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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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Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
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Related Experiment Video

Updated: Oct 15, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Normal mode energy estimation based on reconstructing the incoherent beamformed outputs from a horizontal array.

Duo Zhai1, Fenghua Li1, Bo Zhang1

  • 1State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China.

The Journal of the Acoustical Society of America
|October 31, 2021
PubMed
Summary

This study introduces a novel method for estimating normal mode energy, improving accuracy in shallow water waveguides. The technique enhances source localization and environmental inversion using small-aperture horizontal arrays.

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Area of Science:

  • Underwater acoustics
  • Wave propagation modeling
  • Signal processing

Background:

  • Acoustic fields in underwater environments are often modeled using normal modes.
  • Normal modes are crucial for source localization and environmental inversion.
  • Traditional methods struggle with wavenumber resolution for small-aperture arrays in shallow water.

Purpose of the Study:

  • To propose an original method for normal mode energy estimation.
  • To mitigate energy leakage between modes in shallow water waveguides.
  • To enhance the accuracy of modal analysis for small-aperture horizontal arrays.

Main Methods:

  • Reconstruction of incoherent beamformed outputs in the wavenumber domain for moving sources.
  • Utilizing adaptive beamforming to reduce interference and improve signal-to-noise ratio.
  • Incorporating uncertainty in modal phase velocity into the estimation process.

Main Results:

  • The proposed method effectively removes energy leakage between modes.
  • It provides more accurate modal energy estimates compared to traditional filters (matched filter, least squares, etc.).
  • Validation through simulations and experimental data.

Conclusions:

  • The novel normal mode energy estimation method offers superior performance for small-aperture horizontal arrays.
  • This advancement improves the reliability of source localization and environmental inversion in shallow water.
  • The technique addresses limitations of existing mode filtering approaches.