This paper is concerned with the investigation of the nonlinear eigenvalue problem describing the natural oscillations of a plate with a load that elastically attached to it. We study properties of eigenvalues and eigenfunctions of this eigenvalue problem and prove the existence theorem for eigensolutions. Theoretical results are illustrated by numerical experiments.

This paper is concerned with the investigation of the nonlinear eigenvalue problem describing the natural oscillations of a plate with a load that elastically attached to it. We study properties of eigenvalues and eigenfunctions of this eigenvalue problem and prove the existence theorem for eigensolutions. Theoretical results are illustrated by numerical experiments.

Диссертация посвящена проблеме возникновения шума и вибрации от трубопроводных систем многоэтажных зданий. Предложен способ определения вероятности возникновения повышенных вибраций с помощью модального анализа в программном комплексеANSYS Workbench. Представлены результаты численного анализа влияния длины, диаметра и толщины стенки участка трубопровода на изменение значений частот его собственных колебаний с целью прогноза риска возможных резонансных режимов. Выполнены статистический и регрессионный анализы. / The dissertation discusses the occurrence of noise and vibration from the piping systems of multi-storey buildings. A method for determining the probability of excessive vibrations using modal analysis software complex ANSYS Workbench. The results of the digital analysis of influence of length, diameter and thickness of a wall of the pipeline’s section on change of values of frequencies of its natural oscillations are provided. Statistical and regression analyses are made.

This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.