TY - JOUR
T1 - Stability analysis of inhomogeneous equilibrium for axially and transversely excited nonlinear beam
AU - Kaya-Cekin, Emine
AU - Aulisa, Eugenio
AU - Ibragimov, Akif
AU - Seshaiyer, Padmanabhan
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/9
Y1 - 2011/9
N2 - In this work we consider the dynamical response of a non-linear beam with viscous damping, perturbed in both the transverse and axial direc- tions. The system is modeled using coupled non-linear momentum equations for the axial and transverse displacements. In particular we show that for a class of boundary conditions (beam clamped at the extremes) and uniformly distributed load, there exists a non-uniform equilibrium state. Different mod- els of damping are considered: first, third and fifth order dissipation terms. We show that in all cases in the presence of the damping forces, the excited beam is stable near the equilibrium for any perturbation. An energy estimate approach is used in order to identify the space in which the solution of the perturbed system is stable.
AB - In this work we consider the dynamical response of a non-linear beam with viscous damping, perturbed in both the transverse and axial direc- tions. The system is modeled using coupled non-linear momentum equations for the axial and transverse displacements. In particular we show that for a class of boundary conditions (beam clamped at the extremes) and uniformly distributed load, there exists a non-uniform equilibrium state. Different mod- els of damping are considered: first, third and fifth order dissipation terms. We show that in all cases in the presence of the damping forces, the excited beam is stable near the equilibrium for any perturbation. An energy estimate approach is used in order to identify the space in which the solution of the perturbed system is stable.
KW - Euler-Bernoulli beam
KW - Non-linear partial differential equations
KW - Stability analysis
UR - http://www.scopus.com/inward/record.url?scp=82155166527&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2011.10.1447
DO - 10.3934/cpaa.2011.10.1447
M3 - Article
AN - SCOPUS:82155166527
VL - 10
SP - 1447
EP - 1462
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
SN - 1534-0392
IS - 5
ER -