Stability Analysis of a Nonlinear Plate in Mean Flow

Abstract

A stability analysis of a nonlinear plate clamped to an infinite baffle in mean flow is given. The effect of structural nonlinearities induced by in-plane forces and shearing forces due to stretching of plate bending motion, and that of viscous damping are taken into account in the derivation of the plate equation. The plate flexural displacement is obtained by modal expansion based on Galerkin's method. The critical mean flow speeds at which local instabilities may occur are determined by Routh algorithm. The mechanisms that trigger the local instabilities are uncovered. The effect of structural nonlinearities, and that of plate aspect and plate length/thickness ratios on local instabilities are examined. Numerical examples of the transition from stable to locally unstable vibration, as the mean flow speed exceeds the critical values, are demonstrated. The results show that while the overall amplitude of the plate flexural displacement may be bounded when the mean flow speed exceeds the critical values, plate vibration may be locally unstable, jumping from one equilibrium position to another. Furthermore, the jumping may be random, and the plate vibration may seem chaotic. The results also show that viscous damping may stabilize plate flexural vibration and settle the plate in one of its equilibria.

Microstructural analysis of a carbon fibre reinforced AZ91D magnesium alloy composite

“…This is due to the imposed pressure during solidification, which raises the solidification temperature and increases the cooling rate, which in turn suppresses discontinuousˇprecipitation. 34 It has long been established that discontinuousˇprecipitates nucleate at high-angle incoherent grain boundaries in this alloy and that a Burgers orientation relationship exists betweenˇand˛-Mg. 11,34,35 The present work is in complete agreement with these findings.…”

“…10 Fibres with higher surface energies, such as low-modulus carbon fibres, nucleate moreˇprecipitates than their higher modulus counterparts, resulting in greater precipitate coverage. 11 Interfacialˇprecipitation has been shown to increase with increasing Al content between 2 and 4 wt.%. 12 Furthermore, Diwanji and Hall 12 suggested that there is a local Al enrichment associated withˇprecipitation at the interface, and a depleted zone adjacent to this.…”

“…The extensivě precipitation at the surface of fibres observed in this study is in disagreement with the work by Wu and Zhu. 11 This probably results from a difference in fibre surface energies, however no clear description is available for the fibre type employed by these authors to allow an accurate comparison to be made.…”

“…This contradicts other workers who have examined HM carbon fibre in Mg-Al alloy composites who report continuousˇprecipitation in the matrix remote from interfaces. 11,26 High-resolution electron microscopy revealed a distinct interfacial layer ¾20 nm wide extending around the fibres (Fig. 8(a)).…”

Microsegregation during Solidification of Graphitic Fiber-Reinforced Aluminum Alloys under External Heat Sinks

“…[24] Thus, the lack of significant precipitation of eutectic constituents at the GRF interfaces can be related to small solute segregation at the fiber/melt interfaces. Wu et al [25] have examined various eutectic morphologies exhibited in CF-and GRF-reinforced Mg-based AZ81 composites. It is shown that the Mg 17 Al 12 eutectic constituent is discontinuously precipitated on carbon fibers, but continuously on graphite fibers.…”