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Some Fundamentals of Sound and Vibration
Published in Malcolm J. Crocker, A. John Price, Noise and Noise Control, 2018
Malcolm J. Crocker, A. John Price
This equation is known as the one-dimensional wave equation. Here--ξ is the particle displacement and c is the speed at which waves propagate (speed of sound). Wave equations of identical form may be written with the displacement replaced with the acoustical pressure, particle velocity, fluctuating density, or fluctuating temperature, e.g., ∂2p∂x2−1c2∂2p∂t2=0.(1.22)
Airborne Sound
Published in Dhanesh N. Manik, Vibro-Acoustics, 2017
where ψ¯(x) is the spatial variation of the particle displacement due to wave propagation at the speed of sound. From Equation 3.37, the second time-derivative of particle displacement is given by ∂2ξ˜∂t2=−ω2ψ¯(x)ejωt
Transmission of Sound
Published in Randall F. Barron, Industrial Noise Control and Acoustics, 2002
The magnitude of the particle velocity is related to the magnitude of the particle displacement: |u|=ωXm=ω|ξ|=2πf|ξ|
The Effect of Earthquake Frequency Content on the Internal Forces in the Tunnels Permanent Lining
Published in Journal of Earthquake Engineering, 2022
Mohammad Oliaei, Rouhollah Basirat
Considering that the earthquake records did not have the same duration of earthquakes selected, the duration of all accelerograms is first set to 30 s and then the peak point in this duration is located in a way that earthquake intensity does not exceed 2–5% of the initial intensity. Using this method, in addition to a remarkable reduction in the computation time, the effect of earthquake duration is removed. Figure 3 illustrates 15 accelerograms after equalization. Then, earthquake frequency content including the peak particle velocity (PPV), the peak particle displacement (PPD), and specific energy density (SED) was calculated. Peak ground acceleration (PGA) denotes the maximum ground acceleration recorded during the seismic shaking. PPV denotes the maximum ground velocity recorded during the seismic shaking. This parameter is obtained by integrating the acceleration time history and taking the maximum value of the corresponding velocity-time history. PPD denotes the maximum ground displacement recorded during the seismic shaking by the three components of the seismic station. This parameter is obtained by double integrating the acceleration time history and taking the maximum value of the corresponding displacement time history. The SED is defined by the following equation (Sarma and Yang 1987):
LES-DEM simulations of sediment saltation in a rough-wall turbulent boundary layer
Published in Journal of Hydraulic Research, 2019
Detian Liu, Xiaofeng Liu, Xudong Fu
To further investigate the three random processes and their effects on saltation, a quantitative analysis was conducted. In Fig. 6, the deviations of particle displacement and particle velocity from the mean are plotted (only LES case 1 and log-law case are shown for clarity). The standard deviation σ is calculated to quantify the degree of deviation from the mean motion. One standard deviation is plotted using the dash lines with different colours for each case in Fig. 6. The values are reported in Table 3 for displacement and Table 4 for velocity. For the log-law case, there is no turbulent fluctuation. Therefore, the ratio can be used to quantify the turbulent fluctuation effect. In other words, it can be used to measure how much physical information is lost when the log-law flow field is used to drive saltation. We found that all the ratios were significantly lower than one. On average, the log-law case only resolved about 17% of the variation in streamwise displacement and 40% in spanwise displacement. For saltation velocity, the percentages were 14% and 54% in streamwise and spanwise directions, respectively. Comparing streamwise and spanwise directions, the ratios in the spanwise direction were at least 2–3 times those in the streamwise direction. These results strongly indicate that the use of log-law velocity loses a large percentage of the saltation dynamics. In addition, the loss is severer in the streamwise direction than in the spanwise direction.
Production of acoustic radiation force using ultrasound: methods and applications
Published in Expert Review of Medical Devices, 2018
In recent years, most shear wave elastography (SWE) methods have utilized a single impulsive ARF push of typically 100–800 μs for clinical applications. One reason is due to the requirements of the power source of the clinical or research ultrasound instrument being used and the need to sustain constant power for each push. Additionally, most clinical ultrasound scanners have implemented a time-domain group velocity measurement to quantify the shear wave velocity [49]. The measurement of the shear wave velocity in the time-domain does not require specific frequency-domain information and can be done by identifying features in the time-domain signal such as peak of particle displacement, peak of the particle velocity, or the peak of correlation functions to determine the time-of-flight between different locations [49–56]. As a result, repeated pulses (SDUV, OFUV) are not necessary. Secondly, if shear wave velocity dispersion is to be explored, this can be evaluated using two-dimensional Fourier transform analysis on data from a single ARF push that was pioneered by Bernal et al. and Couade et al. originally for vascular applications [57,58]. This method takes a two-dimensional Fourier transform of spatiotemporal (x,t) wave propagation data to transform to spatial frequency-temporal frequency (k,f) space. The wave velocities at specific frequencies can be extracted by locating peaks (k0, f0) in this Fourier distribution and computing