APPLICATION OF VARIATION METHODS IN SPECTRAL PROBLEMS OF THIN-WALLED SHELLS AND HYDRO-ELASTICITY

V. A. Trotsenko, Yu. V. Trotsenko

The monograph developed a variational method for finding an approximate solution to a singularly perturbed problem of free vibrations of arbitrary thin shells of revolution. The proposed algorithm belongs to the uniform algorithms for a small parameter with the highest derivative in the equations. The application of the Ritz method to finding solutions to problems posed from the standpoint of decomposition of the area of definition of the sought solutions has been developed. Construction of problem solutions is based on the formulation of a generalized functional, for which conjugation conditions are natural boundary conditions. Based on the obtained results, the solutions of a number of spectral problems for equations with discontinuous coefficients, boundary conditions and loads are given. The monograph is intended for scientists and engineers, MSc. and PhD students of the corresponding specialties.

Project "Scientific Book"

Kyiv, Naukova Dumka, 2023

ISBN 978-966-00-1906-5

UDK 539.3:532.5

File https://imath.kiev.ua/monographs/5/monograph.pdf

DOI

Editor O. A. Mykytenko

Reviewers:

O. M. Timokha, Academician of National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences,

Y. M. Kononov, Professor, Doctor of Physical and Mathematical Sciences