Journal of Sound and Vibration 429 (2018) 147–161 Contents lists available at ScienceDirect Journal of Sound and Vibration journal homepage: www.elsevier.com/locate/jsvi Transverse impact of a Hertzian body with an inﬁnitely long Euler-Bernoulli beam Arindam Bhattacharjee , Anindya Chatterjee Mechanical Engineering, IIT Kanpur, India art i cle i n f o abs t ract Article history: We study in detail, using analytical approximations and numerical solution, the transverse Received 16 June 2017 impact interaction of a compact body with an inﬁnitely long Euler-Bernoulli beam. The beam Revised 25 January 2018 is initially stationary, linear and dissipation-free; a Hertzian spring mediates body-beam con- Accepted 29 April 2018 tact; and the body is otherwise rigid. Impact interaction obeys two nonlinear differential Available online 24 May 2018 equations with a fractional order derivative. Prior progress on the inﬁnite-beam problem Handling Editor: L. N. Virgin has been limited. Here we completely characterize the possible contact behaviors in terms of one nondimensional number, S, which governs separations and sustained contact regimes. Keywords: For small S, there is just one contact phase followed by separation. For large S no separation Impact occurs, and sustained contact occurs with decaying oscillations. For intermediate S, separation Hertzian occurs one
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