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Related Concept Videos

Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

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When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
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Fluid Pressure over Curved Plate of Constant Width01:12

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When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
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Fluid Pressure over Flat Plate of Constant Width01:05

Fluid Pressure over Flat Plate of Constant Width

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When a body is submerged in water, it experiences fluid pressure acting normal on its surface and distributed over its area. For better design structures, it is crucial to determine the magnitude and location of the resultant force acting on the surface. In the case of a rectangular plate of constant width submerged in water, the pressure increases with depth, resulting in a linearly varying trapezoidal pressure distribution from the upper to the lower edge of the plate.
The resultant force...
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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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Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
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Transient 3D elastodynamic field in an embedded multilayered anisotropic plate.

Pierric Mora1, Eric Ducasse2, Marc Deschamps3

  • 1Univ. Bordeaux, I(2)M-APy, UMR 5295, F-33400 Talence, France.

Ultrasonics
|April 19, 2016
PubMed
Summary

This study presents a robust algorithm for calculating ultrasonic fields in complex multilayered plates using Laplace transforms. The method accurately models wave interactions, offering an effective alternative for non-destructive testing of composite materials.

Keywords:
Embedded multilayered plateIntegral transform domainNumerical inverse Laplace transformPartial-wave expansionTransient ultrasonic response

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Area of Science:

  • Materials Science
  • Acoustics
  • Non-Destructive Testing (NDT)

Background:

  • Ultrasonic testing is crucial for NDT of composite materials.
  • Existing methods like generalized Lamb wave decomposition can be problematic.
  • A need exists for robust algorithms to calculate ultrasonic fields irrespective of source/receiver positions.

Purpose of the Study:

  • To develop and validate a robust algorithm for calculating ultrasonic fields in 3D embedded multilayered anisotropic and dissipative plates.
  • To customize a time-domain Laplace transform method for ultrasonic source interactions.
  • To provide an effective alternative to generalized Lamb wave decomposition.

Main Methods:

  • Utilized a time-domain analysis based on the Laplace transform.
  • Transformed fields into the 2D Fourier wave-vector domain for plate surface variables.
  • Expressed fields in the partial-wave basis, separating up- and down-going waves.

Main Results:

  • Demonstrated the effectiveness of the Laplace transform method for complex plate configurations.
  • Achieved accurate numerical calculations without problematic mode analysis or poorly convergent series.
  • Validated the algorithm through simulations and experiments on carbon-epoxy and aluminum plates, including Zero Group Velocity (ZGV) conditions.

Conclusions:

  • The Laplace transform-based method is a powerful and computationally efficient tool for analyzing ultrasonic wave propagation in multilayered anisotropic and dissipative plates.
  • This approach complements existing NDT techniques and offers advantages in handling complex scenarios.
  • The developed algorithm is robust and suitable for various applications in composite material analysis.