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Waves
Published in Abdul Al-Azzawi, Photonics, 2017
A mechanical wave is a disturbance that moves through a material. A source of energy is needed to produce mechanical waves. Energy produces the disturbance, and an elastic medium is needed to transmit the disturbance. An elastic medium behaves like an array of particles connected by springs, with each particle at equilibrium, as shown in Figure 17.1.
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.
9 Condition-Based Maintenance Techniques
Published in Jesús R. Sifonte, James V. Reyes-Picknell, Reliability Centered Maintenance-Reengineered, 2017
Jesús R. Sifonte, James V. Reyes-Picknell
Sound is a mechanical wave that requires a medium through which to travel. It is produced by a vibration, which creates waves of pressure that transmit longitudinally through a medium. The medium supports the transmission of sound pressure waves and may be a solid, a liquid, or a gas, or any combination of these. Longitudinal waves are so called because they move through the medium in the same direction as the sound wave. As they move through the molecular structure of the medium, both high and low areas of pressure are created. These fluctuations in pressure are what produce sound that can be detected and measured.
Thermophysical and ultrasonic properties of GdCu under the effect of temperature and pressure
Published in Phase Transitions, 2020
Dharmendra Kumar Pandey, Chandreshvar Prasad Yadav
The phonon is termed as energy quanta of mechanical wave. Its distribution is disturbed after the passage of ultrasonic wave. The process of equilibrium re-establishment of these phonons is relaxational in nature which causes energy dissipation. The re-establishment time of the phonon distribution is called as thermal relaxation time. The energy dissipation of ultrasonic wave is called as ultrasonic attenuation which is directly proportional to thermal relaxation time [17, 22]. Hence, the variation of ultrasonic attenuation in GdCu with temperature and pressure can be understood by the knowledge of lattice part of the thermal conductivity. Therefore, the thermal conductivity (k) of GdCu is evaluated with Equation (14) at different temperature and pressure. Regarding this, the quantities Grüneisen parameter (γ) and Debye temperature (TD) are also calculated using Equation (15) and Equation (16), respectively. The values obtained of TD and γ are given in Tables 1 and 2 while variation of k with temperature and pressure are depicted in Figures 5–6.
Constitutive model for predicting stress-strain behavior of fine-grained sediments using shear-wave velocity
Published in Marine Georesources & Geotechnology, 2020
Wisam R. Muttashar, L. Sebastian Bryson
Low-strain mechanical wave (i.e., seismic wave) velocity is a function of the state conditions and material properties of the medium through which the wave propagates (Santamarina and Cascante 1996; Santamarina et al. 2001; Patel and Singh 2009). As a result, information about the mechanical behavior of a medium at a given stress state can be directly obtained from the measured wave velocity through the medium. In addition, the material properties of the medium do not change in response to propagation of the seismic waves. The information obtained by the interaction between the wave front and the medium can be used to non-destructively evaluate material properties.
Thermo-hydrodynamic effects of the Ethylene reactive flow on convecting hot spots using LES
Published in Chemical Engineering Communications, 2023
Najmeh Hajialigol, Kiumars Mazaheri, Abolfazl Fattahi
The mechanical wave dissipation indicates a decrease in the signal energy (Lighthill 2001). Any reduction in the amplitude of an hot spot, suggests the heat transfer to the base flow from the wave, pointing toward a decrease in the energy of the wave. This can be introduced as an index for dissipation. To avoid any erroneous result, the criterion on the grounds of temporal (or frequency) spectrum is defined in lieu of the spatial domain (A Fattahi et al., 2017; Hajialigol and Mazaheri 2020). A quantitative criterion of dissipation in the frequency domain can thus be derived through (Hajialigol and Mazaheri 2020):