Related Experiment Video
Updated: Jul 16, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring
Published on: November 14, 2025
Energy trapping of thickness-shear vibration modes of elastic plates with functionally graded materials
Abstract:
Energy trapping has important applications in the design of thickness-shear resonators. Considerable efforts have been made for the effective utilization and improvement of energy trapping with variations of plate configurations, such as adding electrodes and contouring. As a new approach in seeking improved energy trapping feature, we analyze thickness-shear vibrations in an elastic plate with functionally graded material (FGM) of in-plane variation of mechanical properties, such as elastic constants and density. A simple and general equation governing the thickness-shear modes is derived from a variational analysis. A plate with piecewise constant material properties is analyzed as an example. It is shown that such a plate can support thickness-shear vibration modes with obvious energy trapping. Bechmann's number for the existence of only one trapped mode also can be determined accordingly.
Related Concept Videos
Elastic Strain Energy for Shearing Stresses
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Members Made of Elastoplastic Material
As the bending moment...
Strain-Energy Density
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
Bending of Members Made of Several Materials
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Elastic Strain Energy for Normal Stresses
If...

