تنزيل وتحميل كتاِب LAMINATION SCHEME AND BOUNDARY CONDITIONS EFFECTS ON THE FREE VIBRATION OF LAMINATED COMPOSITE BEAMS pdf برابط مباشر مجاناً

تنزيل وتحميل كتاِب LAMINATION SCHEME AND BOUNDARY CONDITIONS EFFECTS ON THE FREE VIBRATION OF LAMINATED COMPOSITE BEAMS pdf برابط مباشر مجاناً

وصف LAMINATION SCHEME AND BOUNDARY CONDITIONS EFFECTS ON THE FREE VIBRATION OF LAMINATED COMPOSITE BEAMS pdf

 
In this study, the effects of both lamination scheme and boundary conditions on the natural frequencies of free vibration of laminated composite beams were investigated. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. Lamination schemes for symmetric and non-symmetric laminated beams were studied. Six boundary conditions are considered; clamped _free (CF), hinged _hinged (HH), clamped _clamped (CC), hinged _clamped (HC), hinged _free (HF), free _free (FF). Each beam has either movable ends or immovable ends. 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. Also, It is found that the more constrained beams have the higher values of natural frequencies of transverse vibration. However, the free-free and hinged-free beams are found to have the highest frequencies of transverse vibration amongst all beams although they look less constrained. This behavior is due to the fact that the first mode of the two beams is equal zero (rigid body motion), and replaced by the second mode to be the fundamental mode. The values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only. But for immovable ends, the clamped-free and hinged-free beams have equal frequencies in longitudinal vibration, and those of the other beams are also the same.

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