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Related Concept Videos

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...

Beams with Unsymmetric Loadings

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

Deflection of a Beam

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...

Deformation of a Beam under Transverse Loading

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...

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...

Principal Stresses in a Beam

Principal Stresses in a Beam

In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
Analyzing principal stresses is crucial, especially in...

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Related Experiment Video

Updated: Jun 6, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Twisted hyperbolic-sine-correlated beams.

Siyu Xu, Haiyun Wang, Xiaofeng Peng

|November 22, 2024

Summary

Researchers introduced novel twisted hyperbolic-sine-correlated (THSC) beams. These beams offer control over light

Area of Science:

Optics and Photonics
Beam Physics
Coherence Theory

Background:

Coherence properties of light beams are fundamental to their propagation and applications.
Non-uniformly correlated beams offer unique control over beam characteristics.
Twisted phase structures introduce complex spatial correlations.

Purpose of the Study:

Introduce a new class of spatially non-uniformly correlated beams: twisted hyperbolic-sine-correlated (THSC) beams.
Investigate the propagation dynamics and characteristics of THSC beams.
Demonstrate experimental synthesis and analysis of THSC beams.

Main Methods:

Numerical simulations to analyze beam propagation properties.
Characterization of coherence structure using hyperbolic sine functions and twist phase.

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Last Updated: Jun 6, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

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Published on: March 20, 2017

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

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Published on: August 12, 2013

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Experimental setup for synthesizing and observing THSC beam evolution.

Main Results:

THSC beam propagation is significantly influenced by order numbers and twist factor.
Control over spectral density and orbital angular momentum (OAM) flux density achieved.
Formation of diverse far-field intensity profiles (doughnut, rectangular, dumbbell) and OAM flux distributions (windmill-like).
Observed unique propagation characteristics like diffraction suppression, lateral shifts, and beam rotation.
Experimental validation of synthesized THSC beams and their intensity evolution.

Conclusions:

THSC beams represent a novel class of optical beams with tunable spatial coherence.
The introduced parameters offer precise control over beam propagation and far-field patterns.
Experimental realization confirms the feasibility of generating and studying THSC beams.