Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations

2016 ◽  
Vol 76 ◽  
pp. 70-81 ◽  
Author(s):  
R. Ansari ◽  
A. Shahabodini ◽  
M. Faghih Shojaei
Keyword(s):  
Free Vibration ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Dimensional Theory ◽  
Elastic Foundations

Dynamic Characteristics of Elastic Bonding in Composite Laminates: A Free Vibration Study

2003 ◽  
Vol 70 (6) ◽  
pp. 860-870 ◽  
Author(s):  
K. M. Liew ◽  
J. Z. Zhang ◽  
T. Y. Ng ◽  
J. N. Reddy
Keyword(s):  
Free Vibration ◽  
Composite Laminates ◽  
Present Model ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Bonding Layer ◽  
Dimensional Theory ◽  
Perfect Bonding ◽  
Stress States ◽  
Laminated Structures

In conventional analyses of composite laminates, the assumption of perfect bonding of adjoining layers is well accepted, although this is an oversimplification of the reality. It is possible that the bond strength may be less than that of the laminae. Thus, the study of weak bonding is an interesting focus area. In this study, an elastic bonding model based on three-dimensional theory of elasticity in a layerwise framework is used to study composite laminates. The differential quadrature (DQ) discretization is used to analyze the layerwise model. The present model enables the simulation of actual bonding stress states in laminated structures. The interfacial characteristics of transverse stress continuity as well as the kinematic continuity conditions are satisfied through the inclusion of the elastic bonding layer. The present model is employed to investigate the free vibration of thick rectangular cross-ply laminates of different boundary conditions and lamination schemes.

scholarly journals Three-Dimensional Elasticity Solutions for Sound Radiation of Functionally Graded Materials Plates considering State Space Method

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Tieliang Yang ◽  
Qibai Huang ◽  
Shande Li
Keyword(s):  
State Space ◽  
Functionally Graded Materials ◽  
Three Dimensional ◽  
Sound Radiation ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
State Space Method ◽  
Dimensional Theory ◽  
Graded Materials ◽  
Space Method

This paper presents an analytical study for sound radiation of functionally graded materials (FGM) plate based on the three-dimensional theory of elasticity. The FGM plate is a mixture of metal and ceramic, and its material properties are assumed to have smooth and continuous variation in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. Based on the three-dimensional theory of elasticity and state space method, the governing equations with variable coefficients of the FGM plate are derived. The sound radiation of the vibration plate is calculated with Rayleigh integral. Comparisons of the present results with those of solutions in the available literature are made and good agreements are achieved. Finally, some parametric studies are carried out to investigate the sound radiation properties of FGM plates.

Three-Dimensional Free Vibration Analysis of Functionally Graded Annular Plates on Elastic Foundations via State-Space Based Differential Quadrature Method

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
A. Jodaei ◽  
M. H. Yas
Keyword(s):  
Free Vibration ◽  
State Space ◽  
Present Method ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Elastic Foundations ◽  
Annular Plates

In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.

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