Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Boyang Ding ◽  
Alexander H.-D. Cheng ◽  
Zhanglong Chen
Keyword(s):  
Integral Equation ◽  
Wave Field ◽  
Frequency Domain ◽  
Compressional Wave ◽  
Fundamental Solutions ◽  
Point Force ◽  
Wave Fields ◽  
Wave Effects ◽  
Wave Decomposition ◽  
2D And 3D

Fundamental solutions of poroelastodynamics in the frequency domain have been derived by Cheng et al. (1991, “Integral Equation for Dynamic Poroelasticity in Frequency Domain With BEM Solution,” J. Eng. Mech., 117(5), pp. 1136–1157) for the point force and fluid source singularities in 2D and 3D, using an analogy between poroelasticity and thermoelasticity. In this paper, a formal derivation is presented based on the decomposition of a Dirac δ function into a rotational and a dilatational part. The decomposition allows the derived fundamental solutions to be separated into a shear and two compressional wave components, before they are combined. For the point force solution, each of the isolated wave components contains a term that is not present in the combined wave field; hence can be observable only if the present approach is taken. These isolated wave fields may be useful in applications where it is desirable to separate the shear and compressional wave effects. These wave fields are evaluated and plotted.

Interaction of High Frequency Lamb Waves with Surface-Mount Sensor Adhesives

2013 ◽  
Vol 558 ◽  
pp. 489-500 ◽  
Author(s):  
Patrick Norman ◽  
Claire Davis ◽  
Cédric Rosalie ◽  
Nik Rajic
Keyword(s):  
Wave Field ◽  
Lamb Waves ◽  
Base Material ◽  
Adhesive Layer ◽  
Scattered Wave ◽  
Phase Lag ◽  
Wave Fields ◽  
Surface Mount ◽  
Frequency Regime ◽  
Fibre Bragg Gratings

The application of Lamb waves to damage and/or defect detection in structures is typicallyconfined to lower frequencies in regimes where only the lower order modes propagate in order to simplifyinterpretation of the scattered wave-fields. Operation at higher frequencies offers the potentialto extend the sensitivity and diagnostic capability of this technique, however there are technical challengesassociated with the measurement and interpretation of this data. Recent work by the authorshas demonstrated the ability of fibre Bragg gratings (FBGs) to measure wave-fields at frequencies inexcess of 2 MHz [1]. However, when this work was extended to other thinner plate specimens it wasfound that at these higher frequencies, the cyanoacrylate adhesive (M-Bond 200) used to attach theFBG sensors to the plate was significantly affecting the propagation of the waves. Laser vibrometrywas used to characterise the wave-field in the region surrounding the adhesive and it was found that theself-adhesive retro-reflective tape applied to aid with this measurement was also affecting the wavefieldin the higher frequency regime. This paper reports on an experimental study into the influence ofboth of these materials on the propagating wave-field. Three different lengths of retro-reflective tapewere placed in the path of Lamb waves propagating in an aluminium plate and laser vibrometry wasused to measure the wave-field upstream and downstream of the tape for a range of different excitationfrequencies. The same experiment was conducted using small footprint cyanoacrylate film samplesof different thickness. The results show that both of these surface-mount materials attenuate, diffractand scatter the incoming waves as well as introducing a phase lag. The degree of influence of thesurface layer appears to be a function of its material properties, the frequency of the incoming waveand the thickness and footprint of the surface layer relative to the base material thickness. Althoughfurther work is required to characterise the relative influence of each of these variables, investigationsto date show that for the measurement of Lamb Waves on thin structures, careful considerationshould be given to the thickness and footprint of the adhesive layer and sensor, particularly in the highfrequency regime, so as to minimise their effect on the measurement.

Influence of the Waterline Integral on the Solution of the Frequency-Domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

2014 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
G. J. Lee ◽  
M. S. Shin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Frequency Domain ◽  
Surface Condition ◽  
Numerical Results ◽  
Forward Speed ◽  
Line Integral ◽  
Free Surface Condition ◽  
Surface Green Function

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2003 ◽  
Vol 70 (5) ◽  
pp. 661-667 ◽  
Author(s):  
A. S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
Relaxation Times ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Phase Lag ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. The given model is applicable to three generalized theories of thermoelasticity: the generalized theory with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) and with dual phase-lag (Chandrasekharaiah-Tzou theory) as well as to the dynamic coupled theory. The cases of thermo-viscoelasticity of Kelvin-Voigt model or thermoviscoelasticity ignoring the rheological properties of the volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation (BIE) method, fundamental solutions of the corresponding differential equations are obtained and an example illustrating the BIE formulation is given.

Generation of Regular and Irregular Waves in Navier-Stokes CFD Solvers by Matching With the Nonlinear Potential Wave Solution at the Boundaries

2018 ◽  
Author(s):  
Youngmyung Choi ◽  
Benjamin Bouscasse ◽  
Sopheak Seng ◽  
Guillaume Ducrozet ◽  
Lionel Gentaz ◽  
...  
Keyword(s):  
Viscous Flow ◽  
Open Source ◽  
Cfd Simulation ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Wave Fields ◽  
Flow Solver ◽  
Nonlinear Potential ◽  
Simulation Parameters ◽  
2D And 3D

The capability of wave generation and absorption in a viscous flow solver becomes important for achieving realistic simulations in naval and offshore fields. This study presents an efficient generation of nonlinear wave fields in the viscous flow solver by using a nonlinear potential solver called higher-order spectral method (HOS). The advantages of using a fully nonlinear potential solver for the generation of irregular waves are discussed. In particular, it is shown that the proposed method allows the CFD simulation to start at the time and over the space of interest, retrieved from the potential flow solution. The viscous flow solver is based on the open source library OpenFOAM. The potential solvers used to generate waves are the open source solvers HOS-Ocean and HOS-NWT (Numerical Wave Tank). Several simulation parameters in the CFD solver are investigated in the present study. A HOS wrapper program is newly developed to regenerate wave fields in the viscous flow solver. The wrapper program is validated with OpenFOAM for 2D and 3D regular and irregular waves using relaxation zones. Finally, the extreme waves corresponding to the 1000 year return period condition in the Gulf of Mexico are simulated with the viscous flow solver and the wave elevation is compared with the experiments.

Response of Piezoelectric Solids to Unitary Impulsive Loads: A Computational Approach

1995 ◽  
Author(s):  
Naum Khutoryansky ◽  
Horacio Sosa
Keyword(s):  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Computational Approach ◽  
Slowness Surface ◽  
Plane Wave Decomposition ◽  
Impulsive Loads ◽  
Applied Forces ◽  
Piezoelectric Solids ◽  
Wave Decomposition ◽  
Dimensional Integral

Abstract Fundamental solutions for transient dynamic piezo-electricity are derived through the plane wave decomposition and represented in three alternative manners, namely over the unit sphere, over the material’s slowness surface and over a line of the latter. The computational virtues of the uni-dimensional integral representation are exposed through a numerical example concerning a transversely isotropic piezoelectric ceramic subjected to unitary impulsive applied forces.

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