From Ziegler to Beck’s column: a nonlocal approach
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Tartalom: http://real.mtak.hu/39958/
Archívum: MTA Könyvtár
Gyűjtemény: Status = Published


Type = Article
Cím:
From Ziegler to Beck’s column: a nonlocal approach
Létrehozó:
Challamel, Noël
Kocsis, Attila
Wang, CM
Lerbet, Jean
Kiadó:
Springer
Dátum:
2016
Téma:
QC01 Mechanics / mechanika
TA Engineering (General). Civil engineering (General) / általános mérnöki tudományok
Tartalmi leírás:
This paper is concerned with the dynamic stability of a microstructured elastic column loaded by
circulatory forces. This nonconservative lattice (or discrete) problem is shown to be equivalent to the finite
difference formulation of Beck’s problem (cantilever column loaded by follower axial force). The lattice
problem can be exactly solved from the resolution of a linear difference eigenvalue problem. The first part of
the paper deals with the theoretical and numerical analyses of this discrete Beck’s problem, with a particular
emphasis on the flutter load sensitivity with respect to the discretization parameters, such as the number
of links of the lattice. The second part of the paper is devoted to the elaboration of a nonlocal equivalent
continuum that possesses similar mathematical or physical properties as compared to the original lattice
model. A continualized nonlocal model is introduced first by expanding the difference operators present in the
lattice equations in terms of differential operators. The length scale of the continualized nonlocal model is size
independent. Next, Eringen’s nonlocal phenomenological stress gradient is considered and applied at the beam
scale in allowance for scale effects of the microstructured Beck column. The nonlocal Euler–Bernoulli beam
model is able to capture the softening scale effect of the lattice model, even if the length scale of Eringen’s
model appears to be size dependent in this case. The continualized nonlocal continuum slightly differs from the
Eringen’s one, in the sense that the length scale affecting the static and the inertia terms differs in the deflection
equation. A general parametric study illustrates the capability of each nonlocal model, the phenomenological
and the continualized one, with respect to the reference lattice model. Nonlocal Beck’s column is shown to
be a transient medium from Ziegler’s column (two-degree-of-freedom system) to the local continuous Beck’s
column (with an infinite degree of freedom).
Nyelv:
angol
Típus:
Article
PeerReviewed
info:eu-repo/semantics/article
Formátum:
text
Azonosító:
Challamel, Noël and Kocsis, Attila and Wang, CM and Lerbet, Jean (2016) From Ziegler to Beck’s column: a nonlocal approach. Archive of Applied Mechanics, 86. pp. 1095-1118. ISSN 0939-1533
Kapcsolat:
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