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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

480
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...
480
Deflection of a Beam01:19

Deflection of a Beam

869
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...
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Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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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.
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...
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Impact Loading on a Cantilever Beam01:13

Impact Loading on a Cantilever Beam

995
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.
When an object is dropped onto the free end of a cantilever, its potential energy due to gravity is...
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Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

555
The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments. Initially, this...
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Dynamics of Circular Motion01:30

Dynamics of Circular Motion

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An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
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Related Experiment Video

Updated: Mar 21, 2026

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators
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Controllable circular Airy beams via dynamic linear potential.

Hua Zhong, Yiqi Zhang, Milivoj R Belić

    Optics Express
    |May 4, 2016
    PubMed
    Summary
    This summary is machine-generated.

    We demonstrate control over circular Airy beams using dynamic linear potentials. These potentials can weaken, eliminate, or strengthen the beam

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    Area of Science:

    • Optics and Photonics
    • Nonlinear Optics
    • Beam Propagation

    Background:

    • Circular Airy beams exhibit autofocusing properties.
    • Controlling beam dynamics is crucial for optical applications.

    Purpose of the Study:

    • To investigate controllable spatial modulation of circular autofocusing Airy beams.
    • To explore the effects of dynamic linear potentials on beam autofocusing.

    Main Methods:

    • Theoretical analysis using a novel superposition method of one-dimensional Airy beams.
    • Numerical simulations to validate theoretical predictions.

    Main Results:

    • Dynamic linear potentials can significantly alter the autofocusing behavior.
    • A
    • pushing
    • potential strengthens autofocusing, while a
    • pulling
    • potential weakens or eliminates it.

    Conclusions:

    • Controllable spatial modulation of circular Airy beams is achievable.
    • Dynamic linear potentials offer a versatile tool for manipulating beam autofocusing.