Vibration of functionally graded sandwich doubly curved shells using improved shear deformation theory
|
摘要
Nonlinear forced vibrations and natural frequency of sandwich functionally graded material doubly curved shallow shell with a rectangular base are investigated. The sandwich functionally graded material(FGM) doubly curved shell is subjected to a harmonic point load at centre. The sandwich doubly curved shell with homogeneous face sheets and FGM face sheets is considered respectively when the natural frequencies are studied. Reddy's third order shear deformation theory is expanded in which stretching effects in thickness are considered by introducing the secant function. Hamilton's principle and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the FGM sandwich doubly curved shell. Comparative studies with other shear deformation theories are carried out to validate the present formulation. Navier method is used to discuss the natural vibration frequencies of the FGM sandwich doubly curved shell. Numerical simulation is applied to demonstrate the nonlinear dynamic responses of the FGM sandwich doubly curved shell. Multiple periods, quasi-period and chaos are detected for the dynamic system for different core thickness.
Nonlinear forced vibrations and natural frequency of sandwich functionally graded material doubly curved shallow shell with a rectangular base are investigated. The sandwich functionally graded material(FGM) doubly curved shell is subjected to a harmonic point load at centre. The sandwich doubly curved shell with homogeneous face sheets and FGM face sheets is considered respectively when the natural frequencies are studied. Reddy's third order shear deformation theory is expanded in which stretching effects in thickness are considered by introducing the secant function. Hamilton's principle and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the FGM sandwich doubly curved shell. Comparative studies with other shear deformation theories are carried out to validate the present formulation. Navier method is used to discuss the natural vibration frequencies of the FGM sandwich doubly curved shell. Numerical simulation is applied to demonstrate the nonlinear dynamic responses of the FGM sandwich doubly curved shell. Multiple periods, quasi-period and chaos are detected for the dynamic system for different core thickness.
Nonlinear forced vibrations and natural frequency of sandwich functionally graded material doubly curved shallow shell with a rectangular base are investigated. The sandwich functionally graded material(FGM) doubly curved shell is subjected to a harmonic point load at centre. The sandwich doubly curved shell with homogeneous face sheets and FGM face sheets is considered respectively when the natural frequencies are studied. Reddy's third order shear deformation theory is expanded in which stretching effects in thickness are considered by introducing the secant function. Hamilton's principle and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the FGM sandwich doubly curved shell. Comparative studies with other shear deformation theories are carried out to validate the present formulation. Navier method is used to discuss the natural vibration frequencies of the FGM sandwich doubly curved shell. Numerical simulation is applied to demonstrate the nonlinear dynamic responses of the FGM sandwich doubly curved shell. Multiple periods, quasi-period and chaos are detected for the dynamic system for different core thickness.
引文
1 Li H D,Zhu X,Mei Z Y,et al.Bending of orthotropic sandwich plates with a functionally graded core subjected to distributed loadings.Acta Mech Solid Sin,2013,26:292–301
2 Wang Z X,Shen H S.Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations.Compos Struct,2011,93:2521–2532
3 Natarajan S,Manickam G.Bending and vibration of functionally graded material sandwich plates using an accurate theory.Finite Elem Anal Des,2012,57:32–42
4 Carrera E,Brischetto S,Cinefra M,et al.Effects of thickness stretching in functionally graded plates and shells.Compos Part B-Eng,2011,42:123–133
5 Batra R C,Vidoli S,Vestroni F.Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories.J Sound Vib,2002,257:63–88
6 Pindera M J,Williams T O,Arnold S M.Thermoplstic response of metal-matrix composites with homogenized and functionally graded interfaces.Compos Eng,1994,4:129–145
7 Neves A M A,Ferreira A J M,Carrera E,et al.Static,free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique.Compos Part B-Eng,2013,44:657–674
8 Sid Ahmed Houari M,Tounsi A,Anwar Bég O.Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory.Int J Mech Sci,2013,76:102 –111
