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Related Concept Videos

Deflection of a Beam01:19

Deflection of a Beam

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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
869
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

631
Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
631
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

771
A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
771
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

519
In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the...
519
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

596
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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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Meta-q-plate for complex beam shaping.

Wei Ji1, Chun-Hong Lee2, Peng Chen1

  • 1National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China.

Scientific Reports
|May 7, 2016
PubMed
Summary
This summary is machine-generated.

Researchers developed a novel meta-q-plate for advanced optical beam shaping. This device offers unprecedented control over light

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Area of Science:

  • Optics and Photonics
  • Metamaterials
  • Liquid Crystal Technology

Background:

  • Optical beam shaping is crucial for various applications.
  • Existing methods have limitations in flexibility and control.

Purpose of the Study:

  • To propose and demonstrate a novel meta-q-plate with arbitrarily space-variant optical axes.
  • To achieve unprecedented flexibility in optical vortex manipulation.

Main Methods:

  • Utilized liquid crystal photoalignment with a polarization-sensitive alignment agent.
  • Employed a dynamic micro-lithography system for fabrication.
  • Fabricated meta-q-plates with diverse topological charges and azimuthal angles.

Main Results:

  • Generated complex optical beams with elliptical, asymmetrical, multi-ringed, and hurricane transverse profiles.
  • Demonstrated unprecedented flexibility in manipulating optical vortices.
  • Theoretically analyzed and experimentally verified the properties of hurricane optical vortex beams.

Conclusions:

  • The meta-q-plate design significantly enhances beam shaping capabilities.
  • This technology facilitates point-to-point manipulation of light's polarization and spatial degrees of freedom.
  • Paves the way for advancements in optical manipulation, OAM-based informatics, and quantum optics.