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

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.

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Investigating the Potential of Singly Curved Thin Piezoelectric Transducers for Energy Harvesting and Structural Health Monitoring

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One-dimensional equations for planar piezoelectric curved bars.

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

|November 21, 2007

Summary

Researchers developed simplified one-dimensional equations for piezoelectric curved bars, enabling easier analysis and design of piezoelectric devices. This work aids in understanding coupled mechanical and electrical behaviors in these materials.

Area of Science:

Solid Mechanics
Materials Science
Electrical Engineering

Background:

Derivation of reduced-order models from 3D elasticity is crucial for efficient analysis of complex structures.
Piezoelectric materials exhibit coupled electromechanical behavior, essential for device applications.
Curved bar geometries present unique challenges in mechanical and electrical response modeling.

Discussion:

The study presents a novel set of one-dimensional (1D) equations for coupled extension, flexure, and shear in planar piezoelectric curved bars.
These 1D equations are derived from fundamental 3D equations of piezoelectricity.
The derivation involves power series expansion of mechanical displacement and electric potential in cross-sectional coordinates, retaining lower-order terms.

Key Insights:

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The derived 1D equations simplify the analysis of piezoelectric curved bars.
This simplification is achieved by reducing the dimensionality of the problem while preserving essential physics.
The approach is validated by its utility in practical device design and analysis.

Outlook:

The developed equations can be applied to the design and analysis of various 1D piezoelectric devices.
Further research could explore the application of these equations to more complex geometries or dynamic behaviors.
This work provides a foundation for advanced modeling of piezoelectric structures in micro- and nano-scale devices.