Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function
Joint Authors
Cao, Qiongqiong
Ding, Min
Jiang, Xiugen
Ju, Jinsan
Wang, Hongzhi
Zhang, Peng
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-05-19
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
For beam dynamic finite element analysis, according to differential equation of motion of beam with distributed mass, general analytical solution of displacement equation for the beam vibration is obtained.
By applying displacement element construction principle, the general solution of displacement equation is conversed to the mode expressed by beam end displacements.
And taking the mode as displacement trial function, element stiffness matrix and element mass matrix for beam flexural vibration and axial vibration are established, respectively, by applying principle of minimum potential energy.
After accurate integral, explicit form of element matrix is obtained.
The comparison results show that the series of relative error between the solution of analytical trial function element and theoretical solution is about 1×10-9 and the accuracy and efficiency are superior to that of interpolation trial function element.
The reason is that interpolation trial function cannot accurately simulate the displacement mode of vibrating beam.
The accuracy of dynamic stiffness matrix method is almost identical with that of analytical trial function.
But the application of dynamic stiffness matrix method in engineering is limited.
The beam dynamic element obtained in this paper is analytical and accurate and can be applied in practice.
American Psychological Association (APA)
Cao, Qiongqiong& Ding, Min& Jiang, Xiugen& Ju, Jinsan& Wang, Hongzhi& Zhang, Peng. 2015. Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074193
Modern Language Association (MLA)
Cao, Qiongqiong…[et al.]. Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function. Mathematical Problems in Engineering No. 2015 (2015), pp.1-10.
https://search.emarefa.net/detail/BIM-1074193
American Medical Association (AMA)
Cao, Qiongqiong& Ding, Min& Jiang, Xiugen& Ju, Jinsan& Wang, Hongzhi& Zhang, Peng. Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074193
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074193