Propagation of torsional waves in a circular elastic rod (original) (raw)
Comparison of classical and modern theories of longitudinal wave propagation in elastic rods
16th International Congress on Sound and Vibration. Krakow, Poland, 5-9 July 2009 A unified approach to derivation of different families of differential equations describing the longitudinal vibration of elastic rods and based on the Hamilton variational principle is outlined. The simplest model of longitudinal vibration of the rods does not take into consideration its lateral motion and is described in terms of the wave equation. The more elaborated models were proposed by Rayleigh, Love, Bishop, Mindlin-Herrmann, and multimode models in which the lateral effect plays an important role. Dispersion curves, representing the eigenvalues versus wave numbers, of these models are compared with the exact dispersion curves of isotropic cylinder and conclusions on accuracy of the models are deduced. The Green functions are constructed for the classical, Rayleigh, Bishop, and Mindlin-Herrmann models in which the general solutions of the problem are obtained. The principles of construction of...
Mechanics of Composite Materials, 2008
Keywords: ini tial strain, in com press ible ma te rial, uni di rec tional fi brous com pos ite, wave dis per sion, wave prop a ga tion Within the frame work of a piecewise ho mo ge neous body model and with the use of the three-di men sional linearized the ory of elas tic waves in ini tially stressed bod ies (TLTEWISB), the prop a ga tion of axisymmetric lon gi tu di nal waves in a fi nitely prestrained cir cu lar cyl in der (fi ber) im bed ded in a fi nitely prestrained in fi nite elas tic body (ma trix) is in ves ti gated. It is as sumed that the fi ber and ma trix ma te ri als have the same den sity and are in com press ible. The stress-strain re la tions for them are given through the Treloar po ten tial. Nu mer ical re sults re gard ing the in flu ence of ini tial strains in the fi ber and ma trix on wave dis per sion are pre sented and dis cussed. These re sults are ob tained for the fol low ing cases: the fi ber and ma trix are both with out ini tial strains; only the fi ber is prestretched; only the ma trix is prestretched; the fi ber and ma trix are both prestretched si mul ta neously; the fi ber and ma trix are both precompressed si mul ta neously.
Compressional and torsional wave amplitudes in rods with periodic structures
The Journal of the Acoustical Society of America, 2002
To measure and detect elastic waves in metallic rods a low-frequency electromagnetic-acoustic transducer has been developed. Frequencies range from a few hertz up to hundreds of kilohertz. With appropriate configuration of the transducer, compressional or torsional waves can be selectively excited or detected. Although the transducer can be used in many different situations, it has been tested and applied to a locally periodic rod, which consists of a finite number of unit cells. The measured wave amplitudes are compared with theoretical ones, obtained with the one-dimensional transfer matrix method, and excellent agreement is obtained.
On extensional oscillations and waves in elastic rods
1998
Abstract The authors study the dispersive nature of propagating extensional waves in an infinitely long elastic rod within the framework of the linear theory of a Cosserat rod with two directors. The authors also identify certain material constants in the theory in a manner that is different from those used by others and consequently show that the resulting theory better captures the high-frequency dynamical behavior of three-dimensional rod-like bodies.
Applied Mathematical Modelling, 2009
Torsional wave dispersion Initial stresses Circular cylinder embedded in the infinite medium Third order elastic constants a b s t r a c t Within the framework of the piecewise homogeneous body model with utilization of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modeling of the torsional wave propagation in the initially stressed infinite body containing an initially stressed circular solid cylinder (case 1) and circular hollow cylinder (case 2) are proposed. In these cases, it has been assumed that in the constituents of the considered systems there exist only the normal homogeneous tensional or compressional initial stress acting along the cylinder, i.e. in the direction of wave propagation. In the case where the mentioned initial stresses are not present, the proposed mathematical modeling coincides with that proposed and investigated by other authors within the classical linear theory of elastic waves. The mechanical properties of the cylinder and surrounding infinite medium have been described by the Murnaghan potential. The numerical results related to the torsional wave dispersion and the influence of the mentioned initial stresses on this dispersion are presented and discussed.
On the propagation of intrinsic viscoelastic waves in a cylindrical shell
Journal of Physics: Conference Series, 2022
The article illustrates that viscoelastic wave in an extended cylindrical shell of circular cross-section. To solve boundary value problems used classical methods of mathematical physics. The unwavering quality of the comes about of the work is guaranteed by the rightness of the detailing of issues, the utilize of the classical device of scientific material science and other demonstrated strategies for tackling issues of wave engendering, the consistent legitimacy of the conclusions and the great assentation of the comes about with the uncommon cases known from the references.
Two dimensional wave problems in rotating elastic media
Applied Scientific Research, 1973
The rotation of an elastic medium makes it act anisotropieally and dispersively. The eigenvectors for plane ware propagafion are in general complex and thus the waves are elliptically polarized. In generM the waves are neither pure shear nor pure compressional waves, and their speeds depend on the ratio of rotational frequency of the medium and the angular frequency of the ware.
Waves and Rays in Elastic Continua
Waves and Rays in Elastic Continua, 2014
WAVES AND RAYS IN ELASTIC CONTINUA "Professor Slawinski has written an introductory textbook that rigorously develops the foundations for elastodynamics and wave propagation in anisotropic elastic media in a clear and well written style. The main text is supplemented with many worked examples and suggestions for further reading. This text would be a useful textbook for a senior undergraduate or introductory graduate level, applied mathematics course in waves in elastic media, and as an introduction to research in theoretical seismology." Chris Chapman, Cambridge University "This impressive treatise contains a lucid and comprehensive description of material symmetry in the context of seismic wave propagation. These insights form the foundation of a careful and detailed analysis of seismic waves in anisotropic media. 'Waves & Rays' is very well-suited as a text for a graduate course and as a reference monograph for experts in the field."