Free vibration analysis of two-dimensional functionally graded coated and undercoated substrate structures

2015 ◽  
Vol 60 ◽  
pp. 10-17 ◽  
Author(s):  
Y. Yang ◽  
K.P. Kou ◽  
C.C. Lam ◽  
V.P. Iu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Two Dimensional

A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment

2012 ◽  
Vol 226 (12) ◽  
pp. 2860-2873 ◽  
Author(s):  
AR Setoodeh ◽  
M Ghorbanzadeh ◽  
P Malekzadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Thermal Environment ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Sandwich Beams ◽  
Two Dimensional

In this article, free vibration analysis of elastically supported sandwich beams with functionally graded face sheets subjected to thermal environment is presented. In order to accurately include the transverse shear deformation and the inertia effects, two-dimensional elasticity theory is used to formulate the problem. The layerwise theory in conjunction with the differential quadrature method is employed to discretize the governing equations in the thickness and axial directions, respectively. The material properties of functionally graded face sheets are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution. For the purpose of comparison, the problem under consideration is also solved using two-dimensional finite element method and the first-order shear deformation theory. The accuracy, convergence, and versatility of the method are demonstrated by comparing the results with those of the two aforementioned approaches and also with the existing solutions in literature. Eventually, some new numerical results are presented which depict the effects of different material and geometrical parameters on natural frequencies and mode shapes of the beam.

Two-Dimensional Free Vibration Analysis of Axially Functionally Graded Beams Integrated with Piezoelectric Layers: An Piezoelasticity Approach

2020 ◽  
Vol 12 (04) ◽  
pp. 2050037
Author(s):  
Agyapal Singh ◽  
Poonam Kumari
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Numerical Results ◽  
Two Dimensional ◽  
Kantorovich Method ◽  
Piezoelectric Layers

For the first time, a two-dimensional (2D) piezoelasticity-based analytical solution is developed for free vibration analysis of axially functionally graded (AFG) beams integrated with piezoelectric layers and subjected to arbitrary supported boundary conditions. The material properties of the elastic layers are considered to vary linearly along the axial ([Formula: see text]) direction of the beam. Modified Hamiltons principle is applied to derive the weak form of coupled governing equations in which, stresses, displacements and electric field variables acting as primary variables. Further, the extended Kantorovich method is employed to reduce the governing equation into sets of ordinary differential equations (ODEs) along the axial ([Formula: see text]) and thickness ([Formula: see text]) directions. The ODEs along the [Formula: see text]-direction have constant coefficients, where the ODEs along [Formula: see text]-direction have variable coefficients. These sets of ODEs are solved analytically, which ensures the same order of accuracy for all the variables by satisfying the boundary and continuity conditions in exact pointwise manner. New benchmark numerical results are presented for a single layer AFG beam and AFG beams integrated with piezoelectric layers. The influence of the axial gradation, aspect ratio and boundary conditions on the natural frequencies of the beam are also investigated. These numerical results can be used for assessing 1D beam theories and numerical techniques.

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