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1
Content available Dynamic behaviour of axially functionally graded beam resting on variable elastic foundation
Kumar Saurabh
Archive of Mechanical Engineering
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2020
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LXVII, nr 4
451--470
EN
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.
2
Content available Some closed-form bending formulas for elastically restrained Euler-Bernoulli beams under point and uniformly distributed loads
Yıldırım V.
Journal of Applied Mathematics and Computational Mechanics
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2018
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Vol. 17, nr 3
97--109
EN
The transfer matrix method based on the Euler-Bernoulli beam theory is employed in order to originally achieve some exact analytical formulas for elastically supported beams under a point force together with uniformly distributed force and uniformly distributed couple moments. Those closed-form formulas can be used in a variety of engineering applications especially at the pre-design stage to get an insight into the response of the structure. Contrary to the classical boundary conditions, it is also observed that the Euler-Bernoulli solutions of a beam with elastic supports are sensitive to the ratio of length to thickness (L/h).
3
Content available remote Identification of Crack in Beams Using Eigenfrequency
Majkut L.
Vibrations in Physical Systems
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2004
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Vol. 21
251--254
4
Content available remote Identification of Crack in Beams Based on Measurements of Forced Vibration Amplitudes
Majkut L.
Vibrations in Physical Systems
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2004
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Vol. 21
255--258
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