@article{article_104672, title={Fourier-type integral transforms in modeling of transversal oscillation}, journal={International Journal of Applied Mathematics Electronics and Computers}, volume={3}, pages={18–22}, year={2015}, DOI={10.18100/ijamec.36094}, url={https://izlik.org/JA53MY36AJ}, author={Yaremko, Oleg and Yaremko, Nataliia and Tyapin, Nikita}, keywords={eigenfunction, fourth-order differential equation, fundamental solution, Green’s function.}, abstract={<span lang="EN-US">The model of transversal oscillation for an elastic piecewise-homogeneous rod is constructed. In order to find a solution of this model   a   Fourier-type integral transforms method for the fourth-order differential equations is developed. The decomposition theorem is proved by Cauchy contour integration method </span> <span lang="EN-US">. </span> <span lang="EN-US">The conditions of existence for fundamental solutions of the initial - boundary value problem are established and explicit expressions of these fundamental solutions are found.  </span>}, number={1}