Purpose
– A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues.
Design/methodology/approach
– Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions.
Findings
– In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems.
Originality/value
– To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.
Functionally graded materials (FGMs) are a new kind of composite materials which have a smooth variation of material properties along one or more directions. At each interface, the material is chosen according to specific applications and environment loadings. This paper presents some solutions to study the free vibration of FGM plates made of ceramic and metal. The formulation used is based on Reddys higher order shear deformation plate theory. Material properties are taken to be temperature-dependent, and vary continuously through the thickness direction according to a power law distribution (P-FGM). The plate is assumed to be initially stressed by temperature rise through the thickness. The energy functional of the system is obtained by using energy principles. Free vibration frequencies are then obtained by using a set of characteristic orthogonal polynomials and by applying Ritz method.
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