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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

284
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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Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

593
Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
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Deflection of a Beam01:19

Deflection of a Beam

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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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Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

236
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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Shear on the Horizontal Face of a Beam Element01:16

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353
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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Updated: Nov 5, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
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Twin curvilinear vortex beams.

Zhuang Wang, Zheng Yuan, Yuan Gao

    Optics Express
    |May 14, 2021
    PubMed
    Summary
    This summary is machine-generated.

    Researchers developed twin curvilinear vortex beams (TCVBs), a novel optical beam with unique intensity and phase properties. These beams offer potential applications in optical tweezers for precise particle manipulation along curved paths.

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    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Beam Shaping

    Background:

    • Optical vortex beams are crucial for applications like optical trapping and information transfer.
    • Existing vortex beams typically exhibit radial or helical phase structures.
    • There is a need for novel optical beam structures to expand manipulation capabilities.

    Purpose of the Study:

    • To introduce and theoretically demonstrate a new type of optical vortex beam: twin curvilinear vortex beams (TCVBs).
    • To investigate the generation and properties of TCVBs using Fourier transforms of cylindrically polarized beams.
    • To explore potential applications of TCVBs in optical tweezers.

    Main Methods:

    • Theoretical derivation of TCVB generation via Fourier transform of cylindrically polarized light.
    • Numerical simulations to analyze the intensity and phase distributions of TCVBs.
    • Experimental verification using interference techniques to confirm vortex properties.

    Main Results:

    • Successful theoretical demonstration of TCVB generation with intensity and phase along identical curves.
    • TCVBs exhibit the 'perfect optical vortex' characteristic, independent of topological charge.
    • Interference experiments confirmed the vortex nature and topological charge of the generated TCVBs.

    Conclusions:

    • Twin curvilinear vortex beams represent a novel class of optical beams with unique spatial structures.
    • The demonstrated method provides a viable route for generating TCVBs.
    • TCVBs show promise for advanced applications in optical trapping and manipulation of microparticles.