Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

2014 ◽  
Vol 64 ◽  
pp. 95-105 ◽  
Author(s):  
Ender Cigeroglu ◽  
Hamed Samandari
Keyword(s):  
Carbon Nanotubes ◽  
Differential Quadrature Method ◽  
Free Vibrations ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

DQ Based Methods

2012 ◽  
pp. 316-346 ◽  
Author(s):  
Stefania Tomasiello
Keyword(s):  
Numerical Technique ◽  
Differential Quadrature Method ◽  
Free Vibrations ◽  
Computational Effort ◽  
Differential Quadrature ◽  
Time Dependent ◽  
Quadrature Method ◽  
The Finite Element Method ◽  
Time Domains ◽  
Typical Model

Though relatively unknown, the Differential Quadrature Method (DQM) is a promising numerical technique that produces accurate solutions with less computational effort than other numerical methods such as the Finite Element Method. There are different versions of the former method, so one can refer to a class of methods based on the differential quadrature (DQ) approach. This chapter provides systematic steps to understand DQ based methods: how they work, how to use and develop them, as well as exemplary problems. It is divided into two sections: the first provides fundamentals and theories related to the DQ approach, while the second presents the application of DQ based methods to three significant problems, i.e. free vibrations of a multi-span beam (a typical model for bridge decks and floors), time dependent heat transfer, and vibrations of a rectangular membrane. The main focus is on the application of the method to space-time domains as a whole, an issue not well covered by the current literature.

Vibration and Buckling Analyses of Beams by the Modified Differential Quadrature Method

2000 ◽  
Vol 16 (4) ◽  
pp. 189-195 ◽  
Author(s):  
Y.-T. Chou ◽  
S.-T. Choi
Keyword(s):  
Boundary Conditions ◽  
Present Method ◽  
Differential Quadrature Method ◽  
Free Vibrations ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Timoshenko Beams ◽  
Buckling Loads ◽  
New Formulation ◽  
Excellent Accuracy

ABSTRACTIn this paper the modified differential quadrature method (MDQM) is proposed for static and vibration analyses of beams. Modified weighting matrices are developed and a new formulation process is presented for incorporating boundary conditions such that the numerical error induced by using the δ-method in the original DQM is reduced. The present method is applied to various beam problems, such as static deflections of Euler beams, buckling loads of columns, and free vibrations of Timoshenko beams. Numerical results of the present method are shown to have excellent accuracy when compared to exact values and are more accurate than those obtained by the original DQM. The accuracy and efficiency of the present method have been demonstrated.

Dynamic analysis of multi-walled carbon nanotubes using the differential quadrature method

2009 ◽  
Vol 224 (3) ◽  
pp. 731-744 ◽  
Author(s):  
Ming-Hung Hsu
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Differential Quadrature Method ◽  
Van Der Waals ◽  
Differential Quadrature ◽  
Force Interaction ◽  
Medium Length ◽  
Multi Walled Carbon Nanotubes ◽  
Vibration Mechanism ◽  
Walled Carbon Nanotubes

This work describes a novel modelling scheme to elucidate the frequencies of carbon nanotubes via continuum mechanics by considering the van der Waals force interaction based on differential quadrature simulations, in which nanobeam-bending paradigms are utilized. Exactly how the surrounding elastic medium, length-to-radius ratio, and van der Waals forces of the carbon nanotubes affect the frequencies is also investigated. The proposed modelling scheme is highly promising for advanced carbon nanotube applications. Further elucidation of the vibration mechanism of carbon nanotubes embedded in an elastic medium in this work significantly contributes to efforts to design nano oscillators.

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