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Dynamic behaviour of axially functionally graded beam resting on variable elastic foundation

Kumar Saurabh

Archive of Mechanical Engineering

2020

LXVII, nr 4

451--470

In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. The free vibration problem is formulated using Rayleigh-Ritz method and Hamilton’s principle is applied to generate the governing equations. The results are presented as non-dimensional natural frequencies for different material gradation models and different foundation stiffness variation models. Two distinct boundary conditions viz., clamped-clamped and simply supported-simply supported are considered in the analysis. The results are validated with existing literature and excellent agreement is observed between the results.

Free vibration of axially functionally graded Euler-Bernoulli beams

Kukla S., Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 1

39--44

In this contribution, free vibration of axially functionally graded beams is analysed within the framework of the Euler-Bernoulli beam theory. The beams with uniaxial variation of the elasticity modulus and mass density are approximated by an equivalent beam with piecewise exponentially varying geometrical and material properties. A numerical example for a beam with pinned ends is presented.