9 Alibeigloo A.Three-dimensional thermo-elasticity solution of sandwich cylindrical panel with functionally graded core.Compos Struct,2014,107:458–468
10 Meiche N E,Tounsi A,Ziane N,et al.A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate.Int J Mech Sci,2011,53:237–247
11 Reddy J N,Kim J.A nonlinear modified couple stress-based thirdorder theory of functionally graded plates.Compos Struct,2012,94:1128–1143
12 Xiang S,Jin Y X,Bi Z Y,et al.A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates.Compos Struct,2011,93:2826–2832
13 Malekzadeh P,Ghaedsharaf M.Three-dimensional free vibration of laminated cylindrical panels with functionally graded layers.Compos Struct,2014,108:894–904
14 Mantari J L,Guedes Soares C.A trigonometric plate theory with 5-unknowns and stretching effect for advanced composite plates.Compos Struct,2014,107:396–405
15 Mantari J L,Guedes Soares C.A novel higher-order shear deformation theory with stretching effect for functionally graded plates.Compos Part B-Eng,2013,45:268–281
16 Madhukar S,Singha M K.Geometrically nonlinear finite element analysis of sandwich plates using normal deformation theory.Compos Struct,2013,97:84–90
17 Tounsi A,Houari M S A,Benyoucef S,et al.A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates.Aerosp Sci Technol,2013,24:209–220
18 Carrera E.Historical review of Zig-Zag theories for multilayered plates and shells.Appl Mech Rev,2003,56:287–308
19 Neves A M A,Ferreira A J M,Carrera E,et al.Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects.Adv Eng Softw,2012,52:30 –43
20 Sahoo R,Singh B N.A new shear deformation theory for the static analysis of laminated composite and sandwich plates.Int J Mech Sci,2013,75:324–336
21 Amabili M.Non-linear vibrations of doubly curved shallow shells.Int J Non-linear Mech,2005,40:683–710
22 Amabili M.Nonlinear Vibrations and Stability of Shells and Plates.New York:Cambridge University Press,2008
23 Pradyumna S,Bandyopadhyay J N.Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation.J Sound Vib,2008,318:176–192
24 Tornabene F,Liverani A,Caligiana G.FGM and laminated doubly curved shells and panels of revolution with a free-form meridian:A 2D GDQ solution for free vibrations.Int J Mech Sci,2011,53:446 –470
25 Tornabene F.Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on WinklerPasternak elastic foundations.Compos Struct,2011,94:186–206
26 Viola E,Tornabene F.Free vibrations of three parameter functionally graded parabolic panels of revolution.Mech Res Commun,2009,36:587–594
27 Cinefra M,Belouettar S,Soave M,et al.Variable kinematic models applied to free-vibration analysis of functionally graded material shells.Eur J Mech-A/Solids,2010,29:1078–1087
28 Chorfi S M,Houmat A.Non-linear free vibration of a functionally graded doubly-curved shallow shell of elliptical plan-form.Compos Struct,2010,92:2573–2581
29 Alijani F,Amabili M,Bakhtiari-Nejad F.Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory.Compos Struct,2011,93:2541–2553
30 Alijani F,Amabili M,Karagiozis K,et al.Nonlinear vibrations of functionally graded doubly curved shallow shells.J Sound Vib,2011,330 :1432–1454
31 Wang Q,Shi D,Liang Q,et al.Free vibration of four-parameter functionally graded moderately thick doubly-curved panels and shells of revolution with general boundary conditions.Appl Math Model,2017,42:705–734
32 Tornabene F,Fantuzzi N,Bacciocchi M,et al.MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells.Compos Part B-Eng,2016,99:30–47
33 Useche J,Harnish C.A boundary element method formulation for modal analysis of doubly curved thick shallow shells.Appl Math Model,2016,40:3591–3600
34 Reddy J N.Mechanics of Laminated Composite Plates and Shells:Theory and Analysis.New York:CRC Press,2004
35 Li Q,Iu V P,Kou K P.Three-dimensional vibration analysis of functionally graded material sandwich plates.J Sound Vib,2008,311:498 –515
36 Yang J,Hao Y X,Zhang W,et al.Nonlinear dynamic response of a functionally graded plate with a through-width surface crack.Nonlinear Dyn,2010,59:207–219
37 Pandey S,Pradyumna S.Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory.Eur J Mech-A/Solids,2015,51:55–66
2 Wang Z X,Shen H S.Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations.Compos Struct,2011,93:2521–2532
3 Natarajan S,Manickam G.Bending and vibration of functionally graded material sandwich plates using an accurate theory.Finite Elem Anal Des,2012,57:32–42
4 Carrera E,Brischetto S,Cinefra M,et al.Effects of thickness stretching in functionally graded plates and shells.Compos Part B-Eng,2011,42:123–133
5 Batra R C,Vidoli S,Vestroni F.Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories.J Sound Vib,2002,257:63–88
