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Beams with Symmetric Loadings

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...

Shear on the Horizontal Face of a Beam Element

Shear on the Horizontal Face of a Beam Element

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 first...

Beams

Beams

Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
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Beams with Unsymmetric Loadings

Beams with Unsymmetric Loadings

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Related Experiment Video

Updated: May 30, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Reduced side-lobe Airy beams.

Shane Barwick¹

¹Rocky Mound Engineering, 116 White Pine Court, Macon, Georgia 31216, USA. dsbarwick@cox.net

|August 3, 2011

Summary

Researchers reduced side lobes of finite-energy Airy beams using Fourier space apodization. This technique enhances the central lobe

Area of Science:

Optics and Photonics
Beam Propagation
Wave Phenomena

Background:

Finite-energy Airy beams are of interest due to their central lobe's unique intensity properties.
The Airy function, which defines these beams, exhibits decaying side lobes that can negatively impact applications.
Controlling these side lobes is crucial for optimizing Airy beam performance.

Purpose of the Study:

To investigate a method for suppressing the side lobes of finite-energy Airy beams.
To determine if suppressing side lobes affects the desirable properties of the central lobe.
To enhance the practical utility of Airy beams in various applications.

Main Methods:

Utilized nonsymmetric apodization in Fourier space.
Applied this apodization to modify the spatial frequency components of the Airy beam.

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Last Updated: May 30, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

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Analyzed the resulting beam profile and propagation characteristics.

Main Results:

Demonstrated that nonsymmetric apodization effectively reduces and clips the side lobes of the Airy beam.
Showcased significant enhancement of the central lobe's intensity.
Confirmed that the central lobe's properties remain largely unaffected throughout a substantial propagation distance.

Conclusions:

Nonsymmetric Fourier space apodization is an effective technique for controlling Airy beam side lobes.
This method preserves the advantageous characteristics of the central lobe, making Airy beams more suitable for applications.
The findings offer a pathway to improved optical beam shaping and control.