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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

469
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...
469
Deflection of a Beam01:19

Deflection of a Beam

854
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...
854
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

473
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...
473
Angular Momentum about an Arbitrary Axis01:11

Angular Momentum about an Arbitrary Axis

497
Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into...
497
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

587
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...
587
Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

673
Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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Multi-degree-of-freedom radially self-accelerating beams via angular-spectrum engineering.

Wenyi Ji, Wenxiang Yan, Yiyu Zhao

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    This summary is machine-generated.

    Researchers developed a new method to control multi-degree-of-freedom radially self-accelerating beams (RSABs). This allows for programmable control over their rotation, intensity, trajectory, and orbital angular momentum (OAM) for advanced optical applications.

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    Area of Science:

    • Optics and Photonics
    • Beam Propagation Dynamics
    • Light-Matter Interactions

    Background:

    • Radially self-accelerating beams (RSABs) possess unique rotating propagation and orbital angular momentum (OAM) properties.
    • Applications include optical micromanipulation and metrology.
    • Conventional RSABs have fixed propagation, limiting their use in complex scenarios.

    Purpose of the Study:

    • To propose and demonstrate a flexible framework for designing and controlling multi-degree-of-freedom RSABs (Multi-DoF RSABs).
    • To enable programmable control over key beam characteristics.

    Main Methods:

    • Angular-spectrum engineering approach based on Fourier optics.
    • Design and experimental validation of Multi-DoF RSABs.

    Main Results:

    • Demonstrated independent adjustment of four degrees of freedom: angular velocity, longitudinal intensity, 3D trajectory, and OAM.
    • Experimental results align with theoretical predictions.

    Conclusions:

    • The proposed method provides a flexible framework for designing advanced RSABs.
    • Highlights potential for applications in optical manipulation and microfabrication.