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Deformation in a Circular Shaft

Deformation in a Circular Shaft

One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

Plastic Deformation in Circular Shafts

Plastic Deformation in Circular Shafts

When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...

Deformations in a Symmetric Member in Bending

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...

Deformations in a Transverse Cross Section

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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...

Plastic Deformations

Plastic Deformations

Plastic deformation represents a fundamental concept in materials science, which explains the irreversible change in the shape of a material when it experiences stress beyond its elastic capability. This phenomenon is important in structural engineering, especially in designing and analyzing cantilever beams—structures that are securely fixed at one end and bear loads at the opposite end. When these beams are subjected to loads within their elastic range, they will return to their original...

Plastic Deformations

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It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...

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Related Experiment Video

Updated: Jun 19, 2026

Shrinkage of Dental Composite in Simulated Cavity Measured with Digital Image Correlation

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Published on: July 21, 2014

Q spoiling and directionality in deformed ring cavities.

J U Nöckel, A D Stone, R K Chang

|October 27, 2009

Summary

A new ray-optics model explains how deforming ring cavities from circular shapes degrades high-Q whispering gallery modes. A critical deformation threshold is identified, beyond which mode quality factor (Q) degrades predictably.

Area of Science:

Optics
Nonlinear Dynamics
Cavity Physics

Background:

High-Q whispering gallery modes in ring cavities are sensitive to geometric imperfections.
Understanding mode degradation is crucial for optical device stability and performance.

Purpose of the Study:

To develop a ray-optics model for predicting the degradation of whispering gallery modes in deformed ring cavities.
To investigate the onset and behavior of mode spoiling as a function of cavity deformation.

Main Methods:

Development of a ray-optics model.
Analysis based on the Kolmogorov-Arnol'd-Moser (KAM) theorem from nonlinear dynamics.

Main Results:

A sharp threshold for the onset of Q spoiling was identified.

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The quality factor (Q) degrades as Q ~ (b - b(c))^(-alpha), with alpha approximately 2.4-2.6 beyond the critical deformation b(c).

Escaping light is predicted to emerge in specific directions.

Conclusions:

The ray-optics model successfully describes Q spoiling in deformed ring cavities.
The Kolmogorov-Arnol'd-Moser (KAM) theorem provides a theoretical basis for the observed spoiling threshold.
The findings allow for prediction of light escape directions from deformed cavities.