Quadratic nonlinear torsional hyperelastic waves in isotropic cylinders: Primary analysis of evolution

Nonlinear torsional waves propagating along an infinite isotropic cylinder are considered. The hyperelasticity of the cylinder is described by the Murnaghan potential. An approximate analytical solution of the problem is obtained. The evolution of the initial waveprofile in cylinders made of composite materials reinforced with microscale particles is simulated numerically. It is shown that the approximation used to describe the variation in the amplitude inward the cylinder is quite accurate. Three-dimensional plots of evolution are presented __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 75–85, March 2008.     

Higher-order approximations in the analysis of nonlinear cylindrical waves in a hyperelastic medium

The nonlinear wave equation is solved analytically in cylindrical coordinates using the third-order approximation of the Hankel function. The second-order and third-order solutions are compared. The evolution of the initial wave profile is simulated numerically for different initial frequencies __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 36–45, April 2007.     

A numerical solution of transient torsional wave propagation in a transversely isotropic cylinder

Summary A numerical technique is proposed to obtain the solution for the transient torsional wave propagation in a transversely isotropic cylinder when a torque is suddenly applied to its end surface. The dynamic behavior in the vicinity of the impact end of the transversely isotropic cylinder is studied. The stability and convergence of the present numerical technique and the validity of the numerical solution are examined.