Dynamic Stability of Functionally Graded Beams with Piezoelectric Layers Located on a Continuous Elastic Foundation

Document Type: Research Paper


1 Department of Mathematics, Islamic Azad University, Khorramabad Branch

2 Department of Mechanical Engineering, Islamic Azad University, Khorramabad Branch

3 Faculty of Engineering, Payame Noor University (PNU), Yazd Branch


This paper studies dynamic stability of functionally graded beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The Young’s modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing dynamic equation is established. The effects of the constituent volume fractions, the influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented.


[1] Bailey T., Hubbard Jr.J.E., 1985, Distributed piezoelectric-polymer active vibration control of a cantilever beam. Journal of Guidance Control and Dynamic 8: 605-611.

[2] Crawley E.F., de Luis J., 1987, Use piezoelectric actuators as elements of intelligent structures, AIAA Journal 8: 1373-1385.

[3] Shen M.H., 1994, Analysis of beams containing piezoelectric sensors and actuators, Smart Materials and Structures 3: 439-347.

[4] Pierre C., Dowell E.H., 1985, A study of dynamic instability of plates by an extended incremental harmonic balance method, ASME Transactions, Journal of Applied Mechanics 52: 693-697.

[5] Liu G.R., Peng X.Q., Lam K.Y., 1999, Vibration control simulation of laminated composite plates with integrated piezoelectrics, Journal of Sound and Vibration 220(5): 827-846.

[6] Tzou H.S., Tseng C.I., 1990, Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter system: A piezoelectric finite element approach, Journal of Sound and Vibration 138: 17-34.

[7] Ha S.K., Keilers C., Chang, F.K., 1992, Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators, AIAA Journal 30: 772-780.

[8] Bolotin V.V., 1964, The Dynamic Stability of Elastic Systems, Holden Day, San Francisco.

[9] Briseghella L., Majorana C.E., Pellegrino C., 1998, Dynamic stability of elastic structures: A finite element approach, Computers and Structures 69: 11-25.

[10] Takahashi K., Wu M., Nakazawa N., 1998, Vibration, buckling and dynamic stability of a cantilever rectangular plate subjected to in-plane force, Engineering Mechanics 6: 939-953.

[11] Zhu J., Chen C., Shen Y., Wang S., 2005, Dynamic stability of functionally graded piezoelectric circular cylindrical shells, Materials Letters 59: 477-485.

[12] Reddy J.N., Praveen G.N., 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures 35: 4467-4476.