Effect of initial strains on the propagation of waves in an incompressible cylinder located in an ideal fluid

Abstract

UDC 539.3 As is known, real materials invariably contain initial stresses that are capable of significantly altering the wave properties of hydroelastic systems. Thus, in the study of the laws governing the propagation of waves in solid cylinders located in a fluid, it is necessary to use models that more fully account for the behavior of the actual elastic medium. The model of a prestressed body is one such model. Three-dimensional linearized problems of aerohydroelasticity for arbitrary bodies with initial stresses were formulated in general form in [1] and a method of solution was presented. This study also presented general solutions to coupled problems for an elastic body with initial stresses and a fluid, and it examined the propagation of torsion waves in a preloaded solid circular cylinder placed in a viscous compressible fluid. In our investigation, we use the model referred to above to examine the propagation of axisymmetric longitudinal waves in a prestressed incompressible solid cylinder located in an ideal compressible fluid. §1. We will examine an infinitely long incompressible solid circular cylinder of radius R located in an infinite ideal compressible fluid and subjected to uniform initial strains. The cylinder will be examined in a cylindrical coordinate system (r, 0, z 3) introduced in the initial strain state. We will consider the case when the cylinder is tensioned along the Oz_, 3 axis. With allowance for the incompressibility of the cylinder and the chosen load, we will have