Flexural Free Vibrations of Multistep Nonuniform Beams
Joint Authors
Tan, Guojin
Wang, Wensheng
Jiao, Yu-bo
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-03
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
This paper presents an exact approach to investigate the flexural free vibrations of multistep nonuniform beams.
Firstly, one-step beam with moment of inertia and mass per unit length varying as I(x)=α11+βxr+4 and m(x)=α21+βxr was studied.
By using appropriate transformations, the differential equation for flexural free vibration of one-step beam with variable cross section is reduced to a four-order differential equation with constant coefficients.
According to different types of roots for the characteristic equation of four-order differential equation with constant coefficients, two kinds of modal shape functions are obtained, and the general solutions for flexural free vibration of one-step beam with variable cross section are presented.
An exact approach to solve the natural frequencies and modal shapes of multistep beam with variable cross section is presented by using transfer matrix method, the exact general solutions of one-step beam, and iterative method.
Numerical examples reveal that the calculated frequencies and modal shapes are in good agreement with the finite element method (FEM), which demonstrates the solutions of present method are exact ones.
American Psychological Association (APA)
Tan, Guojin& Wang, Wensheng& Jiao, Yu-bo. 2016. Flexural Free Vibrations of Multistep Nonuniform Beams. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112549
Modern Language Association (MLA)
Tan, Guojin…[et al.]. Flexural Free Vibrations of Multistep Nonuniform Beams. Mathematical Problems in Engineering No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1112549
American Medical Association (AMA)
Tan, Guojin& Wang, Wensheng& Jiao, Yu-bo. Flexural Free Vibrations of Multistep Nonuniform Beams. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112549
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112549