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.

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.

scholarly journals Analysis of Vibrating Timoshenko Beams Using the Method of Differential Quadrature

1993 ◽  
Vol 1 (1) ◽  
pp. 89-93 ◽  
Author(s):  
P.A.A. Laura ◽  
R.H. Gutierrez
Keyword(s):  
Approximate Solution ◽  
Finite Number ◽  
Cross Section ◽  
Numerical Experiments ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Timoshenko Beams ◽  
Collocation Approach ◽  
Polynomial Collocation

The main advantages of the differential quadrature method are its inherent conceptual simplicity and the fact that easily programmable algorithmic expressions are obtained. It was developed by Bellman in the 1970s but only recently has been applied in the solution of technically important problems. Essentially, it consists of the approximate solution of the differential system by means of a polynomial–collocation approach at a finite number of points selected by the analyst. This article reports some numerical experiments on vibrating Timoshenko beams of nonuniform cross-section.

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