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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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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...
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Beams with Unsymmetric Loadings01:17

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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.
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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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Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
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Updated: Jan 11, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Partially coherent persistent hollow beams enabled by cross-phase modulation.

Jun Zeng, Ruyi Li, Zhao Zhang

    Optics Express
    |November 11, 2025
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    Summary
    This summary is machine-generated.

    We introduce partially coherent persistent hollow (PCPH) beams, a new type of light beam. These beams maintain their hollow shape during propagation and are robust in challenging environments.

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    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Wave Propagation

    Background:

    • Partial coherence can improve light propagation stability but often degrades structured intensity profiles.
    • Maintaining central intensity nulls in partially coherent beams is challenging.

    Purpose of the Study:

    • To propose and validate a new class of partially coherent random beams with persistent hollow-core profiles.
    • To investigate the properties and robustness of these beams, termed PCPH beams.

    Main Methods:

    • Generation of PCPH beams using cross-phase modulation.
    • Theoretical analysis of beam propagation and coherence effects.
    • Experimental validation under thermal turbulence.

    Main Results:

    • PCPH beams exhibit persistent hollow-core profiles during far-field propagation.
    • Tunable focusing characteristics and enhanced robustness against environmental disturbances were demonstrated.
    • PCPH beams outperformed conventional vortex beams in maintaining hollow structure under turbulence.

    Conclusions:

    • PCPH beams offer a novel solution for stable propagation of structured light.
    • Their properties make them suitable for applications in optical manipulation and free-space optical communication.
    • PCPH beams show strong potential for robust beam shaping in adverse conditions.