Hamiltonian modelling and buckling analysis of a nonlinear flexible beam with actuation at the bottom

Megha V. Trivedi, Ravi N. Banavar and Paul Kotyczka

Mathematical and Computer Modelling of Dynamical Systems, 2016, vol. 22, issue 5, 475-492

Abstract: The use of beams and similar structural elements is finding increasing application in many areas including micro and nanotechnology devices. For the purpose of buckling analysis and control, it is essential to account for nonlinear terms in the strains while modelling these flexible structures. Further, the Poisson’s effect can be accounted in modelling by the use of a two-dimensional stress–strain relationship. This paper studies the buckling effect for a slender, vertical beam (in the clamped-free configuration) with horizontal actuation at the fixed end and a tip-mass at the free end. Including also the inextensibility constraint of the beam, the equations of motion are derived. A preliminary modal analysis of the system has been carried out to describe candidate post-buckling configurations and study the stability properties of these equilibria. The vertical configuration of the beam under the action of gravity is without loss of generality, since the objective is to model a potential field that determines the equilibria. Neglecting the inextensibility constraint, the equations of motion are then casted in port-Hamiltonian form with appropriately defined flows and efforts as a basis for structure-preserving discretization and simulation. Finally, the finite-dimensional model is simulated to obtain the time response of the tip-mass for different loading conditions.

Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/13873954.2016.1201517 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:nmcmxx:v:22:y:2016:i:5:p:475-492

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/NMCM20

DOI: 10.1080/13873954.2016.1201517

Access Statistics for this article

Mathematical and Computer Modelling of Dynamical Systems is currently edited by I. Troch

More articles in Mathematical and Computer Modelling of Dynamical Systems from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().