Abstract
In the present study, the geometrically non-linear vibrations of thin infinitely long rectangular plates subjected to axial flow and concentrated harmonic excitation are investigated for different flow velocities. The plate is assumed to be periodically simply supported with immovable edges and the flow channel is bounded by a rigid wall. The equations of motion are obtained based on the von Karman non-linear plate theory retaining in-plane inertia and geometric imperfections by employing Lagrangian approach. The fluid is modeled by potential flow and the flow perturbation potential is derived by applying the Galerkin technique. A code based on the pseudo-arc-length continuation and collocation scheme is used for bifurcation analysis. Results are shown through bifurcation diagrams of the static solutions, frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as flow velocity and geometric imperfections, on the stability of the plate and its geometrically non-linear vibration response to harmonic excitation are fully discussed and the convergence of the solutions is verified.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 54-65 |
| Number of pages | 12 |
| Journal | International Journal of Non-Linear Mechanics |
| Volume | 66 |
| DOIs | |
| State | Published - Nov 2014 |
| Externally published | Yes |
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Keywords
- Axial-flow
- Fluid-structure interaction
- Non-linear vibrations
- Plate
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
Cite this
Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow. / Tubaldi, E.; Alijani, F.; Amabili, M.
In: International Journal of Non-Linear Mechanics, Vol. 66, 11.2014, p. 54-65.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow
AU - Tubaldi, E.
AU - Alijani, F.
AU - Amabili, M.
PY - 2014/11
Y1 - 2014/11
N2 - In the present study, the geometrically non-linear vibrations of thin infinitely long rectangular plates subjected to axial flow and concentrated harmonic excitation are investigated for different flow velocities. The plate is assumed to be periodically simply supported with immovable edges and the flow channel is bounded by a rigid wall. The equations of motion are obtained based on the von Karman non-linear plate theory retaining in-plane inertia and geometric imperfections by employing Lagrangian approach. The fluid is modeled by potential flow and the flow perturbation potential is derived by applying the Galerkin technique. A code based on the pseudo-arc-length continuation and collocation scheme is used for bifurcation analysis. Results are shown through bifurcation diagrams of the static solutions, frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as flow velocity and geometric imperfections, on the stability of the plate and its geometrically non-linear vibration response to harmonic excitation are fully discussed and the convergence of the solutions is verified.
AB - In the present study, the geometrically non-linear vibrations of thin infinitely long rectangular plates subjected to axial flow and concentrated harmonic excitation are investigated for different flow velocities. The plate is assumed to be periodically simply supported with immovable edges and the flow channel is bounded by a rigid wall. The equations of motion are obtained based on the von Karman non-linear plate theory retaining in-plane inertia and geometric imperfections by employing Lagrangian approach. The fluid is modeled by potential flow and the flow perturbation potential is derived by applying the Galerkin technique. A code based on the pseudo-arc-length continuation and collocation scheme is used for bifurcation analysis. Results are shown through bifurcation diagrams of the static solutions, frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as flow velocity and geometric imperfections, on the stability of the plate and its geometrically non-linear vibration response to harmonic excitation are fully discussed and the convergence of the solutions is verified.
KW - Axial-flow
KW - Fluid-structure interaction
KW - Non-linear vibrations
KW - Plate
UR - http://www.scopus.com/inward/record.url?scp=84907051005&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84907051005&partnerID=8YFLogxK
U2 - 10.1016/j.ijnonlinmec.2013.12.004
DO - 10.1016/j.ijnonlinmec.2013.12.004
M3 - Article
AN - SCOPUS:84907051005
VL - 66
SP - 54
EP - 65
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
SN - 0020-7462
ER -