Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point MethodReport as inadecuate

Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method - Download this document for free, or read online. Document in PDF available to download.

Shock and Vibration - Volume 2016 2016, Article ID 5891030, 23 pages -

Research Article

Shenzhen Engineering Lab for Wind Environment and Technology, Shenzhen Key Lab of Urban and Civil Engineering Disaster Prevention and Reduction, Shenzhen Graduate School, Harbin Institute of Technology, Guangdong, Shenzhen 518055, China

College of Civil Engineering and Architecture, Guangxi University, Guangxi, Nanning 530004, China

Received 20 September 2015; Revised 24 January 2016; Accepted 7 February 2016

Academic Editor: Miguel Neves

Copyright © 2016 Peng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new model for the free transverse vibration of axially functionally graded FG tapered Euler-Bernoulli beams is developed through the spline finite point method SFPM by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.

Author: Peng Liu, Kun Lin, Hongjun Liu, and Rong Qin



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