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Partial differential equations
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
Mechanical waves propagate through a material medium (solid, liquid, or gas) at a wave speed which depends on the inertial properties of that medium. There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves. In a transverse wave, particles of the medium are displaced in a direction perpendicular to the direction of energy transport. In a longitudinal wave, particles of the medium are displaced in a direction parallel to energy transport. Longitudinal waves are observed, for instance, in elastic bars or rods when their vertical dimensions are small. By placing the x‐axis along the bar’s direction so that its left end coincides with the origin, we can assume that its vibrations are uniform over each cross‐section. Then the longitudinal displacement ux,t $ u\left( {x, t} \right) $ satisfies the one‐dimensional wave equation (11.3.1. In Problems 15 through 20, find longitudinal displacements in rods under the given initial and boundary conditions.
W
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[general, mechanics] The progressive disturbance propagated in a medium by a periodic vibration of the particles of the medium. Transverse wave motion is that in which the vibration of the particles is perpendicular to the direction of propagation. Longitudinal wave motion is that in which the vibration of the particles is parallel to the direction of propagation (seewave).
Waves
Published in John Bird, Newnes Engineering Science Pocket Book, 2012
There are two types of waves, these being transverse and longitudinal waves: Transverse waves are where the particles of the medium move perpendicular to the direction of movement. For example, when a stone is thrown onto a pool of still water, the ripple moves radially outwards but the movement of a floating object shows that the water at a particular point merely moves up and down. Light and radio waves are other examples of transverse waves.Longitudinal waves are where the particles of the medium vibrate back and forth parallel to the direction of the wave travel. Examples include sound waves and waves in springs.
Assessment of Laser-Generated Ultrasonic Total Focusing Method for Battery Cell Foil Weld Inspection
Published in Research in Nondestructive Evaluation, 2023
Dmitriy D. Bruder, Megan E. McGovern, Robin James, Teresa J. Rinker, Vineet Gattani
Only two ultrasonic bulk wave modes exist in a solid infinite medium: longitudinal waves and shear waves. Longitudinal waves, sometimes referred to as dilatational or compressional waves, are waves in which the particle motion is in the same direction as the wave propagation. Shear waves, sometimes referred to as transverse waves, have particle motion perpendicular to the direction of wave propagation in the plane of propagation. When boundaries are present in the medium, these bulk waves interact with the boundaries to produce guided waves (if the wavelength is sufficiently long enough to “see” the boundaries, e.g., the wavelength is on the same order as the plate thickness). In other words, the geometry of the sample will impose boundary conditions on the wave propagation, resulting in guided wave modes. One commonly known example of a guided wave is the surface acoustic wave (SAW), or Rayleigh wave where the boundary condition is that of the stress-free surface. Rayleigh waves propagate close to the surface of the body with the amplitude of wave motion decreasing with depth. This results in an elliptical particle motion that only exists~3 wavelengths below the surface and, for solids, travels at a velocity slightly below the shear wave velocity [18].
Partial Discharge Detection and Localization in Power Transformers based on Acoustic Emission: Theory, Methods, and Recent Trends
Published in IETE Technical Review, 2021
Viral B. Rathod, Ganesh B. Kumbhar, Bhavesh R. Bhalja
AE waves based on their direction of propagation are classified as, Longitudinal waves (Pressure waves): These waves consist of alternate compression and rarefaction forces in the direction of propagation. In these waves, particles vibrate along the direction of propagation. They can propagate through all mediums – solids, liquids, and gases.Transverse waves (Shear waves): In these waves, particles vibrate perpendicular to the direction of propagation. They can propagate through solids but not through liquids and gases.Surface waves (Raleigh-Lamb waves): In these waves, the particle moves in the elliptical path near the surface of the material. They are the complex form of longitudinal and transverse waves.
Weld defect classification using 1-D LBP feature extraction of ultrasonic signals
Published in Nondestructive Testing and Evaluation, 2018
Hongwei Hu, Gang Peng, Xianghong Wang, Zhenhua Zhou
According to the diagram demonstrated in Figure 4, ultrasonic inspection was carried out in a steel plate butt weld specimen. The welding defects consist of slag inclusion (SI), porosity (PO) and incomplete penetration (IP). The angle beam wedge transducers were used to perform transverse wave ultrasonic inspection. The ultrasonic signals were transmitted and received by an OLYMPUS-5072 pulser/receiver and acquired by an ADLINK PCI9820 data acquisition card with a sampling frequency of 60 MHz. To simulate the responses of defects of different sizes and orientations, three positions and three incident angles from the transducer to the welding were employed for each defect. Moreover, two transducers with the centre frequencies of 2.25 and 5 MHz were used for each defect. Fifteen signals were acquired and recorded during every testing. So, there were 270 data-sets for each defect and 810 data-sets in total after experiments.