Development of parabolic-elliptic formulations for bending edge waves on thin elastic plates

Althobaiti, Saad

Abstract

The project is concerned with the analysis of bending edge waves propagating in thin elastic orthotropic plates, and aims at the derivation of explicit formulations for bending edge waves, generalising recent results for isotropic plates. The derived parabolic elliptic formulations provide significant simplification in analysis and allow efficient approximate solutions to a number of dynamic problems, where the contribution of the edge wave is dominant. The effect of the Winkler-Fuss foundation, supporting the plate is also studied.
First, the eigensolutions in terms of a single plane harmonic function are obtained, serving as a basis for further derivations of asymptotic models oriented to extraction of the contribution of the studied localized waves to the overall dynamic response. The proposed models are obtained through a multi-scale perturbation scheme, also employing properties of plane harmonic functions. The approximate formulations for the bending edge wave field include elliptic partial differential equations, describing the decay away from the edge, along with the parabolic equations on the edge associated with wave propagation. Model examples for excitation of the studied waves are investigated, in particular, including impulse edge loading, internal sources and moving loads. Finally, the effect of inhomogeneity arising from a Winkler-Fuss foundation with periodic stiffness is addressed, revealing novel resonant phenomena.

Citation

Althobaiti, S. (2019). Development of parabolic-elliptic formulations for bending edge waves on thin elastic plates. (Thesis). Keele University. Retrieved from https://keele-repository.worktribe.com/output/413323

• Thesis Type: Thesis
• Publicly Available Date: May 26, 2023
• Public URL: https://keele-repository.worktribe.com/output/413323
• Award Date: 2019-06