Anti-plane waves in an elastic thin strip with surface energy

Area of Science:

• Solid Mechanics
• Materials Science
• Surface Physics

Background:

• Surface energy effects are crucial in thin elastic structures.
• Linear Gurtin-Murdoch surface elasticity provides a framework for modeling these effects.
• Understanding wave propagation in such materials is vital for advanced applications.

Purpose of the Study:

• To investigate anti-plane shear wave dynamics in elastic plates considering surface energy.
• To analyze the influence of surface elasticity on dispersion relations.
• To examine boundary conditions simulating attachment to rigid substrates.

Main Methods:

• Formulation of two boundary-value problems for complete shear dynamics.
• Application of linear Gurtin-Murdoch surface elasticity theory.
• Detailed analysis of dispersion relations and their dependence on geometric ratios.

Main Results:

• Dispersion curves are significantly influenced by the ratio of plate thickness to characteristic length.
• Surface energy effects alter wave propagation characteristics.
• Different boundary conditions (free vs. clamped faces) lead to distinct dynamic behaviors.

Conclusions:

• Surface elasticity plays a critical role in the anti-plane dynamics of elastic plates.
• The thickness-to-characteristic length ratio is a key parameter governing wave dispersion.
• The models accurately represent elastic films on rigid substrates with varying attachment quality.