简介:Inthispaper,antiplaneresponseofanisoscelestriangularhilltoincidentSHwavesisstudiedbasedonthemethodofcomplexfunctionandbyusingmovingcoordinatesystem.Thestandingwavefunction,whichcansatisfythegoverningequationandboundarycondition,isprovided.Furthermore,numericalexamplesarepresented;theinfluencesofwavenumberandangleoftheincidentwavesandtheangleofthehill'speakongroundmotionarediscussed.
简介:Inthisstudy,thenull-fieldboundaryintegralequationmethod(BIEM)andtheimagemethodareusedtosolvetheSHwavescatteringproblemcontainingsemi-circularcanyonsandcirculartunnels.Tofullyutilizetheanalyticalpropertyofcirculargeometry,thepolarcoordinatesareusedtoexpandtheclosed-formfundamentalsolutiontothedegeneratekernel,andtheFourierseriesisalsointroducedtorepresenttheboundarydensity.Bycollocatingboundarypointstomatchboundaryconditionontheboundary,alinearalgebraicsystemisconstructed.Theunknowncoefficientsinthealgebraicsystemcanbeeasilydetermined.Inthisway,asemi-analyticalapproachisdeveloped.Followingtheexperienceofnear-trappedmodesinwaterwaveproblemsofthefullplane,thefocusingphenomenonandnear-trappedmodesfortheSHwaveproblemofthehalf-planearesolved,sincethetwoproblemsobeythesamemathematicalmodel.Inthisstudy,itisfoundthattheSHwaveproblemcontainingtwosemi-circularcanyonsandacirculartunnelhasthenear-trappedmodeandthefocusingphenomenonforaspecialincidentangleandwavenumber.Inthissituation,theamplificationfactorfortheamplitudeofdisplacementisover300.
简介:Inthispaper,ananalyticmethodisdevelopedtoaddresssteadySH-wavescatteringandperformdynamicanalysisofmultiplecircularcavitiesinhalfspace.ThescatteredwavefunctionusedforscatteringofSH-wavesbymultiplecircularcavities,whichautomaticallysatisfiesthestress-freeconditionatthehorizontalsurface,isconstructedbyapplyingthesymmetryoftheSH-wavescatteringandthemethodofmulti-polarcoordinatessystem.Applyingthisscatteredwavefunctionandmethodofmovingcoordinates,theoriginalproblemcanbetransformedtotheproblemofSH-wavescatteringbymultiplecircularcavitiesinthefullspace.Finally,thesolutionoftheproblemcanbereducedtoaseriesofalgebraicequationsandsolvednumericallybytruncatingtheinfinitealgebraicequationstothefiniteones.Numericalexamplesareprovidedforcasewithtwocavitiestoshowtheeffectofwavenumber,andthedistancesbetweenthecentersofthecavitiesandfromthecenterstothegroundsurfaceonthedynamicstressconcentrationaroundthecavityimpactedbyincidentsteadySH-wave.