spectral decomposition

Estimates of Speed of Convergence and Equiconvergence of Spectral Decomposition of Ordinary Differential Operators

Authors: Lomov I. S.

The present review contains results of V. A. Il’in and his pupils concerning an assessment of speed of convergence and equiconvergence with a trigonometrical series of Fourier of spectral decomposition of functions on root functions of linear ordinary differential
operators both self-conjugate, and not self-conjugate, set on a final piece of a numerical straight line. The first theorem of V. A. Ilyin of equiconvergence of spectral decomposition for the differential operator of any order is provided. Theorems of the speed of

Non-stationary vibration of growth circular cylindrical shell

Authors: Baryshev A. A., Manzhirov A. V., Lychev S. A.

Small forced vibrations of growing cylindrical shell fixed on circular boundaries is studied in the framework of Kirchhoff–Love shell theory. The process of the accretion are characterized by the continuous adherence of material particles to its facial surface. Since the shell bends during the accretion, its stressed-strained state depends not only on loading, but also on the history of the process of accretion, i.e. the schedule of accretion.

The equilibrium equations of shells in the coordinates of the general form

Authors: Baryshev A. A., Lychev S. A., Manzhirov A. V.

A mathematical model of homogeneous elastic shells is consider under kinematics Reissner–Mindlin type. Through direct (coordinateless) methods of the tensor calculus equations of equilibrium are obtained in terms of displacements in an arbitrary (not necessarily orthogonal) coordinate system, taking into account the asymmetry of the location of the front surface. For a spherical shells proposed procedure for constructing solutions, based on the method of spectral decomposition, which describes the stress-strain state at the potential power and torque static loads.