Low and high frequency approximations to eigenvibrations of string with double contrasts

We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffness inhomogeneity, with heavier part being softer. The limit problem for high frequency approximations depends nonlinearly on the spectral parameter. The quantization of the spectral semiaxis is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation.     

On the separation of isolated solutions of nonlinear integral equations

We present the theoretical justification and a method for practical realization of the process of separation of solutions isolated in a bounded domain for some classes of nonlinear integral equations. We study the problem of construction of a sequence of approximation equations by the method of mechanical quadratures and the problem of existence of solutions of these equations. We also present methods for approximate solution of these equations and obtaina posteriori error estimates.     

Contact Problem for an Elastic Ring Punch and a Half-Space with Initial (Residual) Stresses*

International Applied Mechanics - The problem of contact interaction without friction between an elastic cylindrical ring punch and an elastic half-space with initial (residual) stresses under...     

On One Dynamic Problem for a Multilayer Half-Space with Initial Stresses*

International Applied Mechanics - The influence of initial stresses and surface load velocity on the roots of the characteristic equations that correspond to the equations of motion of compressible...     

Axisymmetric Waves in Prestressed Highly Elastic Composite Material. Long Wave Approximation*

International Applied Mechanics - The statement and method of solving problems on the propagation of axisymmetric harmonic waves in a highly elastic laminated composite material are considered...