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Related Concept Videos

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Bending of Members Made of Several Materials01:11

Bending of Members Made of Several Materials

In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Hooke's Law01:26

Hooke's Law

Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.

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Lamb waves propagation in layered piezoelectric/piezomagnetic plates.

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Love waves propagation in a transversely isotropic piezoelectric layer on a piezomagnetic half-space.

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Updated: Jun 7, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring
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Published on: November 14, 2025

Love waves in functionally graded piezoelectric materials by stiffness matrix method.

Issam Ben Salah1, Yassine Wali, Mohamed Hédi Ben Ghozlen

  • 1Laboratoire de Physique des Matériaux, Faculté des Sciences de Sfax, BP 815, 3018 Sfax, Tunisia. bs_issam@yahoo.fr

Ultrasonics
|November 2, 2010
PubMed
Summary

A numerical matrix method accurately predicts ultrasonic guided wave propagation in functionally graded piezoelectric materials. This approach offers flexibility for analyzing Love wave behavior in layered structures, aiding acoustic device design.

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Last Updated: Jun 7, 2026

Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring
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Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy
07:44

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

Published on: April 27, 2016

Area of Science:

  • Materials Science
  • Acoustics
  • Solid Mechanics

Background:

  • Ultrasonic guided waves are crucial for non-destructive testing and device applications.
  • Functionally graded piezoelectric materials (FGPMs) offer tunable electromechanical properties.
  • Analytical methods for FGPMs can be complex and limited in scope.

Purpose of the Study:

  • To develop and validate a numerical matrix method for analyzing ultrasonic guided wave propagation in FGPM heterostructures.
  • To compare the numerical approach with existing analytical methods.
  • To investigate the influence of material gradients on wave behavior and device performance.

Main Methods:

  • A numerical matrix method based on the stiffness matrix approach was employed.
  • The FGPM layer was stratified into homogeneous layers to apply the ordinary differential equation method.
  • Love wave propagation was analyzed for electrical open and short circuit conditions.

Main Results:

  • The numerical method showed good agreement with analytical solutions, demonstrating its validity.
  • Different gradient variations in mechanical and electrical properties led to opposing effects on wave propagation.
  • The study determined dispersive curves and phase velocities, analyzing the impact of gradient coefficients on electromechanical coupling, stress, electrical potential, and mechanical displacement.

Conclusions:

  • The stiffness matrix method provides a flexible and conceptually simple approach for analyzing ultrasonic guided waves in FGPMs.
  • The findings are valuable for designing high-performance acoustic surface devices and accurately predicting Love wave propagation.
  • Understanding gradient effects is key to optimizing FGPM-based acoustic applications.