Abstract
We study the reflection from a transverse notch and the propagation of a longitudinal decaying traveling wave in a bar by using the simplest model of the stress-strain state in the notch region and obtain the solution dependence on the notch parameters. The solution of the inverse problem permits determining the notch coordinate and the parameter determining its depth and length from the data describing the incident and reflected waves at the observation site.
Similar content being viewed by others
References
B. V. Sidorov and S. A. Martynov, “Recommended Technology of Diagnostics of Buried Pipelines,” Kontrol’. Diagnostika, No. 12, 18–19 (2005)
Yu. V. Van’kov, R. B. Kazakov, and E. R. Yakovleva, “Natural Frequencies as Diagnostic Criteria for Flaw Detection,” Electronic J. “Technical Acoustics,” http://ejta.org, 2003, 5.
M. A. Il’gamov, “Diagnostics of Damage of a Vertical Rod,” Trudy Inst. Mekh. UNTs RAN, No. 5, 201–211 (2007).
G. Biscontin, A. Morassi, and P. Wendel, “Asymptotic Separation of Spectrum in Notched Rods,” J. Vib. Contr. 4(3), 237–251 (1998).
G. M. L. Gladwell, Inverse Problems in Vibration (Kluwer, Dordrecht, 2004; NITs “Regular. Khaotich. Din.,” Moscow-Izhevsk, 2008).
T. Pritz, “Apparent Complex Young’s Modulus of a Longitudinally Vibrating Viscoelastic Rod,” J. Sound Vibr. 77(1), 93–100 (1981).
D. Benatar, D. Rittel, and A. L. Yarin, “Theoretical and Experimental Analysis of Longitudinal Wave Propagation in Cylindrical Viscoelastic Rods,” J. Mech. Phys. Solids 51(8), 1413–1431 (2003).
S. L. Lopatnikov, B. A. Gama, K. Krauthouser, and G. Gillespie, “Applicability of the Classical Analysis of Experiments with Split Hopkins Pressure Bar,” Pis’ma Zh. Techn. Fiz. 30(3), 39–46 (2004) [Tech. Phys. Lett. (Engl. Transl.) 30 (2), 102–105 (2004)].
H. Kolsky, “An Investigation of Mechanical Properties of Materials at Very High Rates of Loading,” Proc. Phys. Soc. London. Ser. B 62(359), 676–700 (1949).
V. V. Meleshko, A. A. Bondarenko, S. A. Dovgii, et al., “Elastic Waveguides: History and the Present,” Mat. Metody Fiz.-Mekh. Polya 51(2), 86–104 (2008).
A. O. Vatul’yan, Inverse Problems in Mechanics of a Deformable Solid (Fizmatlit, Moscow, 2007) [in Russian].
A. O. Vatul’yan and N. O. Soluyanov, “Determining the Location and Dimensions of a Cavity in an Elastic Rod,” Defectoskop. 41(9), 44–56 (2005) [Russ. J. Nondestruct. Test. (Engl. Transl.) 41 (9), 586–593 (2005)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.A. Il’gamov, A.G. Khakimov, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 4, pp. 116–125.
About this article
Cite this article
Il’gamov, M.A., Khakimov, A.G. Reflection of a decaying traveling wave from a notch in a bar. Mech. Solids 46, 589–596 (2011). https://doi.org/10.3103/S0025654411040091
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654411040091