Tree-dimensional Free Vibration of Nano-Composite Plates with Arbitrary Geometry within Couple Stress Theory

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Forouzan, Bahareh | 2013

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Type of Document: M.Sc. Thesis
Language: English
Document No: 44078 (53)
University: Sharif University of Technology
Department: Science and Engineering
Advisor(s): Mohammadi Shoja, Hossein
Abstract:
Based on Hamilton’s principle, a three-dimensional semi-analytical method for the analysis of free vibration of a nano-composite plate within the couple stress theory is developed. Computation of dynamic behavior as well as natural frequencies and mode shapes is interested. In this method, the mechanical displacement functions, in each layer, are defined as product of a base function and a three-dimensional polynomial with unknown coefficients. The base functions are defined with respect to the kinematical boundary condition and the domain geometry. The mode shapes will be obtained and the accuracy of the present approach is demonstrated by comparison it in both classical elasticity and couple stress theory as applied to the following problems: 1- rectangular and circular nano-plates whose exact solutions are available. 2- Rectangular and circular Nano-composite plates with various boundary conditions and a further example involving more complex geometry consisting of an elliptic nano-composite plate with a central star-shape hole
Keywords:
Free Vibration ; Couple Stress ; Nanocomposite Plate ; Three Dimentional Semi-Analytical Solution ; In-Plane Pure Sliding