ON FREE VIBRATION ANALYSIS OF NON-LINEAR PIEZOELECTRIC CIRCULAR SHALLOW SPHERICAL SHELLS BY THE DIFFERENTIAL QUADRATURE ELEMENT METHOD

2001 ◽  
Vol 245 (1) ◽  
pp. 179-185 ◽  
Author(s):  
Y. WANG ◽  
R. LIU ◽  
X. WANG
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Spherical Shells ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Non Linear ◽  
Element Method

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.

DQEM VIBRATION ANALYSES OF NONPRISMATIC BEAMS RESTING ON ELASTIC FOUNDATIONS

2002 ◽  
Vol 02 (01) ◽  
pp. 99-115 ◽  
Author(s):  
CHANG-NEW CHEN
Keyword(s):  
Free Vibration ◽  
Numerical Algorithm ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Elastic Foundations ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Boundary

The development of differential quadrature element method (DQEM) free vibration analysis model of nonprismatic Bernoulli–Euler beams resting on Winkler elastic foundations was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. They prove that the DQEM is efficient. The developed numerical algorithm can be used to analyze the related pressure vessel and piping structures.

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.

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