Waves In Circular Rods Research Articles

Advanced techniques for analyzing solitary waves in circular rods: a sensitivity visualization study

Advanced techniques for analyzing solitary waves in circular rods: a sensitivity visualization study

Correction Factors of the Approximate Theories for Axisymmetric Modes of Longitudinal Waves in Circular Rods

Correction Factors of the Approximate Theories for Axisymmetric Modes of Longitudinal Waves in Circular Rods

Propagation of elastic waves in circular rods homogeneous over the cross section

Propagation of elastic waves in circular rods and in rods with a cylindrical cavity is numerically studied. The influence of the rod size on the wave propagation velocity is analyzed. A phenomenon of repeated rebound in short homogeneous rods is described.

Torsional rod wave scattering from tapering between regions of different cross-sections

Previously (Engan 1998) we have studied the scattering of torsional waves in circular rods with a free surface where the rod diameter is subject to abrupt diameter changes. Here, we discuss the scattering of torsional waves from tapered regions and, in particular, transmission of the fundamental torsional mode. The calculations are based on a mode expansion technique in which propagating as well as cut-off modes are taken into account. The tapered region is approximated by numerous steps separated by uniform rod parts arranged so that they closely render the taper shape. Transfer matrices for all steps and uniform parts are combined to yield the desired transmission coefficient through the taper region. Numerical results of the frequency variation of fundamental mode transmission are presented, depending on geometrical parameters, such as taper length and the diameters of the two uniform adjacent rod parts. The dependence of the transmission on taper shape is demonstrated by calculating the response of various shapes.

Torsional wave scattering from a diameter step in a rod

The propagation and scattering of torsional waves in circular rods of infinite length with a free surface that have an abrupt diameter change is discussed. A mode expansion technique involving propagating and cut-off modes is applied to obtain numerical results for a range of parameter values. The calculated results are compared with simplified models valid in the high- and low-frequency regions, respectively. The calculations show that higher radial modes have strong influence at higher frequencies. In particular, near the cut-off frequencies both amplitude and phase responses are strongly influenced. It is further found that the approximation accuracy results depend on the number of modes used in the modal expansion. It is demonstrated that in order to obtain an accuracy (as judged from convergence) that is sufficient for typical parameters chosen, all propagating modes plus a few cut-off modes should be included in the calculations.

Distortion of Dispersive Waves in Rods Subjected to Local Heating

A new model one-dimensional wave equation is constructed, which is adapted for the study of longitudinal waves in rods having some inhomogeneities in physical properties and/or in geometry. This equation is then applied to scattering of longitudinal waves in circular rods, where the elastic constants such as Young's modulus and Poisson's ratio become locally inhomogeneous along their axes due to local heating. In the experiments, strain waves are produced by impacting cylindrical bullets at one end of a stainless steel rod which is heated locally at its intermediate portion. The main interests are devoted to the dispersion effect on waves scattered by the inhomogeneities and also the validity of the present equation.

Numerical analysis of longitudinal elastic-plastic waves with radial effects

The two-dimensional problem of longitudinal elastic-plastic waves in circular rods taking radial-inertia effects into account is solved based on the finite-element method and an explicit integration algorithm. The elastic-plastic constitutive equations are the yield criterion of von Mises with isotropic work hardening and the Prandtl-Reuss flow rule. Numerical results are shown for the region near the impact end of a semi-infinite rod for two sets of boundary conditions, namely prescribed longitudinal velocity and prescribed longitudinal stress at the bar end. The lateral motion of the struck end is assumed to be unrestrained (zero shear stress). The numerical results show response characteristics which deviate from the one-dimensional solution and which are in a good qualitative agreement with a number of experimental observations reported in the literature. These impact test results have been examined with respect to the predictions in order to separate radial- and strain-rate effects. Several specific calculations for the various test conditions have been performed to obtain quantitative agreement with experimental observations.

Propagation of electromagnetic waves in circular rods in torsion

Invariance considerations are employed to write down constitutive equations governing the propagation of electromagnetic waves in isotropic materials with a centre of symmetry which are subject to a static deformation. It is assumed that the dielectric displacement and magnetic induction vectors are linear functions of the electric and magnetic field intensities, respectively, but are general polynomial functions in the quantities which specify the deformation. The theory is employed to examine propagation along circular cylindrical rods in torsion. Rotating waves are produced whose speed of propagation and rate of rotation depend upon the magnitude of the deformation and the properties of the material. The nature of these waves is examined for the general case where there is no restriction either upon the amount of torsion or upon the magnitude of the effect. When the amount of torsion, or the dependence of the effect upon deformation is small, solutions can be obtained based upon those for the propagation of waves in undeformed materials.