The dynamic characteristics of a non-closed cylindrical shell with elliptical cross-section under the rigidly fixed of one and two ends are numerically determined. The system of computer-aided design and execution of engineering analysis by finite elements – FEMAP with solver NX NASTRAN – is used. A comparative analysis of the dependence of the natural frequencies on the opening angle relative to the major and minor semi-axes is carried out. The character of the first modes of free vibrations is investigated.
Прикладная механика, 56, № 4, с. 3-14 (2020) | Рубрика: 04.15
An effect of the different static axisymmetric loadings in the range of the subcritical deformations on the natural frequencies of elastic systems composed of shells of revolution with various geometry is analyzed. Some features of the low-frequency section of the spectrum of vibrations of the compound system are illustrated as compared with the corresponding frequencies of some zero-curvature shells.
Прикладная механика, 56, № 4, с. 27-37 (2020) | Рубрика: 04.15
A statement of the problem on the forced resonant vibrations and dissipative heating of a hinged viscoelastic elastomeric plate under cyclic loading is given for the particular case of the membrane prestress forces application. An effect of the elastomer properties, level of press, and the heat transfer conditions on the amplitude-frequency and temperature-frequency characteristics of the forced vibrations, as well as the response of the material below the melting temperature, is studied in details.
The optimal control problem of oscillations of the string with the given initial finite conditions and non-separated values of the derivatives of deflection functions at the intermediate moments with the quality criteria given on the whole time interval is considered. The problem is solved by the method of separation of variables and the theory of optimal control of finite-dimensional systems with non-separated multipoint intermediate conditions. As an application of the proposed approach, an optimal control action is constructed for the string oscillations with the given nonlocal values of the velocities of string points at the two intermediate moments.
Прикладная механика, 56, № 4, с. 87-96 (2020) | Рубрика: 04.15
Марчук А.В., Ренейская С.В., Лещук О.Н. «Трехмерный анализ свободных колебаний слоистых композитных плит на основе полуаналитического метода конечных элементов» Прикладная механика, 56, № 4, с. 97-116 (2020)
Within the framework of the spatial theory of elasticity, two variants of the semi-analytical finite element method are constructed as applied to the study of the frequencies of free vibrations and the modes of distribution of displacements in them. An analysis by two methods is considered as proof of its reliability. An analysis is carried out of the frequencies of free vibrations and the corresponding modes of distribution of displacements of a laminated composite plate, when the two opposite edges are free and the other two are hinged. A plate with a free bottom surface, a rigidly fixed bottom surface and resting on an elastic base in the form of a layer of finite capacity is considered, taking into account its inertial properties. The high accuracy of the proposed models in the problems under consideration is demonstrated. The inadmissibility of neglecting the inertial properties of bases is pointed.
Прикладная механика, 56, № 4, с. 97-116 (2020) | Рубрика: 04.16