On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method

2021 ◽  
Vol 257 ◽  
pp. 113150 ◽  
Author(s):  
M.S.H. Al-Furjan ◽  
Ali hatami ◽  
Mostafa Habibi ◽  
Lijun Shan ◽  
Abdelouahed Tounsi
Keyword(s):  
Differential Quadrature Method ◽  
Higher Order ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Generalize Differential Quadrature

scholarly journals Higher-Order Nonlinear Vibration Analysis of Timoshenko Beams by the Spline-Based Differential Quadrature Method

2007 ◽  
Vol 14 (6) ◽  
pp. 407-416 ◽  
Author(s):  
Hongzhi Zhong ◽  
Minmao Liao
Keyword(s):  
Differential Quadrature Method ◽  
Nonlinear Effects ◽  
Higher Order ◽  
Differential Quadrature ◽  
Radius Of Gyration ◽  
Quadrature Method ◽  
Timoshenko Beams ◽  
Axial Deformation ◽  
B Splines ◽  
Transverse Shear Strains

Higher-order nonlinear vibrations of Timoshenko beams with immovable ends are studied. The nonlinear effects of axial deformation, bending curvature and transverse shear strains are considered. The nonlinear governing differential equations are solved using a spline-based differential quadrature method (SDQM), which is constructed based on quartic B-splines. Ratios of the nonlinear to the linear frequencies are extracted and their variations with the ratio of amplitude to radius of gyration are examined. In contrast to the well-recognized finding for the nonlinear fundamental frequency of beams, some higher-order nonlinear frequencies decrease with the increase of ratio of amplitude to radius of gyration.

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