Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method

2009 ◽  
Vol 321 (1-2) ◽  
pp. 342-362 ◽  
Author(s):  
S.C. Pradhan ◽  
T. Murmu
Keyword(s):  
Differential Quadrature Method ◽  
Mechanical Vibration ◽  
Sandwich Beam ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Elastic Foundations

Effects of carbon nanotube reinforcements on vibration suppression of magnetorheological fluid sandwich beam

2019 ◽  
Vol 30 (7) ◽  
pp. 1053-1069 ◽  
Author(s):  
M Talebitooti ◽  
M Fadaee
Keyword(s):  
Carbon Nanotube ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Differential Quadrature Method ◽  
Sandwich Beam ◽  
Core Layer ◽  
Magnetorheological Fluid ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fluid Core

Vibration suppression of a carbon nanotube–reinforced sandwich beam with magnetorheological fluid core is numerically investigated by employing the differential quadrature method. The beam has functionally graded carbon nanotube–reinforced composite base and constraining layers while its core layer is made of magnetorheological fluid. Four different types of distribution of carbon nanotubes along the thickness direction are considered. The extended rule of mixture is used to explain the effective material properties of the base and constraining layers of the beam. The equations of motion and corresponding boundary conditions are derived by applying Hamilton’s principle, and then these coupled differential equations are transformed into a set of algebraic equation applying the differential quadrature method. Natural frequencies and loss factors are extracted and compared with those available in literature. Convergence study has been performed to verify stability of the method. Effects of various parameters such as magnetic field intensity, mode number, and thickness of the magnetorheological fluid core layer on the natural frequencies and loss factors are studied.

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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