Transient Elastic Waves in Anisotropic Plates

1967 ◽  
Vol 34 (1) ◽  
pp. 104-110 ◽  
Author(s):  
R. A. Scott ◽  
Julius Miklowitz
Keyword(s):  
Elastic Waves ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Elastic Solid ◽  
Field Analysis ◽  
Material Symmetry ◽  
Anisotropic Plates ◽  
Linear Elastic ◽  
Isotropic Media ◽  
Wavelength Approximation

The equations of motion of a linear elastic solid have been used to study the propagation of transient compressional disturbances in anisotropic plates, generated by several types of surface and edge loadings. A particular orientation of the axes of material symmetry was chosen, and several classes of anisotropic media have been considered. From the exact solutions obtained, a far-field analysis based on a low-frequency, large-wavelength approximation is given; and numerical results are presented for copper, ice, zinc, beechwood, and several isotropic media for comparison purposes.

Elastic Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Elastic Waves ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Elastic Solid ◽  
Stress And Strain ◽  
Field Equations ◽  
Strain Stress ◽  
Thermodynamic Variables ◽  
Dynamic Variables

This chapter focuses on the mathematics of elastic waves. In the case of a continuous medium, the field equations of physics (yielding the dynamic and thermodynamic variables) arise from three conservation equations: conservation of mass, momentum and energy. For an elastic medium, these equations of motion are known as Navier equations, which give rise to a rich variety of stress waves. There are two dynamic variables in an elastic solid: stress and strain. Stress and strain are linearly related in small-amplitude deformations; this relation is expressed by Hooke's law. The chapter first introduces the basic notation for elastic waves before discussing the solutions for plane waves. It also considers surface waves and Love waves.

ELASTIC WAVES ALONG A CYLINDRICAL BORE

Geophysics ◽  
1962 ◽  
Vol 27 (3) ◽  
pp. 327-333 ◽  
Author(s):  
J. E. White
Keyword(s):  
Elastic Waves ◽  
Low Frequency ◽  
Elastic Solid ◽  
Approximate Expression ◽  
Compressional Wave ◽  
Axially Symmetric ◽  
Low Frequencies ◽  
Phase Velocities ◽  
Pierre Shale ◽  
Limiting Case

This paper concerns axially symmetric solutions for waves propagating along a cylinder in an infinite elastic solid. Solutions are presented describing unattenuated propagation along the axis at phase velocities higher than shear and compressional speeds in the solid, in contradiction to earlier publications. Special attention is given to the limiting case of phase velocity equal to compressional speed in the solid, which at low frequencies very closely approximates the coupling of a fluid‐filled borehole to a plane compressional wave in the surrounding solid. Comparison with some experiments in a uniform section of Pierre shale show excellent agreement at low frequencies. In the low‐frequency limit, these solutions reduce to an approximate expression for borehole coupling published earlier by the author.

Transient elastic waves in an inhomogeneous layer

1970 ◽  
Vol 60 (2) ◽  
pp. 383-392 ◽  
Author(s):  
R. A. Scott
Keyword(s):  
Elastic Waves ◽  
Harmonic Wave ◽  
Low Frequency ◽  
Field Approximation ◽  
Inhomogeneous Layer ◽  
Far Field ◽  
Lateral Loads ◽  
Wavelength Approximation ◽  
Formal Solutions ◽  
Large Wavelength

abstract The excitation, by lateral loads, of transients in a layer of a transversely inhomogeneous solid with constant speeds of propagation is considered. Formal solutions in terms of the modes of harmonic wave propagation are developed, and from these and a low frequency, large wavelength approximation a far-field approximation to the response is derived.

Wave-front singularities for two-dimensional anisotropic elastic waves

1972 ◽  
Vol 72 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Robert G. Payton
Keyword(s):  
Point Source ◽  
Wave Front ◽  
Elastic Waves ◽  
Elastic Solid ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Anisotropic Elastic

AbstractWave-front singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d–½ where d measures distance away from the front. However, in certain exceptional cases singularities of order d–-n where n = ¼, ⅔, ¾, may be encountered.

Comparison of high- and low-frequency electromagnetic field analysis

1993 ◽  
Vol 3 (3) ◽  
pp. 363-371 ◽  
Author(s):  
A. Konrad ◽  
I. A. Tsukerman
Keyword(s):  
Electromagnetic Field ◽  
Low Frequency ◽  
Field Analysis

scholarly journals Numerical Modelling and Optimization of Two-Dimensional Phononic Band Gaps in Elastic Metamaterials with Square Inclusions

2021 ◽  
Vol 11 (7) ◽  
pp. 3124
Author(s):  
Alya Alhammadi ◽  
Jin-You Lu ◽  
Mahra Almheiri ◽  
Fatima Alzaabi ◽  
Zineb Matouk ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Tungsten Carbide ◽  
Composite Structure ◽  
Elastic Waves ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Filling Fraction ◽  
Carbide Composite ◽  
Elastic Metamaterials ◽  
Tungsten Carbide Composite

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

2016 ◽  
Vol 32 (3) ◽  
pp. 297-311
Author(s):  
T.-Y. Zhao ◽  
H.-Q. Yuan ◽  
B.-B. Li ◽  
Z.-J. Li ◽  
L.-M. Liu
Keyword(s):  
Thermal Shock ◽  
High Frequency ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Cantilever Plate ◽  
Analysis Method ◽  
Multiple Frequency ◽  
Width Direction ◽  
Blade Tip ◽  
High Frequency Vibrations

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

scholarly journals Diffraction of plane elastic waves by a crack, with application to a problem of brittle fracture

1963 ◽  
Vol 3 (3) ◽  
pp. 325-339 ◽  
Author(s):  
M. Papadopoulos
Keyword(s):  
Elastic Waves ◽  
Scattered Field ◽  
Velocity Potential ◽  
Elastic Solid ◽  
Step Function ◽  
Free Surface Waves ◽  
Dependent Variables ◽  
Smooth Plane ◽  
New Feature ◽  
Set Up

AbstractA crack is assumed to be the union of two smooth plane surfaces of which various parts may be in contact, while the remainder will not. Such a crack in an isotropic elastic solid is an obstacle to the propagation of plane pulses of the scalar and vector velocity potential so that both reflected and diffracted fields will be set up. In spite of the non-linearity which is present because the state of the crack, and hence the conditions to be applied at the surfaces, is a function of the dependent variables, it is possible to separate incident step-function pulses into either those of a tensile or a compressive nature and the associated scattered field may then be calculated. One new feature which arises is that following the arrival of a tensile field which tends to open up the crack there is necessarily a scattered field which causes the crack to close itself with the velocity of free surface waves.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

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