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Related Concept Videos

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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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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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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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

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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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Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

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A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by...
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Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

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Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
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Gridless three-dimensional compressive beamforming with the Sliding Frank-Wolfe algorithm.

Gilles Chardon1, Ulysse Boureau2

  • 1Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, Gif-sur-Yvette, 91190, France.

The Journal of the Acoustical Society of America
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PubMed
Summary
This summary is machine-generated.

The Sliding Frank-Wolfe algorithm efficiently estimates 3D source locations and amplitudes using gridless compressive beamforming. This method offers improved performance and numerical efficiency for sparse signal recovery.

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Area of Science:

  • Signal Processing
  • Electromagnetics
  • Optimization Algorithms

Background:

  • Compressive beamforming enables source localization and amplitude estimation.
  • Existing methods often face limitations with basis mismatch and constraints on source models or array geometry.
  • Accurate three-dimensional (3D) source localization remains a challenge.

Purpose of the Study:

  • To investigate the Sliding Frank-Wolfe algorithm for gridless compressive beamforming.
  • To estimate the 3D position and amplitudes of multiple sources from single and multi-snapshot measurements.
  • To address the basis mismatch issue in source recovery.

Main Methods:

  • Applied the Sliding Frank-Wolfe algorithm to solve an infinite-dimensional optimization problem.
  • Promoted sparsity in solutions to recover sources without basis mismatch.
  • Developed a variant for greedy source identification.

Main Results:

  • Successfully recovered sources by promoting sparsity and avoiding basis mismatch.
  • The algorithm demonstrated effectiveness without constraints on source models or array geometry.
  • Experimental and simulation results validated the method's performance and numerical efficiency in 3D settings.

Conclusions:

  • The Sliding Frank-Wolfe algorithm is a powerful tool for gridless compressive beamforming.
  • It provides accurate 3D source localization and amplitude estimation.
  • The method offers a computationally efficient and robust alternative to existing techniques.