PSI - Issue 23

Viacheslav Mokryakov et al. / Procedia Structural Integrity 23 (2019) 143–148 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

148

6

5. Conclusion An infinite elastic rod of circular cross-section, in which axisymmetric Pochhammer – Chree longitudinal waves are excited, is considered. The mechanical characteristics of the material correspond to the properties of the steel. The maximal tensions and shears in the rod under conditions of zero mode for frequencies up to 3 MHz are considered. It is shown that at low frequencies the maximal tension ( ≲ 1.3 MHz) and shear ( ≲ 1.7 MHz) occur on the rod axis. It was shown that the maximum extension on the axis can be 3.164 times greater than on the surface, and the maximum shift is 4.056 times. From this we can make conclusion. If you control the strength of the rod structure by measuring the surface stresses, you must introduce a correction depending on the vibration frequency, taking into account the effect of localization of stresses on the axis. Acknowledgements The author is grateful to Prof. S.V. Kuznetsov and Prof. Yu. N. Radaev for valuable advice. The work is supported by the Russian Foundation for Basic Research (Project № 19-01-00100). Pochhammer, L., 1876. Ueber die Fortpflanzungsgeschwindigkeiten kleiner Schwingungen in einem unbegrenzten isotropen Kreiscylinder. J. Reine Angew. Math. V. 81. S. 324-336. Chree, C., 1886. Longitudinal vibrations of a circular bar. Quart. J. Pure Appl. Math. V. 21. P. 287-298. Chree, C., 1889. The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solutions and applications. Trans. Cambridge Philos. Soc. V. 14. P. 250-309. Field, G.S., 1931. Velocity of sound in cylindrical rods. Canadian J. Research. V.5. P.619-624. Hudson, G.E., 1943. Dispersion of elastic waves in solid circular cylinders. Phys. Rev. V. 63. P. 46-51. Kolsky, H. , 1955. Stress waves in solids. Oxford. pp. 194. Redwood, M., Lamb, J., 1957. On propagation of high frequency compressional waves in isotropic cylinders. Proc. Phys. Soc. Section B. London. V.70. N.1. P.136-143. Onoe, M., McNiven, H.D., Mindlin, R.D., 1962. Dispersion of axially symmetric waves in elastic rods. Trans. ASME J. Appl. Mech. V. 29. P. 729-734. Hutchinson, J. R., Percival, C. M., 1968. Higher modes of longitudinal wave propagation in thin rod. J. Acoust. Soc. Amer. V. 44. P. 1204-1210. Zemanek, J., 1972. An experimental and theoretical investigation of elastic wave propagation in a cylinder. J. Acoust. Soc. Amer. V. 51. P. 265 283. Graff, K.F., 1991. Wave motion in elastic solids. New York: Dover, 692 p. Kovalev, V.A., Radaev, Y.N., 2010. Wave problems of the field theory and thermomechanics. Saratov: Saratov University Press, pp. 340. Zhou, W. et al., 2016. Guided torsional wave generation of a linear in-plane shear piezoelectric array in metallic pipes. Ultrasonics. V. 65. P. 69 – 77. Garcia-Sanchez, D. et al., 2016. Acoustic confinement in superlattice cavities. Phys. Rev. A. V. 94. P. 033813-1 - 033813-6. Othman, R. 2017. A fractional equation to approximate wave dispersion relation in elastic rods. Strain. V. 53. N. 4. e12228. P. 1-10. Li, Zh., Jing, L., Murch, R., 2017. Propagation of monopole source excited acoustic waves in a cylindrical high-density polyethylene pipeline. J. Acoust. Soc. Amer. V.142. P.3564-3579. Zima, B., Rucka, M., 2018. Guided ultrasonic waves for detection of debonding in bars partially embedded in grout. Constr. Build. Mat. V. 168. P. 124 – 142. Ilyashenko, A.V., Kuznetsov, S.V., 2018. Pochhammer – Chree waves: polarization of the axially symmetric modes. Arch. Appl. Mech. V. 88. N. 8. P. 1385-1394. Cerv J. et al., 2016. Wave motion in a thick cylindrical rod undergoing longitudinal impact. Wave Motion. V. 66. P. 88-105. References