Mathematical analysis of localised bending waves in thin elastic structures

Abstract

In this thesis, an extensive investigation is carried out to analyse the mechanical behaviour of surface waves, specifically the bending edge waves. These waves are guided by the free boundary of a thin plate supported by an elastic foundation. They are also studied in a circular cylindrical shell, both semi-infinite and infinite in extent. The examination of the dispersion of the bending edge wave is carried out within the framework of the classical Kirchho↵-Love assumptions of thin plates and shells. An in-depth analysis of the influence of the mechanical properties, such as di↵erent types of material anisotropy, i.e., piezoelectric, piezomagnetic, functionally graded (FG), thermoelasticity, porosity, and external point loads, is conducted. These investigations also examine the e↵ects of the microstructure, including surface elasticity and the couple stress theory of the medium, on the dispersion of bending edge waves. The implementation of asymptotic methods in the dispersion of the bending edge wave on plates and shells enables us to derive an approximate dispersion relation, allowing for a systematic mathematical analysis to extract the e↵ects of the di↵erent mechanical properties involved in the considered model.