https://doi.org/10.1140/epjp/i2017-11751-x
Regular Article
A new fractional nonlocal model and its application in free vibration of Timoshenko and Euler-Bernoulli beams
1
Faculty of Mechanical Engineering, Urmia University, Urmia, Iran
2
Poznan University of Technology, Institute of Structural Engineering, Piotrowo 5 Street, 60-695, Poznan, Poland
3
School of Mechanics and Civil Engineering, China University of Mining and Technology, 221116, Xuzhou, China
4
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, 221116, Xuzhou, China
* e-mail: st_z.rahimi@urmia.ac.ir
Received:
20
March
2017
Accepted:
12
October
2017
Published online:
21
November
2017
The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2017
