Low frequency acoustic response of a periodic layer of spherical inclusions in an elastic solid to a normally incident plane longitudinal wave

2000 ◽  
Author(s):  
K. Maslov
Keyword(s):  
Longitudinal Wave ◽  
Low Frequency ◽  
Elastic Solid ◽  
Acoustic Response ◽  
Spherical Inclusions ◽  
Incident Plane ◽  
Periodic Layer ◽  
Plane Longitudinal Wave

Longitudinal wave propagation in an infinite isotropic elastic plate with a penny-shaped crack

1969 ◽  
Vol 66 (2) ◽  
pp. 439-442
Author(s):  
H. S. Paul
Keyword(s):  
Longitudinal Wave ◽  
Elastic Plate ◽  
Mixed Boundary ◽  
Elastic Solid ◽  
Vertical Displacement ◽  
Dual Integral Equation ◽  
Positive Direction ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Plane Longitudinal Wave

The stress distribution, subject to a constant pressure over the entire surface of a penny-shaped crack is discussed by Sneddon(4). Recently, Robertson (3) has considered the diffraction of a plane longitudinal wave by a penny-shaped crack on a semi-infinite elastic solid. In the present analysis, the propagation of longitudinal wave in an infinite isotropic elastic plate with a penny-shaped crack in the middle has been investigated. The plane longitudinal wave is moving in the positive direction of z-azis and is impinging on the surface of the penny-shaped crack. The dual integral equation technique of Noble(l) is utilized to solve the mixed boundary-value problem. The analysis closely follows the method used in the author's previous paper (2). The vertical displacement is analysed numerically.

Elastodynamic Response of a Chain of Particles

1999 ◽  
Author(s):  
Vikram K. Kinra ◽  
Benjamin K. Henderson ◽  
Konstantin Maslov
Keyword(s):  
Linear Chain ◽  
Interparticle Distance ◽  
Integral Number ◽  
Viscoelastic Matrix ◽  
Spherical Inclusions ◽  
Incident Plane ◽  
The Matrix ◽  
Elastodynamic Response ◽  
A Chain ◽  
Plane Longitudinal Wave

Abstract The reflection of an axially incident plane longitudinal wave from a linear chain of identical spherical inclusions embedded in a viscoelastic matrix is measured. The reflection spectrum is characterized by a sequence of resonances corresponding to the Floquet condition, where an integral number of half-wavelengths in the matrix spans the interparticle distance.

Wave Function Expansions and Perturbation Method for the Diffraction of Elastic Waves by a Parabolic Cylinder

1967 ◽  
Vol 34 (4) ◽  
pp. 915-920 ◽  
Author(s):  
S. A. Thau ◽  
Yih-Hsing Pao
Keyword(s):  
Wave Function ◽  
Separation Of Variables ◽  
Low Frequency ◽  
Elastic Solid ◽  
Compressional Wave ◽  
Parabolic Cylinder ◽  
Infinite Matrix ◽  
Elastic Solids ◽  
Incident Plane ◽  
Scattered Fields

The dynamic response, including the stresses at the surface, of a rigid parabolic cylinder in an infinite elastic solid is studied for an incident plane compressional wave. The method of separation of variables in parabolic coordinates is used. With the wave function for one of the scattered waves expanded into a series of those for the other wave, the total scattered fields are then determined numerically by inverting a truncated infinite matrix. The same problem is solved also by a recently developed method of perturbation which describes the two waves in elastic solids in terms of wave functions with a common wave speed. With the latter method, the total scattered waves are determined analytically for the various orders of perturbation, and these results supplement the numerical wave function expansion results in the low-frequency range.

Diffraction of a plane longitudinal wave by a penny-shaped crack

1967 ◽  
Vol 63 (1) ◽  
pp. 229-238 ◽  
Author(s):  
Ian A. Robertson
Keyword(s):  
Longitudinal Wave ◽  
Constant Pressure ◽  
Elastic Solid ◽  
Entire Surface ◽  
Positive Direction ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Distribution Of Stress ◽  
Plane Longitudinal Wave

Introduction. The distribution of stress produced in the interior of an infinite elastic solid when a constant pressure is applied over the entire surface of a penny-shaped crack has been solved by Sneddon(6), (7). The problem considered here is the closely allied one of a plane longitudinal wave, harmonic in time, moving in the positive direction of the z-axis and impinging on the surface of a penny-shaped crack. The analysis follows the methods adopted for dealing with an axisymmetrical vibrating punch acting on a semi-infinite elastic solid, Robertson (5).

The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

1966 ◽  
Vol 33 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Joseph F. Shelley ◽  
Yi-Yuan Yu
Keyword(s):  
Stress Field ◽  
Uniaxial Tension ◽  
Elastic Solid ◽  
Displacement Function ◽  
Hydrostatic Tension ◽  
Series Form ◽  
Spherical Inclusions ◽  
Spherical Cavities ◽  
In Series ◽  
The Common

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

scholarly journals Design and Experimental Validation of a Metacomposite Made of an Array of Piezopatches Shunted on Negative Capacitance Circuits for Vibroacoustic Control

2013 ◽  
Author(s):  
F. Tateo ◽  
M. Collet ◽  
M. Ouisse ◽  
M. N. Ichchou ◽  
K. A. Cunefare
Keyword(s):  
New Technologies ◽  
Control Method ◽  
Low Frequency ◽  
Elastic Solid ◽  
Numerical Approach ◽  
Anomalous Behavior ◽  
Phononic Crystals ◽  
Underlying Structure ◽  
Negative Capacitance ◽  
New Class

In the last few decades, researchers have given a lot of attention to new engineered materials with the purpose of developing new technologies and devices such as mechanical filters, low frequency sound and vibration isolators, and acoustic waveguides. For instance, elastic phononic crystals may come to mind. They are materials with elastic or fluid inclusions inside a matrix made of an elastic solid. The anomalous behavior in phononic crystals arises from interference of waves propagating within an inhomogeneous material. The inclusions inside the matrix cause strong modifications of scattering properties. However, the application of phononic crystals is still limited to sonic frequencies. In fact, band gaps can be generated only when the acoustic wavelength is comparable to the distance between the inclusion. In order to overcome this limitation, a new class of metamaterial has been proposed: meta composite. This new class of material can modify the dynamics of the underlying structure using a bidimensional array of electromechanical transducers, which are composed by piezo patches connected to a synthetic negative capacitance. In this study, an application of the Floquet-Bloch theorem for vibroacoustic power flow optimization will be presented. In the context of periodically distributed, damped 2D mechanical systems, this numerical approach allows one to compute the multimodal waves dispersion curves into the entire first Brillouin zone. This approach also permits optimization of the piezoelectric shunting electrical impedance, which controls energy diffusion into the proposed semiactive distributed set of cells. Experiments performed on the examined structure illustrates the effectiveness of the proposed control method. The experiment requires a rectangular metallic plate equipped with seventyfive piezopatches, controlled independently by electronic circuits. More specifically, the out-of-plane displacements and the averaged kinetic energy of the controlled plate are compared in two different cases (control system on/off). The resulting data clearly show how this proposed technique is able to dampen and selectively reflect the incident waves.

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