Compound Circular Cylinder Research Articles

The influence of Murnaghan constants on the propagation of a torsional wave in pre-stretched compound circular cylinders

The propagation of torsional waves in prestressed compound circular cylinders is investigated modeling them by a piecewise-homogeneous body and using the three-dimensional linearized theory of elastic waves in prestressed body. It is assumed that the elastic relations for the components of the cylinders include the Murnaghan potential. The numerical investigations are performed for bronze (Br) or brass (Pr) (for the solid cylinder) and steel (St) (for the hollow cylinder). The effect of the variation of the geometric (the ratio of the thickness of the outer cylinder to the radius of the inner cylinder) and mechanical parameters on the dispersion curves are analyzed using the numerical results obtained

Dispersion Relations of Axisymmetric Wave Propagation in Finite Pre-Stretched Compound Circular Cylinders Made from Highly Elastic Incompressible Materials

Dispersion Relations of Axisymmetric Wave Propagation in Finite Pre-Stretched Compound Circular Cylinders Made from Highly Elastic Incompressible Materials

Axisymmetric longitudinal wave propagation in a finite prestretched compound circular cylinder made of incompressible materials

The propagation of an axisymmetric longitudinal wave in a finite prestrained compound (composite) cylinder is investigated using a piecewise-homogeneous body model and the three-dimensional linearized theory of wave propagation in prestressed body [13–15]. The inner and outer cylinders are assumed to be made of incompressible neo-Hookean materials. Numerical results on the influence of the prestrains in the inner and outer cylinders on wave dispersion are presented and discussed. These results are obtained for the case where the inner solid cylinder is stiffer than the outer hollow cylinder. In particular, it is established that the pretension of the cylinders increases the wave velocity

Dynamic viscoelastic effects on sound wave scattering by an eccentric compound circular cylinder

The classical method of separation of variables in conjunction with the translational addition theorem for cylindrical wave functions are employed to obtain an exact solution for two-dimensional interaction of a harmonic plane acoustic wave with an infinitely long (visco)elastic circular cylinder which is eccentrically coated by another (visco)elastic material and is submerged in an ideal unbounded acoustic medium. The novel features of Havriliak–Negami model for dynamic viscoelastic material behaviour are used to take the rheological properties of the coating (and/or core) material into consideration. The analytical results are illustrated with numerical examples in which a steel rod eccentrically coated with (an eccentric steel shell filled with) dissipative materials of distinct viscoelastic properties is insonified by plane sound waves at selected angles of incidence. The effects of incident wave frequency, angle of incidence, core eccentricity and dynamic viscoelastic material properties on the backscattered form function spectra are examined. Limiting cases are considered and fair agreements with available solutions are obtained.

Axisymmetric longitudinal wave propagation in pre-stressed compound circular cylinders

Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed body the axisymmetric longitudinal wave propagation in the pre-stretched compound cylinder is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinder are given through the Murnagan potential. It is established that the influence of the initial stretching of the cylinders on the longitudinal wave dispersion has not only a quantitative, but also a qualitative character. The concrete numerical investigation were made for steel, tungsten (W) (as a material for the solid cylinder) and aluminium (Al) (as a material for hollow cylinder). A lot of numerical results on the wave dispersion in the compound cylinders from tungsten (W) and aluminium (Al) are presented.

Decay rates for the compound circular cylinder

An exact linear elasticity solution developed by the author for the decay of self-equilibrating end loads applied to a hollow circular cylinder is extended here to determine decay rates for a compound circular cylinder of two materials having different stiffness; only axisymmetric loads are considered. The results are of interest not only as a quantification of Saint-Venant's Principle (SVP), but also because the minimum decay rate indicates the rate of load transfer and hence the maximum extent of a transition region where load is transferred from one cylinder to another. As with the semi-infinite plane strain sandwich, one of the few other geometries amenable to mathematical analysis, rates of decay can be so slow that routine invocation of SVP is not justified. The rate of load transfer from a stiff inner cylinder to a more flexible concentric cylinder is affected by the ratio of the elastic properties and also the diameter ratio. For load transfer to be effected over minimum distance the difference in stiffness should be small; when the difference in stiffness is large, rapid load transfer can be achieved by keeping the diameter ratio small.