TY - JOUR

T1 - Nonlinear dynamics of elastic rods using Cosserat theory

T2 - modelling and simulation

AU - Cao, Dengqing

AU - Tucker, Robin

PY - 2008/1/15

Y1 - 2008/1/15

N2 - 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.

AB - 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.

KW - Cosserat model

KW - Nonlinear dynamics

KW - Slender rod

KW - Modelling and simulation

KW - Femlab

KW - Matlab

U2 - 10.1016/j.ijsolstr.2007.08.016

DO - 10.1016/j.ijsolstr.2007.08.016

M3 - Journal article

VL - 45

SP - 460

EP - 477

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 2

ER -