Abstract
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.
| Original language | English |
|---|---|
| Article number | 105230 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 85 |
| Issue number | 85 |
| DOIs | |
| Publication status | Published - Jun 2020 |
Funding
This research was supported by the Horizon 2020 grant No 778360 . Dr. Piotr Skrzypacz is indebted to Prof. Dongming Wei from the Mathematics Department at the Nazarbayev University for fruitful discussions.
Keywords
- Cantilever beam
- Lumped mass model
- Periodic solution and resonances
- Swelling pressure
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics