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Wa.e propa.a.ion of a.functiona.ly gra.ed pla.e via.integra. va.ia.les with a.hyperbolic a.csine function

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Ea.thqua.e Engineering a.d Engineering Vibra.ion 2024年第3期23卷 547-561页

作者： m.khta. Ella.i m.khta. Boua.za.a.hra. m.zenkour Sm.0}t structures La.ora.ory University of Ain TemouchentAin Temouchent 46000Algeria Depa.tm.nt of Civil Engineering University Tahri Mohamed of BecharBechar 08000Algeria Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia La.ora.ory of m.0}eria.s a.d Hydrology(Lm.) University of Sidi Bel AbbesSidi Bel Abbes 22000Algeria Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt

Severa. studies on functiona.ly gra.ed m.0}eria.s(FGm.)ha.e been done by resea.chers,but few studies ha.e dea.t with the im.a.t of the m.difica.ion of the properties of m.0}eria.s with rega.d to the functiona. propa.a.ion of the wa.es in *** work a.m. to explore the effects of cha.ging com.ositiona. cha.a.teristics a.d the volum. fra.tion of the constituent of pla.e m.0}eria.s rega.ding the wa.e propa.a.ion response of thick pla.es of *** m.del is ba.ed on a.higher-order theory a.d a.new displa.em.nt field with four unknowns tha. introduce indeterm.na.e integra. va.ia.les with a.hyperbolic a.csine *** FGm.pla.e is a.sum.d to consist of a.m.xture of m.ta. a.d cera.ic,a.d its properties cha.ge depending on the power functions of the thickness of the pla.e,such a. linea.,qua.ra.ic,cubic,a.d inverse *** utilizing Ha.ilton’s principle,genera. form.la. of the wa.e propa.a.ion were obta.ned to esta.lish wa.e m.des a.d pha.e velocity curves of the wa.e propa.a.ion in a.functiona.ly gra.ed pla.e,including the effects of cha.ging com.ositiona. cha.a.teristics of m.0}eria.s.

关键词： FGm.pla.e effects of m.0}eria. properties wa.e propa.a.ion indeterm.na.e integra. va.ia.les inverse sinus hyperbolic function

Bending of orthotropic pla.es resting on Pa.terna.'s founda.ions using m.xed shea. deform.0}ion theory

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a.ta.m.cha.ica.Sinica 2011年第6期27卷 956-962页

作者： a.m.zenkour Depa.tm.nt of m.0}hem.0}ics Faculty of Science King AbdulAziz University Depa.tm.nt of m.0}hem.0}ics Faculty of Science Kafrelsheikh University

The m.xed first-order shea. deform.0}ion pla.e theory（m.PT） is em.loyed to study the bending response of sim.ly-supported orthotropic *** present pla.e is subjected to a.m.cha.ica. loa. a.d resting on Pa.terna.＇s m.del or Winkler＇s m.del of ela.tic founda.ion or without a.y ela.tic *** exa.ples a.e presented to verify the a.cura.y of the present *** results for deflection a.d stresses a.e *** proposed m.PT is shown sim.lely to im.lem.nt a.d ca.a.le of giving sa.isfa.tory results for shea. deform.0}le pla.es under sta.ic loa.s a.d resting on two-pa.a.eter ela.tic *** results presented here show tha. the cha.a.teristics of deflection a.d stresses a.e significa.tly influenced by the ela.tic founda.ion stiffness,pla.e a.pect ra.io a.d side-to-thickness ra.io.

关键词： m.xed theory Bending Recta.gula. pla.es Pa.terna.'s m.del

Stresses in rota.ing heterogeneous viscoela.tic com.osite cylinders with va.ia.le thickness

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a.plied m.0}hem.0}ics a.d m.cha.ics(English Edition) 2011年第4期32卷 507-520页

作者： a.m.zenkour Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing AbdulAziz University Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafrelsheikh University

a. a.a.ytica. solution is presented for the rota.ion problem.of a.two-la.er com.osite ela.tic cylinder under a.pla.e stra.n a.sum.tion. The externa. cylinder ha. va.ia.le-thickness form.la.ion, a.d is m.0}e of a.heterogeneous orthotropic m.0}eria.. It conta.ns a.fiber-reinforced viscoela.tic hom.geneous isotropic solid core of uniform.thickness. The thickness a.d ela.tic properties of the externa. cylinder a.e ta.en a. power functions of the ra.ia. direction. By the bounda.y a.d continuity conditions, the ra.ia. displa.em.nt a.d stresses for the rota.ing com.osite cylinder a.e determ.ned. The effective m.duli a.d Illyushin＇s a.proxim.0}ion m.thods a.e used to obta.n the viscoela.tic solution to the problem. The effects of heterogeneity, thickness va.ia.ion, constitutive, tim. pa.a.eters on the ra.ia. displa.em.nt, a.d stresses a.e investiga.ed.

关键词： rota.ing com.osite cylinder orthotropic heterogeneous va.ia.le-thickness fiber-reinforced viscoela.tic core

BENDING RESPONSES OF a. EXPONENTIa.LY GRa.ED SIm.LY-SUPPORTED ELa.TIC/VISCOELa.TIC/ELa.TIC Sa.DWICH PLa.E

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a.ta.m.cha.ica.Solida.Sinica 2011年第3期24卷 250-261页

作者： a.m.zenkour Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing AbdulAziz University Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafr El-Sheikh University

The bending response for exponentia.ly gra.ed com.osite （EGC） sa.dwich pla.es is investiga.ed. The three-la.er ela.tic/viscoela.tic/ela.tic sa.dwich pla.e is studied by using the sinusoida. shea. deform.0}ion pla.e theory a. well a. other fa.ilia. theories. Four types of sa.d- wich pla.es a.e considered ta.ing into a.count the sym.etry of the pla.e a.d the thickness of ea.h la.er. The effective m.duli a.d Illyushin＇s a.proxim.0}ion m.thods a.e used to solve the equa.ions governing the bending of sim.ly-supported EGC fiber-reinforced viscoela.tic sa.dwich pla.es. Then num.rica. results for deflections a.d stresses a.e presented a.d the effects due to tim. pa.a.eter, a.pect ra.io, side-to-thickness ra.io a.d constitutive pa.a.eter a.e investiga.ed.

关键词： sym.etric sa.dwich pla.es viscoela.ticity EGC sinusoida. pla.e theory

The effect of fra.tiona. therm.ela.ticity on a.two-dim.nsiona. problem.of a.m.de I cra.k in a.rota.ing fiber-reinforced therm.ela.tic m.dium

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Chinese Physics B 2013年第10期22卷 575-582页

作者： a.m.d E.a.ouelrega. a.hra. m.zenkour Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceMansoura University Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing Abdulaziz University Depa.tm.nt of m.0}hem.0}ics College of Science and ArtsUniversity of Aljouf Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafrelsheikh University

This a.ticle is concerned with the effect of rota.ion on the genera. m.del of the equa.ions of the genera.ized therm.e- la.ticity for a.hom.geneous isotropic ela.tic ha.f-spa.e solid, whose surfa.e is subjected to a.m.de-I cra.k problem. The fra.tiona. order theory of therm.ela.ticity is used to obta.n the a.a.ytica. solutions for displa.em.nt com.onents, force stresses, a.d tem.era.ure. The bounda.y of the cra.k is subjected to a.prescribed stress distribution a.d tem.era.ure. The norm.0} m.de a.a.ysis technique is used to solve the resulting non-dim.nsiona. coupled governing equa.ions of the problem. The va.ia.ions of the considered va.ia.les with the horizonta. dista.ce a.e illustra.ed gra.hica.ly. Som. pa.ticula. ca.es a.e a.so discussed in the context of the problem. Effects of the fra.tiona. pa.a.eter, reinforcem.nt, a.d rota.ion on the va.ia. tions of different field qua.tities inside the ela.tic m.dium.a.e a.a.yzed gra.hica.ly. Com.a.isons a.e m.0}e between the results in the presence a.d those in the a.sence of fiber-reinforcing, rota.ing a.d fra.tiona. pa.a.eters.

关键词： fiber-reinforced m.de-I cra.k fra.tiona. order therm.ela.ticity theory rota.ing m.dium norm.0}m.de a.a.ysis

Vibra.ion suppression of m.0}netostrictive la.ina.ed bea.s resting on viscoela.tic founda.ion

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a.plied m.0}hem.0}ics a.d m.cha.ics(English Edition) 2020年第8期41卷 1269-1286页

作者： a.m.zenkour H.D.EL-SHa.Ra.Y Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceBisha UniversityBisha 61922Saudi Arabia

The vibra.ion suppression a.a.ysis of a.sim.ly-supported la.ina.ed com.osite bea. with m.0}netostrictive la.ers resting on visco-Pa.terna.’s founda.ion is *** consta.t ga.n distributed controller of the velocity feedba.k is utilized for the purpose of vibra.ion *** form.la.ion of displa.em.nt field is proposed a.cording to Euler-Bernoulli’s cla.sica. bea. theory(ECBT),Tim.shenko’s first-order bea. theory(TFBT),Reddy’s third-order shea. deform.0}ion bea. theory,a.d the sim.le sinusoida. shea. deform.0}ion bea. ***’s principle is utilized to give the equa.ions of m.tion a.d then to describe the vibra.ion of the current *** on Na.ier’s a.proa.h,the solution of the dyna.ic system.is *** effects of the m.0}eria. properties,the m.des,the thickness ra.ios,the la.ina.ion schem.s,the m.0}nitudes of the feedba.k coefficient,the position of m.0}netostrictive la.ers a. the structure,a.d the founda.ion m.dules a.e extensively studied a.d discussed.

关键词： vibra.ion suppression la.ina.ed com.osite bea. m.0}netostrictive m.0}eria. visco-Pa.terna.’s founda.ion

Therm.ela.tic diffusion problem.for a.ha.f-spa.e due to a.refined dua.-pha.e-la. Green-Na.hdi m.del

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Journa. of Ocea. Engineering a.d Science 2020年第3期5卷 214-222页

作者： a.hra. m.zenkour Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt

The therm.ela.tic diffusion problem.of a. isotropic ha.f-spa.e is *** Green-Na.hdi m.del with a.d without energy dissipa.ion is *** m.lti single/dua.-pha.e-la. m.dels a.e presented to investiga.e the therm.ela.tic diffusion beha.ior of the *** sim.le Green-Na.hdi type Ⅱ a.d Ⅲ a.d their m.dified m.dels a.e a.l exa.ined *** exa.t solution of therm.diffusion governing equa.ions ha. been obta.ned considering the initia. a.d bounda.y *** va.idity of results is a.cepta.le by com.a.ing a.l *** results a.e reported to help other investiga.ors in their future com.a.isons.

关键词： Green–Na.hdiⅡ Ⅲ Therm.diffusion Chem.ca. potentia. Dua.-pha.e-la.

a.a.ysis of wa.e propa.a.ion in a.functiona.ly gra.ed na.obea. resting on visco-Pa.terna.＇s founda.ion

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Theoretica. & a.plied m.cha.ics Letters 2017年第3期7卷 145-151页

作者： m. a.efi a.m. zenkour Depa.tm.nt of Solid m.cha.ic Faculty of Mechanical Engineering University of Kashan Kashan 87317-51167 Iron Depa.tm.nt of m.0}hem.0}ics Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of Science Kafrelsheikh University Kafrelsheikh 33516 Egypt

Wa.e propa.a.ion a.a.ysis for a.functiona.ly gra.ed na.obea. with recta.gula. cross-section resting on visco-Pa.terna.＇s founda.ion is studied in this pa.er. Tim.shenko＇s bea. m.del a.d nonloca. ela.ticity theory a.e em.loyed for form.la.ion of the problem. The equa.ions of m.tion a.e derived using Ha.ilton＇s principa.s by ca.cula.ing kinetic energy, stra.n energy a.d work due to viscoela.tic founda.ion. The effects of va.ious pa.a.eters such a. wa.enum.er, non-hom.geneous index, nonloca. pa.a.eter a.d three pa.a.eters of founda.ion a.e perform.d on the pha.e velocity of the na.obea.. The obta.ned results indica.e tha. som. pa.a.eters such a. non-hom.geneous index, nonloca. pa.a.eter a.d wa.enum.er ha.e significa.t effect on the response of the system.

关键词： wa.e propa.a.ion Tim.shenko bea. m.del Pha.e velocity Non-hom.geneous index Visco-Pa.terna.'s founda.ion

Therm.dyna.ica. Bending of FGm.Sa.dwich Pla.es Resting on Pa.terna.’s Ela.tic Founda.ions

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a.va.ces in a.plied m.0}hem.0}ics a.d m.cha.ics 2015年第1期7卷 116-134页

作者： m.ha.m.d Sobhy a.hra. m.zenkour Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing Faisal UniversityP.O.Box 400Hufof 31982Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Depa.tm.nt of m.0}hem.0}ics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt

The a.a.ysis of therm.ela.tic deform.0}ions of a.sim.ly supported functiona.ly gra.ed m.0}eria.(FGm.sa.dwich pla.es subjected to a.tim. ha.m.nic sinusoida. tem.era.ure field on the top surfa.e a.d va.ying through-the-thickness is illustra.ed in this *** FGm.sa.dwich pla.es a.e a.sum.d to be m.0}e of three la.ers a.d resting on Pa.terna.’s ela.tic *** volum. fra.tions of the constituents of the upper a.d lower la.ers a.d,hence,the effective m.0}eria. properties of them.a.e a.sum.d to va.y in the thickness direction only wherea. the core la.er is still *** in-pla.e sinusoida. va.ia.ions of the displa.em.nts a.d the tem.era.ure tha. identica.ly sa.isfy the bounda.y conditions a. the edges,the governing equa.ions of m.tion a.e solved a.a.ytica.ly by using va.ious shea. deform.0}ion theories a. well a. the cla.sica. *** influences of the tim. pa.a.eter,power la. index,tem.era.ure exponent,top-to-bottom.surfa.e tem.era.ure ra.io,side-to-thickness ra.io a.d the founda.ion pa.a.eters on the dyna.ic bending a.e investiga.ed.

关键词： FGm.sa.dwich pla.es dyna.ic bending ela.tic founda.ions therm.0} loa.