TY - JOUR
T1 - Exact Closed-form Free Vibration Analysis of Moderately Thick Rectangular Functionally Graded Plates with Two Bonded Piezoelectric Layers
TT - تحلیل دقیق پاسخ-بسته ارتعاشات آزاد ورق های نسبتاً ضخیم مستطیلی ساخته شده از مواد هدفمند با لایه پیزوالکتریک
JF - mdrsjrns
JO - mdrsjrns
VL - 11
IS - 3
UR - http://mme.modares.ac.ir/article-15-11164-en.html
Y1 - 2011
SP - 57
EP - 74
KW - FGM
KW - FGM
KW - Natural frequency
KW - Mindlin theory
KW - Power-Low Distribution
N2 - In this paper, free vibration analysis of moderately thick smart FG rectangular plate is presented on the basis of Mindlin plate theory. This structure is composed of a host FG plate and two bonded piezoelectric layers. The plate has two opposite edges simply supported (i.e., Levy-type rectangular plates). The closed circuit piezoelectric layers can be used as an actuator. According to a power-law distribution of the volume fraction of the constituents, material properties vary continuously through the thickness of host plate. Using Hamilton's principle and Maxwell electrostatic equation, six complex coupled equations are introduced. These equations are exactly solved introducing the new potential and auxiliary functions as well as using separation of variables method. The accuracy of the frequencies is verified by the available literature and the finite element method. The present exact solution can accurately predict not only the out of plane, but also the in-plane modes of FG plate. Finally, the effects of various parameters such as boundary conditions, gradient index and thickness of piezoelectric layers on the natural frequency are investigated.
M3
ER -