PROPAGATION OF LINEAR WAVES IN MULTILAYERED STRUCTURAL - INHOMOGENEOUS CYLINDRICAL SHELLS

Abstract

In this paper, axisymmetric viscoelastic waves in an extended cylindrical shell of circular cross section are considered. The study of axisymmetric viscoelastic waves in multilayer cylindrical systems with the maximum possible use of analytical methods is relevant for the development of a new generation of sounding techniques for wells. The aim of the work is to study the propagation of axisymmetric viscoelastic waves in extended multilayer cylindrical structures, to determine the volumetric structure variant from the responses of one-way sounding using a priori information about the possible structure of the system. The paper uses classical methods of mathematical physics, applied to solving boundary value problems in a cylindrical coordinate system, the spatial Fourier transform, the method of complex amplitudes for the variable components of the displacement vector and the stress tensor. The low-frequency resonances of a cylindrical shell are investigated. The physical laws of the formation of the pitch of its fundamental tone are determined sounding. The impossibility of propagation along the casing of wells is proved low-frequency surface waves, as well as SH-polarization waves at axisymmetric excitation. The thin-walled cylindrical shell in the low-frequency region has two fundamental resonance associated with the resonance of the shell as a whole and resonance of each individual section as a ring. Beats of these frequencies the basic tone of the sound of an extended shell of this type is determined. At frequencies below the cutoff of higher modes, all the features of the dispersion natural waves in the wall of a circular cylinder shell are described approximate algebraic equation of the third degree. One the real root of this equation corresponds to the zero mode antisymmetric Lamb wave, and one of the other two complex conjugate, describes the zero mode of the symmetric wave.