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Related Concept Videos

Beams01:30

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.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...
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...
Shear on the Horizontal Face of a Beam Element01:16

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 with Symmetric Loadings01:15

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...
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.
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Impact Loading on a Cantilever Beam01:13

Impact Loading on a Cantilever Beam

The analysis of a cantilever beam with a circular cross-section subjected to impact loading at its free end illustrates the conversion of potential energy from a dropped object into kinetic energy, which is then absorbed by the beam as strain energy. This process is crucial for understanding how materials behave under dynamic loads, which is important in fields such as construction and aerospace.
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High-speed Particle Image Velocimetry Near Surfaces
11:59

High-speed Particle Image Velocimetry Near Surfaces

Published on: June 24, 2013

Virtual source for an Airy beam.

Shaohui Yan1, Baoli Yao, Ming Lei

  • 1State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China.

Optics Letters
|November 21, 2012
PubMed
Summary
This summary is machine-generated.

Researchers found a virtual source to create Airy waves. This method generates freely accelerating, non-diffracting Airy beams and includes corrections for non-paraxial conditions.

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Area of Science:

  • Optics and Photonics
  • Theoretical Physics

Background:

  • Airy beams are known for their unique properties, including self-acceleration and resistance to diffraction.
  • Understanding the generation and behavior of Airy beams is crucial for applications in optical manipulation and imaging.

Purpose of the Study:

  • To identify a virtual source for generating Airy waves.
  • To derive a spectral integral expression for Airy waves.
  • To determine nonparaxial corrections to the paraxial Airy beam.

Main Methods:

  • Derivation of a spectral integral expression for Airy waves.
  • Analysis of the paraxial limit to obtain the Airy beam.
  • Calculation of the first two orders of nonparaxial corrections.

Main Results:

  • Identification of a virtual source for Airy wave generation.
  • The derived spectral expression yields a freely accelerating, nondiffracting, finite energy Airy beam in the paraxial limit.
  • The first two orders of nonparaxial corrections to the paraxial Airy beam were determined.
  • A connection was established between the Airy wave and the complex source point spherical wave.

Conclusions:

  • The study successfully identified a virtual source for Airy wave generation.
  • The derived spectral representation provides a comprehensive description of Airy waves, including nonparaxial effects.
  • The findings offer new insights into the fundamental properties and generation of Airy beams.