The scattering of acoustic waves by a cylinder with a non-uniform elastic coating

Study of the dispersion properties of cylindrical waveguides with variable properties

“…The boundary value problem for γ 1 has the follow ing form: or in components (7) Part of the vector components of the solutions in (7) are determined in explicit form, Y 21 = 1, Y 41 = 0, and the solution for the remaining components is found from the boundary value problem (8) which is solved numerically. Note that in the impor tant particular case of inhomogeneity, when = const, which corresponds to a constant Poisson coefficient, problem (8) has the exact solution (9) The boundary value problem for γ 2 has the form…”

“…In the general case, it is also solved numerically and determines parameter t, which enters into the system (11) Considering Y 11 and Y 31 to have been found at the previous state of integrating (8), from the second equation (11) via integration and uncomplicated transformations, we find (12) In particular case (9), when the solution to the aux iliary problems is written in explicit form, parameter t, which determined the angle of inclination of the first dispersion curve, is also found in explicit form, and is expressed through the variable Young's modulus: (13) which in fact characterizes the pivotal mode for the waveguide with variable elastic properties.…”

“…The regularities of wave propagation in an isotropic cylinder are explained in sufficient detail in [5,6]. In recent years, interest has grown in different generalizations of such problems for a cylindrical waveguide in the pres ence of various types of anisotropy [7] or inhomogene ity in the form of layering or a functionally gradient structure [8][9][10][11][12][13][14][15]. The problem of scattering of a plane sound wave by a solid cylinder with a radially inhomo geneous elastic cover has been considered in [7].…”

“…The problem of scattering of a plane sound wave by a solid cylinder with a radially inhomo geneous elastic cover has been considered in [7]. By combining numerical and semianalytical methods, the features of the formation of wave fields in boreholes with a radially inhomogeneous ruptured zone have been studied in [8,9]. In [10][11][12][13][14][15], similar problems have been analyzed for layered and functionally gradient cyl inders in the presence of a polynomial form of radial inhomogeneity.…”

The scattering of a plane sound wave by an elastic cylinder with a discrete-layered covering

“…9 The scattering of sound waves by an absolutely rigid cylinder with an inhomogeneous elastic coating has been considered. 10 The problem of the scattering of an inclined incident plane sound wave by an elastic cylinder with a radially inhomogeneous covering has been solved. 11 Below we solve the problem of the scattering of a plane monochromatic sound wave, incident obliquely on an elastic circular cylinder with a discrete-layered covering.…”