Analysis of a Piezoelectric Actuator and Receiver on an Elastic Half-Space Subjected to Harmonic Electric Excitation

1993 ◽  
Author(s):  
Shuo-Hung Chang ◽  
Ching-San Lin
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Piezoelectric Actuator ◽  
Analytical Solutions ◽  
Electric Potential ◽  
Excitation Frequency ◽  
Elastic Half Space ◽  
Electric Excitation ◽  
Analytical Formulas ◽  
Good Agreement

Abstract Analytical solutions are formulated for the displacement, stress, and electric potential in piezoelectric actuator and receiver on an elastic half-space. The surface wave is taken into account when the piezoelectric actuator is subjected to the harmonic electric excitation. The derived analytical formulas are used to compute the output potential of piezoelectric receiver. Experiment measurements are performed and compared with numerical results in good agreement. The influence of excitation frequency, material property and dimension of the piezoelectric material is presented.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Love Wave in an Isotropic Half-Space with a Graded Layer

2013 ◽  
Vol 325-326 ◽  
pp. 252-255
Author(s):  
Li Gang Zhang ◽  
Hong Zhu ◽  
Hong Biao Xie ◽  
Jian Wang
Keyword(s):  
Shear Modulus ◽  
Half Space ◽  
Analytical Solutions ◽  
Love Wave ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Vibration Model ◽  
General Dispersion ◽  
Functionally Graded Layer

This work addresses the dispersion of Love wave in an isotropic homogeneous elastic half-space covered with a functionally graded layer. First, the general dispersion equations are given. Then, the approximation analytical solutions of displacement, stress and the general dispersion relations of Love wave in both media are derived by the WKBJ approximation method. The solutions are checked against numerical calculations taking an example of functionally graded layer with exponentially varying shear modulus and density along the thickness direction. The dispersion curves obtained show that a cut-off frequency arises in the lowest order vibration model.

Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1980-1987
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Half Space ◽  
Rotation Rate ◽  
Secular Equation ◽  
Elastic Half Space ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.

scholarly journals Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

2021 ◽  
Vol 15 (1) ◽  
pp. 30-36
Author(s):  
Askar Kudaibergenov ◽  
Askat Kudaibergenov ◽  
Danila Prikazchikov
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Moving Load ◽  
Elastic Half Space ◽  
Elementary Functions ◽  
Material Models ◽  
Line Load ◽  
Transient Regimes ◽  
Surface Wave Field ◽  
Asymptotic Formulation

Abstract The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

Contact Area Variation in Elastic Indentation Problems

2009 ◽  
Author(s):  
Roman Riznychuk
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Elastic Half Space ◽  
Exact Expression ◽  
Rigid Punch ◽  
Contact Pressure Distribution ◽  
Area Variation

Contact problem of the frictionless indentation of elastic half-space by smooth rigid punch of curved profile is investigated. An exact expression of the contact pressure distribution for a curved profile punch in terms of integral involving the pressure distribution for sequence of flat punches is derived. The method is illustrated and validated by comparison with some well-known analytical solutions.

scholarly journals Reduced model for the surface dynamics of a generally anisotropic elastic half-space

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190590 ◽  
Author(s):  
Yibin Fu ◽  
Julius Kaplunov ◽  
Danila Prikazchikov
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Travelling Waves ◽  
Moving Load ◽  
Multiple Scale ◽  
Elastic Half Space ◽  
Surface Dynamics ◽  
Near Surface ◽  
Surface Resonance ◽  
Anisotropic Elastic

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v  −  v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

1962 ◽  
Vol 52 (1) ◽  
pp. 27-36
Author(s):  
J. T. Cherry
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Poisson’S Ratio ◽  
Horizontal Stress ◽  
Elastic Half Space ◽  
The Body ◽  
Body Waves ◽  
Poisson's Ratio ◽  
A Value

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

Transient fundamental solutions for a transversely isotropic elastic half space

1993 ◽  
Vol 442 (1916) ◽  
pp. 505-531 ◽  
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
Two Dimensional

This paper is concerned with the study of transient response of a transversely isotropic elastic half-space under internal loadings and displacement discontinuities. Governing equations corresponding to two-dimensional and three-dimensional transient wave propagation problems are solved by using Laplace–Fourier integral transforms and Laplace−Hankel integral transforms, respectively. Explicit general solutions for displacements and stresses are presented. Thereafter boundary-value problems corresponding to internal transient loadings and transient displacement discontinuities are solved for both two-dimensional and three-dimensional problems. Explicit analytical solutions for displacements and stresses corresponding to internal loadings and displacement discontinuities are presented. Solutions corresponding to arbitrary loadings and displacement discontinuities can be obtained through the application of standard analytical procedures such as integration and Fourier expansion to the fundamental solutions presented in this article. It is shown that the transient response of a medium can be accurately computed by using a combination of numerical quadrature and a numerical Laplace inversion technique for the evaluation of integrals appearing in the analytical solutions. Comparisons with existing transient solutions for isotropic materials are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses due to a buried circular patch load are presented to portray some features of the response of a transversely isotropic elastic half-space. The fundamental solutions presented in this paper can be used in the analysis of a variety of transient problems encountered in disciplines such as seismology, earthquake engineering, etc. In addition these fundamental solutions appear as the kernel functions in the boundary integral equation method and in the displacement discontinuity method.

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