6 Pindera M J,Williams T O,Arnold S M.Thermoplstic response of metal-matrix composites with homogenized and functionally graded interfaces.Compos Eng,1994,4:129–145
7 Neves A M A,Ferreira A J M,Carrera E,et al.Static,free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique.Compos Part B-Eng,2013,44:657–674
8 Sid Ahmed Houari M,Tounsi A,Anwar Bég O.Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory.Int J Mech Sci,2013,76:102 –111
9 Alibeigloo A.Three-dimensional thermo-elasticity solution of sandwich cylindrical panel with functionally graded core.Compos Struct,2014,107:458–468
10 Meiche N E,Tounsi A,Ziane N,et al.A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate.Int J Mech Sci,2011,53:237–247
11 Reddy J N,Kim J.A nonlinear modified couple stress-based thirdorder theory of functionally graded plates.Compos Struct,2012,94:1128–1143
12 Xiang S,Jin Y X,Bi Z Y,et al.A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates.Compos Struct,2011,93:2826–2832
13 Malekzadeh P,Ghaedsharaf M.Three-dimensional free vibration of laminated cylindrical panels with functionally graded layers.Compos Struct,2014,108:894–904
14 Mantari J L,Guedes Soares C.A trigonometric plate theory with 5-unknowns and stretching effect for advanced composite plates.Compos Struct,2014,107:396–405
15 Mantari J L,Guedes Soares C.A novel higher-order shear deformation theory with stretching effect for functionally graded plates.Compos Part B-Eng,2013,45:268–281
16 Madhukar S,Singha M K.Geometrically nonlinear finite element analysis of sandwich plates using normal deformation theory.Compos Struct,2013,97:84–90
17 Tounsi A,Houari M S A,Benyoucef S,et al.A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates.Aerosp Sci Technol,2013,24:209–220
18 Carrera E.Historical review of Zig-Zag theories for multilayered plates and shells.Appl Mech Rev,2003,56:287–308
19 Neves A M A,Ferreira A J M,Carrera E,et al.Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects.Adv Eng Softw,2012,52:30 –43
20 Sahoo R,Singh B N.A new shear deformation theory for the static analysis of laminated composite and sandwich plates.Int J Mech Sci,2013,75:324–336
21 Amabili M.Non-linear vibrations of doubly curved shallow shells.Int J Non-linear Mech,2005,40:683–710
22 Amabili M.Nonlinear Vibrations and Stability of Shells and Plates.New York:Cambridge University Press,2008
23 Pradyumna S,Bandyopadhyay J N.Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation.J Sound Vib,2008,318:176–192
24 Tornabene F,Liverani A,Caligiana G.FGM and laminated doubly curved shells and panels of revolution with a free-form meridian:A 2D GDQ solution for free vibrations.Int J Mech Sci,2011,53:446 –470
25 Tornabene F.Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on WinklerPasternak elastic foundations.Compos Struct,2011,94:186–206
26 Viola E,Tornabene F.Free vibrations of three parameter functionally graded parabolic panels of revolution.Mech Res Commun,2009,36:587–594
27 Cinefra M,Belouettar S,Soave M,et al.Variable kinematic models applied to free-vibration analysis of functionally graded material shells.Eur J Mech-A/Solids,2010,29:1078–1087
28 Chorfi S M,Houmat A.Non-linear free vibration of a functionally graded doubly-curved shallow shell of elliptical plan-form.Compos Struct,2010,92:2573–2581
29 Alijani F,Amabili M,Bakhtiari-Nejad F.Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory.Compos Struct,2011,93:2541–2553
30 Alijani F,Amabili M,Karagiozis K,et al.Nonlinear vibrations of functionally graded doubly curved shallow shells.J Sound Vib,2011,330 :1432–1454
31 Wang Q,Shi D,Liang Q,et al.Free vibration of four-parameter functionally graded moderately thick doubly-curved panels and shells of revolution with general boundary conditions.Appl Math Model,2017,42:705–734
32 Tornabene F,Fantuzzi N,Bacciocchi M,et al.MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells.Compos Part B-Eng,2016,99:30–47
33 Useche J,Harnish C.A boundary element method formulation for modal analysis of doubly curved thick shallow shells.Appl Math Model,2016,40:3591–3600
34 Reddy J N.Mechanics of Laminated Composite Plates and Shells:Theory and Analysis.New York:CRC Press,2004
35 Li Q,Iu V P,Kou K P.Three-dimensional vibration analysis of functionally graded material sandwich plates.J Sound Vib,2008,311:498 –515
36 Yang J,Hao Y X,Zhang W,et al.Nonlinear dynamic response of a functionally graded plate with a through-width surface crack.Nonlinear Dyn,2010,59:207–219
37 Pandey S,Pradyumna S.Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory.Eur J Mech-A/Solids,2015,51:55–66