Propagation of Natural Waves on a Multilayer Viscoelastic Cylindrical Body Containing the Surface of a Weakened Mechanical Contact

Abstract

In this work, the study of the problems associated with the propagation of natural waves in multilayer viscoelastic cylindrical bodies with a weakened mechanical contact is discussed. A detailed analysis of well-known works devoted to this problem is given. A mathematical formulation, a technique, and an algorithm for studying the damping properties of natural waves in multilayered cylindrical mechanical systems with a weakened mechanical contact are developed. The solution of the considered problem was obtained by the method of separating the variables based on the theory of potential functions (special functions).The complex roots (phase velocities) of the dispersion transcendental equation for given wavenumbers are determined numerically by the Muller method. The phase and group velocities of a structurally heterogeneous mechanical system at various geometric and physical-mechanical parameters for the elements of the mechanical system are investigated. It was established that the real parts of the wave velocity will increase by only a few percent, and the imaginary parts for structurally heterogeneous mechanical systems radically change; the phase velocities (real parts of the complex velocity) of natural waves with an increasing wave numbers around the cylinder circumference of structurally heterogeneous mechanical systems first decrease and then begin to increase. A mechanical effect was discovered for structurally heterogeneous mechanical systems, which provides damping for the waves of the mechanical system as a whole.