Stability of Functionally Graded Beams with Piezoelectric Layers Based on the First Order Shear Deformation Theory
Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.
[1] J. Ari-Gur, T. Weller, J. Singer, Experimental and theoretical studies
of columns under axial impact, Int. J. Solid Struct. 18 (7) (1982) 619-
641.
[2] H.E. Lindberg, A.L. Florence, Dynamic Pulse Buckling, Martinus
Nijhoff Publishers, The Netherlands, 1987.
[3] N. Jones, Recent studies on the dynamic plastic behavior of structures,
Appl. Mech. Rev. 42 (4) (1989) 95-115.
[4] Meressi T, Paden B. Buckling control of a flexible beam using
piezoelectric actuators. J Guidance Control Dyn 1993;16(5):977-80.
[5] Thompson SP, Loughlan J. The active buckling control of some
composite column strips using piezoelectric actuators. Compos Struct
1995;32:59-67.
[6] de Faria AR, de Almeida SFM. Enhancement of pre-buckling
behavior of composite beams with geometric imperfections using
piezoelectric actuators. Composites Part B: Eng 1999;30(1):43-50.
[7] Tzou HS, Wan GC. Distributed structural dynamics control of flexible
manipulatorsÔÇöI. Structural dynamics and distributed viscoelastic
actuator. Computers and Structures 1990;35(6):669-677.
[8] Ha SK, Keilers C, Chang FK. Finite element analysis of composite
structures containing distributed piezoceramic sensors and actuators
AIAA Journal 1992;30(3):772-780.
[9] Abramovich H, Livshits A. Dynamic behavior of cross-ply laminated
beams with piezoelectric actuators. Composite Structures
1993;25:371-379.
[10] Kim J, Varadan VV, Varadan VK, Bao XQ. Finite element modelling
of a smart cantilever plate and comparison with experiments Smart
Materials and Structures 1996;5:165-70.
[11] Tzou HS, Tseng CI. Distributed piezoelectric sensor/actuator design
for dynamic measurement/control of distributed parameter system.
Journal of Sound and Vibration 1990;138:17-34.
[12] Robinson DH, Reddy JN. Analysis of piezoelectrically actuated beams
using a layer-wise displacement theory. Computers and Structures
1991;41:265-79.
[13] Saravanos DA, Heyliger PR. Coupled layer-wise analysis of
composite beams with embedded piezoelectric sensors and actuators J
Intell Mater Syst Struct 1995;6:350-63.
[14] Crawley EF, de Luis J. Use of piezoelectric actuators as elements of
intelligent structures. AIAA Journal 1987;25:1373-85.
[15] LaPeter, C.M., Cudney, H.H., 1991, "Design methodology for
piezoelectric actuators, Smart Structures and Materials", Proceedings
of the Annual Meeting of the ASME, 16, 139-143.
[16] Dobrucki, A.B., Pruchnicki P., 1997, "Theory of piezoelectric
axisymmetric bimorph", Sensors and Actuators A, 58, 203-212.
[17] Chandrashekhara, K., Bhatia, K., 1993, "Active buckling control of
smart composite plates finite element analysis", Smart Materials and
Structures, 2, 31-39.
[18] Chase, J.G., Bhashyam S., 1999, "Optimal stabilization of plate
buckling", Smart Materials and Structures, 8, 204-211.
[19] Reddy J.N. and Praveen G.N., Nonlinear Transient Thermoelastic
Analysis of Functionally Graded Ceramic-metal Plates, International
Journal of. Solids and Structures, Vol. 35, 1998, pp. 4467-4476.
[20] Wang C.M., Reddy J.N., 2000, "Shear Deformable Beams and Plates",
Oxford, Elsevier.
[21] Reddy J.N., 2004, " Mechanics of Laminated Composite Plates and
Shells Theory and Analysis", New York, CRC.
[22] Karami Khorram abadi M., Khazaeinejad P. and Jenabi J.,
"Mechanical Buckling of Functionally graded Beam with Piezoelectric
Actuators", NCME, 2008.
[1] J. Ari-Gur, T. Weller, J. Singer, Experimental and theoretical studies
of columns under axial impact, Int. J. Solid Struct. 18 (7) (1982) 619-
641.
