TY - JOUR
T1 - Exact solutions for free vibrations of functionally graded thick plates on elastic foundations
AU - Lü, C. F.
AU - Lim, C. W.
AU - Chen, W. Q.
PY - 2009/11
Y1 - 2009/11
N2 - Free vibration analysis of functionally graded thick plates on elastic foundation is carried out based on three-dimensional elasticity. An isotropic plate is assumed with Young's modulus and mass density varying exponentially through the thickness, and Poisson's ratio remaining constant. The state space method is used to derive an exact solution for a simply supported plate by expanding the state variables in trigonometric dual series. The effects of interaction between the plate surface and a Pasternak foundation are treated as the traction boundary conditions of the plate. The solution procedure is validated by comparing with established results for a homogeneous plate. Finally, the influences of foundation stiffness, foundation support, and gradient index on the natural frequencies are investigated.
AB - Free vibration analysis of functionally graded thick plates on elastic foundation is carried out based on three-dimensional elasticity. An isotropic plate is assumed with Young's modulus and mass density varying exponentially through the thickness, and Poisson's ratio remaining constant. The state space method is used to derive an exact solution for a simply supported plate by expanding the state variables in trigonometric dual series. The effects of interaction between the plate surface and a Pasternak foundation are treated as the traction boundary conditions of the plate. The solution procedure is validated by comparing with established results for a homogeneous plate. Finally, the influences of foundation stiffness, foundation support, and gradient index on the natural frequencies are investigated.
KW - Exact solution
KW - Free vibration
KW - Functionally graded thick plates
KW - Pasternak foundation
KW - State space method
KW - Three-dimensional elasticity
UR - http://www.scopus.com/inward/record.url?scp=70449356635&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-70449356635&origin=recordpage
U2 - 10.1080/15376490903138888
DO - 10.1080/15376490903138888
M3 - RGC 21 - Publication in refereed journal
SN - 1537-6494
VL - 16
SP - 576
EP - 584
JO - Mechanics of Advanced Materials and Structures
JF - Mechanics of Advanced Materials and Structures
IS - 8
ER -