https://doi.org/10.1140/epjp/s13360-021-02153-w
Regular Article
Free in-plane vibration analysis of elastically restrained functionally graded porous plates with porosity distributions in the thickness and in-plane directions
1
State Key Laboratory of High Performance Complex Manufacturing, Central South University, 410083, Changsha, People’s Republic of China
2
Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic and Transportation Engineering, Central South University, 410075, Changsha, People’s Republic of China
3
Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, 410075, Changsha, People’s Republic of China
4
National and Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Central South University, 410075, Changsha, People’s Republic of China
Received:
11
August
2021
Accepted:
6
November
2021
Published online:
24
January
2022
A unified solution for free in-plane vibration analysis of elastically functionally graded restrained porous plates (FGPP) with porosity distributions in the thickness and in-plane directions in the framework of a semi-analytical solution is proposed for the first time. The segment technique, penalty function and energy principle are used to establish the motion equation of porous plates. The boundary conditions are simulated by setting of penalty function. The displacement tolerance function of porous plates is expressed by Jacobian series, which is introduced into the energy expression. Then a set of simple linear equations can be obtained by partial differential operation of unknown expansion coefficients. By compared results obtained by the current method, FEM and experiment, the correctness and accuracy of this model are validated. On the above basis, comprehensive parametric investigations are carried out to analyze the behavior of vibration of FGPP with respect to a several factors. The numerical results presented in this paper can lay a foundation for future research in this field.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
