eigenfunctions.

Mode-Series Expansion of Solutions of Elasticity Problems for a Strip

Authors: Kossovich L. Y., Yurko V. A., Kirillova I. V.

Oscillations of a strip are considered as a plane problem of elasticity theory. Description of oscillation modes is provided. Properties of eigenvalues and eigenfunctions are studied for a boundary value problem for their amplitudes. Green’s function is constructed as a kernel of the inverse operator. Completeness and expansion theorems are proved which allow one to solve problems for finite and infinite membranes under arbitrary boundary conditions.

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.