Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow

E. Tubaldi, F. Alijani, M. Amabili

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)54-65
Number of pages12
JournalInternational Journal of Non-Linear Mechanics
Volume66
DOIs
StatePublished - Nov 2014
Externally publishedYes

Fingerprint

Nonlinear Vibration
Rectangular Plate
Axial flow
Nonlinear Stability
Flow velocity
Defects
Bifurcation (mathematics)
Potential flow
Imperfections
Channel flow
Equations of motion
Frequency response
Harmonic
Excitation
Pseudo-arc
Immovable
Phase Plane
Plate Theory
Fluids
Arc length

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 journalArticle

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AU - Alijani, F.

AU - Amabili, M.

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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.

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