[2] H.E. Lindberg, A.L. Florence, Dynamic Pulse Buckling, Martinus
Nijhoff Publishers, The Netherlands, 1987.
[3] N. Jones, Recent studies on the dynamic plastic behavior of structures,
Appl. Mech. Rev. 42 (4) (1989) 95-115.
[4] Meressi T, Paden B. Buckling control of a flexible beam using
piezoelectric actuators. J Guidance Control Dyn 1993;16(5):977-80.
[5] Thompson SP, Loughlan J. The active buckling control of some
composite column strips using piezoelectric actuators. Compos Struct
1995;32:59-67.
[6] de Faria AR, de Almeida SFM. Enhancement of pre-buckling
behavior of composite beams with geometric imperfections using
piezoelectric actuators. Composites Part B: Eng 1999;30(1):43-50.
[7] Tzou HS, Wan GC. Distributed structural dynamics control of flexible
manipulatorsÔÇöI. Structural dynamics and distributed viscoelastic
actuator. Computers and Structures 1990;35(6):669-677.
[8] Ha SK, Keilers C, Chang FK. Finite element analysis of composite
structures containing distributed piezoceramic sensors and actuators
AIAA Journal 1992;30(3):772-780.
[9] Abramovich H, Livshits A. Dynamic behavior of cross-ply laminated
beams with piezoelectric actuators. Composite Structures
1993;25:371-379.
[10] Kim J, Varadan VV, Varadan VK, Bao XQ. Finite element modelling
of a smart cantilever plate and comparison with experiments Smart
Materials and Structures 1996;5:165-70.
[11] Tzou HS, Tseng CI. Distributed piezoelectric sensor/actuator design
for dynamic measurement/control of distributed parameter system.
Journal of Sound and Vibration 1990;138:17-34.
[12] Robinson DH, Reddy JN. Analysis of piezoelectrically actuated beams
using a layer-wise displacement theory. Computers and Structures
1991;41:265-79.
[13] Saravanos DA, Heyliger PR. Coupled layer-wise analysis of
composite beams with embedded piezoelectric sensors and actuators J
Intell Mater Syst Struct 1995;6:350-63.
[14] Crawley EF, de Luis J. Use of piezoelectric actuators as elements of
intelligent structures. AIAA Journal 1987;25:1373-85.
[15] LaPeter, C.M., Cudney, H.H., 1991, "Design methodology for
piezoelectric actuators, Smart Structures and Materials", Proceedings
of the Annual Meeting of the ASME, 16, 139-143.
[16] Dobrucki, A.B., Pruchnicki P., 1997, "Theory of piezoelectric
axisymmetric bimorph", Sensors and Actuators A, 58, 203-212.
[17] Chandrashekhara, K., Bhatia, K., 1993, "Active buckling control of
smart composite plates finite element analysis", Smart Materials and
Structures, 2, 31-39.
[18] Chase, J.G., Bhashyam S., 1999, "Optimal stabilization of plate
buckling", Smart Materials and Structures, 8, 204-211.
[19] Reddy J.N. and Praveen G.N., Nonlinear Transient Thermoelastic
Analysis of Functionally Graded Ceramic-metal Plates, International
Journal of. Solids and Structures, Vol. 35, 1998, pp. 4467-4476.
[20] Wang C.M., Reddy J.N., 2000, "Shear Deformable Beams and Plates",
Oxford, Elsevier.
[21] Reddy J.N., 2004, " Mechanics of Laminated Composite Plates and
Shells Theory and Analysis", New York, CRC.
[22] Karami Khorram abadi M., Khazaeinejad P. and Jenabi J.,
"Mechanical Buckling of Functionally graded Beam with Piezoelectric
Actuators", NCME, 2008.
@article{"International Journal of Electrical, Electronic and Communication Sciences:52451", author = "M. Karami Khorramabadi and A. R. Nezamabadi", title = "Stability of Functionally Graded Beams with Piezoelectric Layers Based on the First Order Shear Deformation Theory", abstract = "Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.
", keywords = "Stability, Functionally graded beam, First order
shear deformation theory, Piezoelectric layer.", volume = "4", number = "11", pages = "1613-4", }
