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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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Deflection of a Beam01:19

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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.
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Prismatic Beams: Problem Solving01:15

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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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Shear on the Horizontal Face of a Beam Element01:16

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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 energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a plane electromagnetic wave with E0 and B0 as the peak electric and magnetic fields and traveling along the x-axis, the time-varying energy flux can be given by the following equation:
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Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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Intensity-symmetric Airy beams.

P Vaveliuk, Alberto Lencina, Jose A Rodrigo

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |September 15, 2015
    PubMed
    Summary
    This summary is machine-generated.

    Researchers introduce novel intensity-symmetric Airy beams in rectangular coordinates. These unique optical beams exhibit autofocusing, self-bending, and reversal propagation, with potential applications in optical trapping and waveguide writing.

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    Area of Science:

    • Optics and Photonics
    • Nonlinear Optics
    • Beam Propagation

    Background:

    • Airy beams are known for their unique propagation dynamics.
    • Paraxial beams in rectangular coordinates typically lack the complex behaviors observed in these novel beams.
    • Understanding beam symmetry is crucial for controlling light-matter interactions.

    Purpose of the Study:

    • To theoretically, numerically, and experimentally investigate a new class of intensity-symmetric Airy beams.
    • To explore the unique propagation characteristics, including autofocusing, collapse, self-bending, and reversal.
    • To demonstrate the potential applications of these beams in optical technologies.

    Main Methods:

    • Theoretical analysis based on spectral phase symmetries and Fourier transforms (cosine and sine).
    • Numerical simulations to model beam propagation.
    • Experimental generation and characterization of the intensity-symmetric Airy beams.

    Main Results:

    • Introduced symmetric and antisymmetric Airy beams with intensity symmetry in rectangular coordinates.
    • Observed autofocusing, collapse, self-bending, and reversal propagation.
    • Demonstrated experimental generation, confirming theoretical predictions.
    • Highlighted unique asymmetric intensity distribution with respect to the Fourier plane.

    Conclusions:

    • The novel intensity-symmetric Airy beams exhibit unprecedented propagation dynamics in a rectangular frame.
    • These beams offer new possibilities for applications such as planar waveguide writing and optical trapping.
    • The findings expand the understanding of light beam behavior and control.