Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams | Zendy

Ahmad Shahba | Zendy; Reza Attarnejad | Zendy; Shahin Hajilar | Zendy

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Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams

Author(s) -

Ahmad Shahba,

Reza Attarnejad,

Shahin Hajilar

Publication year - 2011

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/2011/591716

Subject(s) - vibration , beam (structure) , axial symmetry , boundary value problem , finite element method , materials science , young's modulus , euler's formula , transverse plane , timoshenko beam theory , elasticity (physics) , mathematical analysis , structural engineering , mathematics , geometry , composite material , physics , engineering , acoustics

Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finite element method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

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