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Dynamic behavior of nonuniform functionally graded euler-bernoulli beams under multiple moving forces

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The dynamic behavior of nonuniform Euler-Bernoulli beams made of transversely functionally graded material under multiple moving forces is studied by the finite element method. The beam cross-section is assumed to vary in the width direction by two different types. A simple finite element formulation, accounting for variation of the material properties through the beam thickness and the shift in the physically neutral surface, is derived and employed in the study. | Vietnam Journal of Mechanics, VAST, Vol. 37, No. 3 (2015), pp. 151 – 168 DOI:10.15625/0866-7136/37/3/4075 DYNAMIC BEHAVIOR OF NONUNIFORM FUNCTIONALLY GRADED EULER-BERNOULLI BEAMS UNDER MULTIPLE MOVING FORCES Le Thi Ha1 , Nguyen Dinh Kien2,∗ , Vu Tuan Anh3 University of Transport and Communications, Vietnam 2 Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam 3 Hanoi University of Science and Technology, Vietnam 1 Hanoi ∗ E-mail: ndkien@imech.ac.vn Received June 02, 2014 Abstract. The dynamic behavior of nonuniform Euler-Bernoulli beams made of transversely functionally graded material under multiple moving forces is studied by the finite element method. The beam cross-section is assumed to vary in the width direction by two different types. A simple finite element formulation, accounting for variation of the material properties through the beam thickness and the shift in the physically neutral surface, is derived and employed in the study. The exact variation of the cross-sectional profile is employed in evaluation of the element stiffness and mass matrices. The dynamic response of the beam is computed with the aid of the implicit Newmark method. The numerical results show that the derived finite element formulation is capable to assess accurately the dynamic characteristics of the beam by using just several elements. The effect of the moving speed, material inhomogeneity and section profile on the dynamic behavior of the beams is investigated. The influence of the distance between the forces as well as the number of forces on the dynamic response is also examined and highlighted. Keywords: Functionally graded beam, physically neutral surface, moving force, dynamic behavior, finite element method. 1. INTRODUCTION Functionally graded materials (FGMs) have received much attention from engineers and researchers since they were first initiated by Japanese scientists in 1984 [1]. FGMs are produced by continuously varying volume .