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Related Concept Videos

Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

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 designer...
Deflection of a Beam01:19

Deflection of a Beam

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...
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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 stress...
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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Shearing Stresses in a Beam: Problem Solving01:14

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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...
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Related Experiment Video

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Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
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Published on: April 1, 2020

Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations.

Yajun Li1

  • 1yajun_li@yahoo.com

Applied Optics
|August 12, 2011
PubMed
Summary

This study presents an exact solution for nonparaxial ray tracing through Risley prisms, crucial for free-space optical communications. The findings enable precise beam steering and customizable scan patterns for advanced optical systems.

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Area of Science:

  • Optics and Photonics
  • Free-Space Optical Communications

Background:

  • Risley prisms are optical components used for beam steering.
  • Accurate modeling is essential for applications like free-space optical communications.

Purpose of the Study:

  • To derive an exact solution for nonparaxial ray tracing through Risley prisms.
  • To compare the exact solution with existing third-order theory.
  • To explore the synthesis of scan patterns using Risley prisms.

Main Methods:

  • Nonparaxial ray tracing was performed for four Risley prism configurations.
  • The exact solution was compared against predictions from third-order theory.
  • The generalized exact solution was used to investigate scan pattern synthesis.

Main Results:

  • The exact solution provides accurate predictions for Risley prism systems.
  • Differences between the exact solution and third-order theory were quantified for various materials.
  • The study demonstrates control over scan pattern generation through prism motion.

Conclusions:

  • The exact solution offers a more precise method for analyzing Risley prism performance.
  • This work advances the understanding and application of Risley prisms in optical systems.
  • The findings facilitate the design of systems with tailored beam steering and scanning capabilities.