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Structural Engineering and Mechanics
  Volume 70, Number 2, April25 2019, pages 199-207
DOI: http://dx.doi.org/10.12989/sem.2019.70.2.199
 


Vibration analysis of rotating beam with variable cross section using Riccati transfer matrix method
Mahdi Feyzollahzadeh and Mahdi Bamdad

 
Abstract
    In this paper, a semi-analytical method will be discussed for free vibration analysis of rotating beams with variable cross sectional area. For this purpose, the rotating beam is discretized through applying the transfer matrix method and assumed the axial force is constant for each element. Then, the transfer matrix is derived based on Euler-Bernoulli\'s beam differential equation and applying boundary conditions. In the following, the frequencies of the rotating beam with constant and variable cross sections are determined using the transfer matrix method in several case studies. In order to eliminate numerical difficulties in the transfer matrix method, the Riccati transfer matrix is employed for high rotation speed and high modes. The results are compared with the results of the finite elements method and Rayleigh-Ritz method which show good agreement in spite of low computational cost.
 
Key Words
    Riccati; transfer matrix method; rotating beam; cross section; natural frequency
 
Address
Mahdi Feyzollahzadeh and Mahdi Bamdad: Mechanical and Mechatronics Engineering, Mechatronic Research Lab, Shahrood University of Technology, Shahrood, Iran
 

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