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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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Gauss's Law: Spherical Symmetry01:26

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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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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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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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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Related Experiment Video

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Symmetric Pearcey Gaussian beams.

You Wu, Jiajia Zhao, Zejia Lin

    Optics Letters
    |May 14, 2021
    PubMed
    Summary

    A novel symmetric Pearcey Gaussian beam (SPGB) exhibits enhanced focusing intensity and controllable properties. This new beam, demonstrated in theory and experiment, shows potential for particle guiding applications.

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    Area of Science:

    • Optics and Photonics
    • Beam Physics
    • Nonlinear Optics

    Background:

    • Autofocusing beams offer unique propagation dynamics.
    • Pearcey integrals are known for complex beam shaping.
    • Symmetric Airy beams have demonstrated controllable focusing.

    Purpose of the Study:

    • Introduce a new type of autofocusing and symmetric beam.
    • Investigate the focusing properties and controllability of the novel beam.
    • Explore the potential of the beam for particle guiding.

    Main Methods:

    • Theoretical derivation of the symmetric Pearcey Gaussian beam (SPGB).
    • Experimental generation and characterization of the SPGB.
    • Analysis of beam intensity distribution, focal length, and vortex guiding capabilities.

    Main Results:

    • The SPGB demonstrates focusing intensity approximately 1.32 times stronger than symmetric Airy beams.
    • Four off-axis main lobes split into symmetrically bending trajectories after focusing.
    • Rectangular intensity distribution and focal length are adjustable via distribution factors.
    • Successful demonstration of vortex guiding by embedding an off-axis vortex into the SPGB.

    Conclusions:

    • The novel SPGB offers enhanced focusing and controllable beam shaping.
    • The SPGB's properties make it suitable for applications in particle guiding.
    • This work introduces a new class of beams with potential for further optical research.