonlocal linear vibration models using a computer algebra system.

In the paper, on the examples of a string and beam, resonance vibrations in linear elastic systems that result from nonlocal boundary conditions (even if external forces are lacking) are considered. Formulas of exact solutions of the corresponding boundary-value problems are presented. These formulas are used for evaluation of the solutions and for construction of plots. Computer algebra system Mathematica was used for derivation and analysis of the exact solutions and for development of software packages designed for evaluation of the derived formulas and solution visualization. The authors believe that results of this study can be used to explain the causes for the vibration of the Tacoma and Volgograd bridges in 1940 and 2010, respectively. [ABSTRACT FROM AUTHOR]