Golden Ratio in the Point Heat Source Induced Horizontal and Vertical Displacements of an Isotropic Elastic Half Space

2010 ◽  
Author(s):  
Feng-Tsai Lin ◽  
John C. -C. Lu
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Golden Ratio ◽  
Elastic Half Space ◽  
Point Heat Source ◽  
Vertical Displacements

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

Thermoelastic Solutions for Thermal Distributions Moving Over Half Space Surfaces and Application to the Moving Heat Source

1988 ◽  
Vol 55 (1) ◽  
pp. 87-92 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Fourier Transform ◽  
Heat Source ◽  
Half Space ◽  
Elastic Half Space ◽  
Temperature Wave ◽  
Exact Results ◽  
Moving Heat Source ◽  
Exponential Fourier Transform

A method is developed for obtaining fundamental thermal and thermoelastic solutions for thermal distributions moving over the surface of an elastic half space. This method uses the concept of a moving temperature wave along with a novel form of an exponential Fourier transform. The technique is developed and then demonstrated on the example of a moving heat source. Exact results are matched with results from Carslaw and Jaeger (1959) and Barber (1984).

scholarly journals Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017 ◽  
Vol 39 (4) ◽  
pp. 365-374
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Le Thi Hue
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Elastic Half Space ◽  
Displacement Amplitude ◽  
Vertical Displacements ◽  
Thin Elastic Layer

This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the  Rayleigh wave H/V ratio.

Surface Displacement of a Convective Elastic Half-Space Under an Arbitrarily Distributed Fast-Moving Heat Source

1965 ◽  
Vol 87 (3) ◽  
pp. 729-734 ◽  
Author(s):  
F. F. Ling ◽  
V. C. Mow
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Fast Moving ◽  
Constant Velocity ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Two Dimensional ◽  
Moving Heat Source ◽  
Thermoelasticity Theory

A solution of the normal displacement of the elastic half-space under an arbitrarily distributed fast-moving heat source of constant velocity within the two-dimensional quasi-static, uncoupled thermoelasticity theory is presented. The surface of the half-space is allowed to dissipate heat by convection. Moreover, an example associated with the problem of elastohydrodynamics is given.

Note on the use of reciprocity theorem for obtaining radiation patterns

1965 ◽  
Vol 55 (2) ◽  
pp. 277-281 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Far Field ◽  
Radiation Patterns ◽  
Vertical Displacements ◽  
Field Radiation ◽  
P And Sv Waves

Abstract Expressions for the horizontal and vertical displacements at the surface of an elastic half space when plane harmonic P or SV waves are incident at any given angle are already known. On the basis of the reciprocity theorem, these expressions are used to obtain “far-field” radiation patterns of P and SV waves due to horizontal and vertical forces applied at the free surface.

Sign in / Sign up

Export Citation Format

Share Document