In this study, the effect of the fiber orientation on the natural frequencies of free vibration of laminated composite beams was investigated. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. In that model, a three-noded element with three degrees of freedom at each node is assumed. Numerical results were obtained for symmetric and non-symmetric laminated beams, and verified by comparisons with other relevant works. Also, some special cases, which related to the title, were studied and presented. The angle of fibers orientation, which measured from the longitudinal axis of the beam, is varied from to . It is found that both symmetrically and anti-symmetrically laminated beams of similar size and end conditions have equal natural frequencies which, generally, decrease as the angle of orientation increases.
Keywords: Finite element method, first order shear deformation theory, free vibration, laminated composites, natural
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بسم الله الرحمن الرحيم
السلام عليكم ورحمة الله وبركاته
مجهود طيب أخي د. أسامة.
جزاكم الله تعالى خيرًا، وبارك فيكم،
وزادكم من واسع فضله سُبحانه.
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a lot thanks
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