TY - JOUR
T1 - Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions
AU - Meesala, Vamsi C.
AU - Hajj, Muhammad R.
N1 - Publisher Copyright:
© The Author(s) 2018.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.
AB - The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.
KW - Parametric excitation
KW - boundary conditions
KW - cantilever beam–mass systems
KW - method of multiple scales
KW - perturbation methods
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U2 - 10.1177/1077546318809853
DO - 10.1177/1077546318809853
M3 - Review article
AN - SCOPUS:85060655073
SN - 1077-5463
VL - 25
SP - 485
EP - 496
JO - JVC/Journal of Vibration and Control
JF - JVC/Journal of Vibration and Control
IS - 3
ER -