The Timoshenko beam model of the differential quadrature element method

1999 ◽  
Vol 24 (1) ◽  
pp. 65-69 ◽  
Author(s):  
C.-N. Chen
Keyword(s):  
Timoshenko Beam ◽  
Differential Quadrature ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Method

Differential Quadrature Element Method for the Analysis of Vibration of Frame Structures Having Nonprismatic Members Considering Warping Torsion

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Vibration Analysis ◽  
Differential Quadrature ◽  
Frame Structures ◽  
Rigorous Solution ◽  
Discrete Eigenvalue ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Domain Boundaries ◽  
Eigenvalue System ◽  
Element Method

Abstract The differential quadrature element method (DQEM) and the extended differential quadrature (EDQ) have been proposed by the author. The EDQ is used to the DQEM vibration analysis frame structures. The element can be a nonprismatic beam considering the warping due to torsion. The EDQ technique is used to discretize the element-based differential eigenvalue equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall discrete eigenvalue system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the overall discrete eigenvalue system. Mathematical formulations for the EDQ-based DQEM vibration analysis of nonprismatic structures considering the effect of warping torsion are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained.

Vibration Analysis of Discontinuous Mindlin Plates by Differential Quadrature Element Method

1999 ◽  
Vol 121 (2) ◽  
pp. 204-208 ◽  
Author(s):  
F.-L. Liu ◽  
K. M. Liew
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Mindlin Plate ◽  
Quadrature Method ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Method

A new numerical technique, the differential quadrature element method (DQEM), has been developed for solving the free vibration of the discontinuous Mindlin plate in this paper. By the DQEM, the complex plate domain is decomposed into small simple continuous subdomains (elements) and the differential quadrature method (DQM) is applied to each continuous subdomain to solve the problems. The detailed formulations for the DQEM and the connection conditions between each element are presented. Several numerical examples are analyzed to demonstrate the accuracy and applicability of this new method to the free vibration analysis of the Mindlin plate with various discontinuities which are not solvable directly using the differential quadrature method.

Differential quadrature element model updating of frame structures

2013 ◽  
Vol 228 (7) ◽  
pp. 1094-1107 ◽  
Author(s):  
Laleh Fatahi ◽  
Shapour Moradi
Keyword(s):  
Optimization Problem ◽  
Artificial Bee Colony ◽  
Element Model ◽  
Differential Quadrature ◽  
Design Parameters ◽  
Modal Parameters ◽  
Bee Colony ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Method

The following study deals with improving the vibration model of structures obtained by the differential quadrature element method. To this end, first, an initial model of the structure is constructed using the differential quadrature element method in which the values of several physical parameters are unknown. Then, an optimization problem is defined to find the optimum values of the design parameters. In fact, the aim is to minimize an objective function that consists of the weighted sum of the squared errors between the modal parameters (i.e. the natural frequencies, the mode shapes, and the damping ratios) of the differential quadrature element and the experimental models. To solve the optimization problem, a robust evolutionary algorithm, namely the artificial bee colony, is utilized. To verify the effectiveness of the presented approach, the experimental data obtained from the modal testing of a plane frame are utilized to update its differential quadrature element model. The results show that the updating process is successfully performed utilizing artificial bee colony, and the updated differential quadrature element model better represents the vibration behavior of the real structure. Besides, the sensitivities of the eigenvalues of the model with respect to the design parameters are also evaluated to demonstrate the effect of changing the design parameters in the modal parameters of the model.

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