Thickness-shear vibration analysis of circular quartz crystal plates by a differential quadrature hierarchical finite element method

2015 ◽  
Vol 131 ◽  
pp. 1073-1080 ◽  
Author(s):  
Bo Liu ◽  
Yufeng Xing ◽  
Wei Wang ◽  
Weidong Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Quartz Crystal ◽  
Differential Quadrature ◽  
Shear Vibration ◽  
Hierarchical Finite Element Method ◽  
Thickness Shear ◽  
Element Method ◽  
Hierarchical Finite Element

An Differential Quadrature Finite Element and the Differential Quadrature Hierarchical Finite Element Methods for the Dynamics Analysis of on Board Shaft

2021 ◽  
Author(s):  
Saimi Ahmed ◽  
Hadjoui Abdelhamid ◽  
Bensaid Ismail ◽  
Fellah Ahmed
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Element Methods ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Weighting Coefficient ◽  
Quadrature Method ◽  
Hierarchical Finite Element Method ◽  
Element Method ◽  
Hierarchical Finite Element

In this paper the dynamic analysis of a shaft rotor whose support is mobile is studied. For the calculation of kinetic energy and stiffness energy, the beam theory of Euler Bernoulli was used, and the matrices of elements and systems are developed using two methods derived from the differential quadrature method (DQM). The first method is the Differential Quadrature Finite Element Method (DQFEM) systematically, as a combination of the Differential Quadrature Method (DQM) and the Standard Finite Element Method (FEM), which has a reduced computational cost for problems in dynamics. The second method is the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) which is used by expressing the matrices of the hierarchical finite element method in a similar form to that of the Differential Quadrature Finite Element Method and introducing an interpolation basis on the element boundary of the hierarchical finite element method. The discretization element used for both methods is a three-dimensional beam element. In the differential quadrature finite element method (DQFEM), the mass, gyroscopic and stiffness matrices are simply calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The sampling points are determined by the Gauss-Lobatto node method. In the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) the same approaches were used, and the cubic Hermite shape functions and the special Legendre polynomial Rodrigues shape polynomial were added. The assembly of the matrices for both methods (DQFEM and DQHFEM) is similar to that of the classical finite element method. The results of the calculation are validated with the h- and hp finite element methods and also with the literature.

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