Shear Wave Models in Linear and Nonlinear Elastic Materials
Date
2020-05-13
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0002-6454-669X
Type
Thesis
Degree Level
Masters
Abstract
Nonlinear shear wave models are of significant importance in a large number of areas, including engineering and seismology. The study of such wave propagation models has helped in the prediction and exploration of hidden resources in the Earth. Also, the frequent occurrences of earthquakes and the damage they cause to lives and properties are of more significant concern to the society. Augustus Edward Hough Love studied horizontally polarized shear waves (Love surface waves) in homogeneous elastic media. In the current thesis, after presenting some basic concepts of linear and nonlinear elasticity, we discuss linear Love waves in both isotropic and anisotropic elastic media, and consider extended linear and nonlinear wave propagation models in elastic media, including models of nonlinear Love-type surface waves. A new general partial differential equation model describing the propagation of one- and two-dimensional Love-type shear waves in incompressible hyperelastic materials is derived, holding for an arbitrary form of the stored energy function. The results can be further generalized to include an arbitrary viscoelastic contribution. We also discuss aspects of Hamiltonian mechanics in finite- and infinite-dimensional systems and present Hamiltonian formulations of some nonlinear wave models discussed in this thesis.
Description
Keywords
Love waves, Hyperelastic materials, Stored energy density, Anisotropic media, Elastic media, Incompressible, Hamiltonian
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Mathematics