TY - JOUR
T1 - Analysis of the lumped mass model for the cantilever beam subject to Grob's swelling pressure
AU - Skrzypacz, Piotr
AU - Bountis, Anastasios
AU - Nurakhmetov, Daulet
AU - Kim, Jong
PY - 2020/6
Y1 - 2020/6
N2 - The lumped mass model is derived from a one-mode Galerkin discretization with the Gauss–Lobatto quadrature applied to the non-linear swelling pressure term. Our reduced-order model of the problem is then analyzed to study the essential dynamics of an elastic cantilever Euler–Bernoulli beam subject to the swelling pressure described by Grob's law. The solutions to the initial value problem for the resulting nonlinear ODE are proved to be always periodic. The numerical solution to the derived lumped mass model satisfactorily matches the finite difference solution of the dynamic beam problem. Including the effect of oscillations at the base of the beam, we show that the model exhibits resonances that may crucially influence its dynamical behavior.
AB - The lumped mass model is derived from a one-mode Galerkin discretization with the Gauss–Lobatto quadrature applied to the non-linear swelling pressure term. Our reduced-order model of the problem is then analyzed to study the essential dynamics of an elastic cantilever Euler–Bernoulli beam subject to the swelling pressure described by Grob's law. The solutions to the initial value problem for the resulting nonlinear ODE are proved to be always periodic. The numerical solution to the derived lumped mass model satisfactorily matches the finite difference solution of the dynamic beam problem. Including the effect of oscillations at the base of the beam, we show that the model exhibits resonances that may crucially influence its dynamical behavior.
KW - Cantilever beam
KW - Lumped mass model
KW - Periodic solution and resonances
KW - Swelling pressure
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U2 - 10.1016/j.cnsns.2020.105230
DO - 10.1016/j.cnsns.2020.105230
M3 - Article
AN - SCOPUS:85080087102
VL - 85
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
M1 - 105230
ER -