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Nonlinear dynamics of elastic rods using Cosserat theory: Modelling and simulation

Research output: Contribution to journalJournal article

Published

Journal publication date15/01/2008
JournalInternational journal of solids and structures
Journal number2
Volume45
Number of pages18
Pages460-477
Original languageEnglish

Abstract

The method of Cosserat dynamics is employed to explore the nonplanar nonlinear dynamics of elastic rods. The rod, which is assumed to undergo flexure about two principal axes, extension, shear and torsion, are described by a general geometrically exact theory. Based on the Cosserat theory, a set of governing partial differential equations of motion with arbitrary boundary conditions is formulated in terms of the displacements and angular variables, thus the dynamical analysis of elastic rods can be carried out rather simply. The case of doubly symmetric cross-section of the rod is considered and the Kirchoff constitutive relations are adopted to provide an adequate description of elastic properties in terms of a few elastic moduli. A cantilever is given as a simple example to demonstrate the use of the formulation developed. The nonlinear dynamic model with the corresponding boundary and initial conditions are numerically solved using the Femlab/Matlab software packages. The corresponding nonlinear dynamical responses of the cantilever under external harmonic excitations are presented through numerical simulations.