Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface

This paper studies the influence of the imperfectness of the contact condition on the torsional wave propagation in the initially stressed (stretched) bi-material compounded circular cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stresses Bodies. The mathematical formulation of the corresponding eigen-value problem is formulated and the solution method for that is developed. The two cases considered are the bi-material compounded cylinder consists of the solid inner and surrounding hollow outer cylinders (Case 1); the bi-material compounded cylinder consists of the hollow inner and surrounding hollow outer cylinders (Case 2). The mechanical relations of the cylinders’ materials are written through the Murnaghan potential. It is proven that the imperfectness of the contact condition does not influence the asymptotic-limit values of the wave propagation velocity. Moreover, the numerical results on the effects of the imperfectness of the boundary condition on the influence of the initial stresses on the wave propagation velocity are presented and discussed.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.     

Propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder imbedded in a finitely prestrained infinite elastic body

Within the framework of a piecewise homogeneous body model and with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), the propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder (fiber) imbedded in a finitely prestrained infinite elastic body (matrix) is investigated. It is assumed that the fiber and matrix materials have the same density and are in compressible. The stress-strain relations for them are given through the Treloar potential. Numerical results regarding the influence of initial strains in the fiber and matrix on wave dispersion are presented and discussed. These results are obtained for the following cases: the fiber and matrix are both without initial strains; only the fiber is prestretched; only the matrix is prestretched; the fiber and matrix are both prestretched simultaneously; the fiber and matrix are both precompressed simultaneously. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 665–684, September–October, 2008.     

Elastic wave propagation in a cylindrical bore situated in a micropolar elastic medium with stretch

Propagation of surface elastic waves in a cylindrical bore through a micropolar elastic medium with stretch is analysed in two cases. In the first case, the cylindrical bore is considered empty while in the second case, the bore is filled with homogeneous inviscid liquid. In both the problems, period equations are obtained in closed form. The problem of Banerji and Sengupta [2,3] has been reduced as a special case. Numerical calculations have been performed for a particular model and results obtained are presented graphically. It is noticed that the effect of micropolarity on dispersion curve is significant while the effect of micro-stretch on dispersion curve is not appreciable.