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Smart Structures and Systems
  Volume 25, Number 6, June 2020, pages 669-678

Dynamic behavior of axially functionally graded simply supported beams
Abdellatif Selmi

    This paper focuses on the free vibration analysis of axially functionally graded (FG) Euler-Bernoulli beams. The material properties of the beams are assumed to obey the linear law distribution. The complexities in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using the Differential Transformation Method (DTM). Natural frequencies and corresponding normalized mode shapes are calculated. Validation targets are experimental data or finite element results. Different parameters such as reinforcement distribution, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. The delivered results prove the capability and the robustness of the applied method. The studied parameters are demonstrated to be very crucial for the normalized natural frequencies and mode shapes.
Key Words
    differential transformation method; functionally graded material; mode shape; natural frequency
(1) Abdellatif Selmi:
Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia;
(2) Abdellatif Selmi:
Ecole Nationale d'Ingénieurs de Tunis (ENIT), Civil Engineering Laboratory, B.P. 37, Le belvédère 1002, Tunis, Tunisia.

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