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Shear on the Horizontal Face of a Beam Element

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To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's...

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Related Experiment Video

Updated: Apr 30, 2026

High-speed Particle Image Velocimetry Near Surfaces

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Published on: June 24, 2013

Virtual source of a Pearcey beam.

Dongmei Deng, Chidao Chen, Xin Zhao

|May 3, 2014

Summary

A virtual source generates Pearcey wave families. A new expression for the paraxial Pearcey beam (PB) includes nonparaxial corrections for enhanced accuracy in diffraction analysis.

Area of Science:

Optics and Photonics
Mathematical Physics

Background:

Pearcey beams are non-diffracting wave solutions.
Accurate modeling of nonparaxial effects is crucial for advanced optical applications.

Purpose of the Study:

To demonstrate a virtual source for generating Pearcey wave families.
To derive a closed-form expression for the Pearcey wave and its paraxial limit.
To obtain an infinite series expression for nonparaxial corrections to the paraxial Pearcey beam (PB).

Main Methods:

Utilizing a virtual source model.
Deriving closed-form and series expressions.
Employing perturbative series of complex-source-point spherical waves.
Applying integral representations of Pearcey waves.

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Main Results:

A virtual source yielding Pearcey wave families is demonstrated.
A closed-form expression for the Pearcey wave is derived, simplifying to the paraxial PB.
An infinite series expression for nonparaxial corrections to the PB is obtained, offering arbitrary accuracy.
The first three terms of the nonparaxial correction series are provided.

Conclusions:

The derived expressions provide a more accurate description of Pearcey beams beyond the paraxial approximation.
This work enhances the understanding and potential applications of Pearcey beams in optical systems.
The infinite series offers a flexible approach for achieving high-accuracy results in nonparaxial beam propagation.