Fast and slow interaction of elastic waves with platonic clusters

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

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Numerical and Experimental Study on Suppression Effect of Acoustic Black Hole on Vibration Transmission of Refrigerator Compressor

Applied Sciences ◽

10.3390/app11188622 ◽

2021 ◽

Vol 11 (18) ◽

pp. 8622

Author(s):

Xiaofei Du ◽

Qidi Fu ◽

Jianrun Zhang ◽

Chaoyong Zong

Keyword(s):

Numerical Simulation ◽

Black Hole ◽

Vibration Suppression ◽

Structural Vibration ◽

Flexural Wave ◽

Response Analysis ◽

Flexural Waves ◽

Suppression Effect ◽

Support Plate ◽

The Time Domain

The acoustic black hole (ABH) structures have the potential to achieve structural vibration suppression and noise reduction through the effect of the ABH on the concentration and manipulation of flexural waves. In this paper, a new solution is proposed to embed 2-D ABHs on the support plate to suppress the transmission of compressor vibration to the refrigerator body. The vibration and acoustic measurement experiment of the compressor, the support plate and the refrigerator body, and the coherence analysis of the vibration signals and acoustic signal are carried out to determine the influence of the compressor vibration on the vibration of the refrigerator body and the radiation sound of the back wall. The concentration and manipulation effects of 2-D ABH on flexural waves are verified by numerical simulation of flexural wave propagation in the time domain. FEM models of the original support plate and the damping ABH support plate are established to investigate the comprehensive effect of the 2-D ABHs and the damping layers on the vibration characteristics of the support plate through vibration modal and dynamic response analysis. Numerical simulation results show that the 2-D damping ABHs can suppress the vibrations generated by the compressor at specific frequencies in the middle and high-frequency bands from being transmitted to the refrigerator body through the support plate.

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SCATTERING OF ELASTIC WAVES FROM DEPTH‐DEPENDENT INHOMOGENEITIES

Geophysics ◽

10.1190/1.1440625 ◽

1976 ◽

Vol 41 (3) ◽

pp. 441-458 ◽

Cited By ~ 101

Author(s):

Paul G. Richards ◽

Clint W. Frasier

Keyword(s):

Time Domain ◽

Elastic Waves ◽

P Waves ◽

Simple Method ◽

Transmitted Waves ◽

Short Period ◽

Scattering Of Elastic Waves ◽

The Time Domain ◽

Thick Crust ◽

Zero Frequency

We have studied scattered pulse shapes by modeling inhomogeneities as a sequence of infinitesimally thin homogeneous layers. With oblique incidence of plane P or SV waves, the reflected‐converted‐transmitted waves are obtained by taking the calculus limit for the sum of primary interactions of the incident wave with all layer boundaries. The resulting scattered waves thus present themselves naturally in the time domain. For an incident impulse, the scattered pulse shape is merely an analytic function of the depth from which scatter has taken place within the inhomogeneity. The direct application of this simple method appears to be new, and we have found it remarkably accurate when compared with methods in which higher‐order boundary interactions are also retained (i.e., Haskell methods and an adaptation in the time domain which also keeps all multiples). In specific studies of P-waves incident (up to 30 degrees away from the vertical) upon a 5 km thick crust‐mantle transition, between materials having impedance ratio 1:2.8, we find the scattered pulse shapes are given adequately by our theory, for the passband of short‐period seismometers. Indeed, the theory remains remarkably accurate even for long periods, being in error by only 8 per cent at zero frequency.

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