Transverse impact of a Hertzian body with an infinitely long Euler-Bernoulli beam

Transverse impact of a Hertzian body with an infinitely long Euler-Bernoulli beam We study in detail, using analytical approximations and numerical solution, the transverse impact interaction of a compact body with an infinitely long Euler-Bernoulli beam. The beam is initially stationary, linear and dissipation-free; a Hertzian spring mediates body-beam contact; and the body is otherwise rigid. Impact interaction obeys two nonlinear differential equations with a fractional order derivative. Prior progress on the infinite-beam problem 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. For small S, there is just one contact phase followed by separation. For large S no separation occurs, and sustained contact occurs with decaying oscillations. For intermediate S, separation occurs one or more times, followed eventually by sustained contact. The number of separations can be large over a small range of S. A semi-analytical approximation matches well the smaller-S behavior until first separation. A separate asymptotic approximation matches the long-time sustained contact behavior for higher S, independent of the intervening number of separations. The two approximations work on overlapping ranges of S. Neither approximation captures the multiple separations of intermediate S, where we use full numerics with a published recipe for fractional order systems. The numerics match the abovementioned analytical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Sound and Vibration Elsevier

Transverse impact of a Hertzian body with an infinitely long Euler-Bernoulli beam

Loading next page...
 
/lp/elsevier/transverse-impact-of-a-hertzian-body-with-an-infinitely-long-euler-DUW2npMAj5
Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0022-460X
eISSN
1095-8568
D.O.I.
10.1016/j.jsv.2018.04.040
Publisher site
See Article on Publisher Site

Abstract

We study in detail, using analytical approximations and numerical solution, the transverse impact interaction of a compact body with an infinitely long Euler-Bernoulli beam. The beam is initially stationary, linear and dissipation-free; a Hertzian spring mediates body-beam contact; and the body is otherwise rigid. Impact interaction obeys two nonlinear differential equations with a fractional order derivative. Prior progress on the infinite-beam problem 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. For small S, there is just one contact phase followed by separation. For large S no separation occurs, and sustained contact occurs with decaying oscillations. For intermediate S, separation occurs one or more times, followed eventually by sustained contact. The number of separations can be large over a small range of S. A semi-analytical approximation matches well the smaller-S behavior until first separation. A separate asymptotic approximation matches the long-time sustained contact behavior for higher S, independent of the intervening number of separations. The two approximations work on overlapping ranges of S. Neither approximation captures the multiple separations of intermediate S, where we use full numerics with a published recipe for fractional order systems. The numerics match the abovementioned analytical results.

Journal

Journal of Sound and VibrationElsevier

Published: Sep 1, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off