The limiting absorption principle (LAP), the radiation conditions and the expansion theorem

2010 ◽  
pp. 231-265
Author(s):  
D. Yafaev
Keyword(s):  
Expansion Theorem ◽  
Limiting Absorption Principle ◽  
Radiation Conditions

WAVE FRONTS AND THE RADIATION PRINCIPLE

2007 ◽  
Vol 19 (08) ◽  
pp. 805-821
Author(s):  
D. EIDUS
Keyword(s):  
Wave Equation ◽  
Inhomogeneous Media ◽  
Parameter Family ◽  
Acoustic Oscillations ◽  
Wave Fronts ◽  
Limiting Absorption Principle ◽  
Radiation Conditions

We are concerned with the construction of Sommerfeld-type radiation conditions for stationary acoustic oscillations in inhomogeneous media with densities independent of r. It is shown that such radiation conditions exist iff there exists a one-parameter family of closed homothetic star-shaped (with respect to origin) wave fronts. These radiation conditions select the same solutions of the reduced wave equation as the limiting absorption principle.

The propagation of waves in an elastic half-space containing a cylindrical cavity

1970 ◽  
Vol 67 (3) ◽  
pp. 689-710 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Half Space ◽  
Cylindrical Cavity ◽  
Elastic Half Space ◽  
System Of Equations ◽  
Expansion Theorem ◽  
Elastic Potentials ◽  
Time Harmonic ◽  
Propagation Of Waves ◽  
Radiation Conditions ◽  
Conditions At Infinity

AbstractThe problem of the propagation of time harmonic waves in an isotropic elastic half-space containing a submerged cylindrical cavity is solved analytically. Linear plane strain conditions are assumed. Using an expansion theorem proved in a previous paper (Gregory (3)), the elastic potentials are expanded in a series form which automatically satisfies the governing equations, the conditions of zero stress on the flat surface, and the radiation conditions at infinity. The conditions of prescribed normal and tangential stresses on the cavity walls are shown to lead to an infinite system of equations for the expansion coefficients. This system of equations is shown to be a regular L2-system of the second kind and from its unique l2-solution, the solution to the problem is constructed. The fundamental questions of existence and uniqueness are fully treated and methods are described for constructing the solution.Three applications of the general theory are presented dealing respectively with the production, amplification and reflexion of Rayleigh waves.

Wave propagation dynamics in a fractional Zener model with stochastic excitation

2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Wave Propagation ◽  
Constitutive Equation ◽  
Equations Of Motion ◽  
Weak Form ◽  
Stochastic Excitation ◽  
Expansion Theorem ◽  
Zener Model ◽  
Dissipation Inequality ◽  
Regularity Properties ◽  
Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

Investigation Into Thermal Stress Characteristics of Pipe-in-Pipe Under High Temperature Condition

2018 ◽  
Author(s):  
Si-Hwa Jeong ◽  
Min-Gu Won ◽  
Nam-Su Huh ◽  
Yun-Jae Kim ◽  
Young-Jin Oh ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
High Temperature ◽  
Temperature Distribution ◽  
Heat Transfer Analysis ◽  
Piping System ◽  
Curved Pipe ◽  
High Temperature Condition ◽  
Single Pipe ◽  
Radiation Conditions

In this paper, the thermal stress characteristics of the pipe-in-pipe (PIP) system under high temperature condition are analyzed. The PIP is a type of pipe applied in sodium-cooled faster reactor (SFR) and has a different geometry from a single pipe. In particular, under the high temperature condition of the SFR, the high thermal stress is generated due to the temperature gradient occurring between the inner pipe and outer pipe. To investigate the thermal stress characteristics, three cases are considered according to geometry of the support. The fully constrained support and intermediate support are considered for case 1 and 2, respectively. For case 3, both supports are applied to the actual curved pipe. The finite element (FE) analyses are performed in two steps for each case. Firstly, the heat transfer analysis is carried out considering the thermal conduction, convection and radiation conditions. From the heat transfer analysis, the temperature distribution results in the piping system are obtained. Secondly, the structural analysis is performed considering the temperature distribution results and boundary conditions. Finally, the effects of the geometric characteristics on the thermal stress in the PIP system are analyzed.

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