Vibration analysis of simply supported beam-type vibration absorber

Beam-type structures have wide applications, for example civil or mechanical engineering. A simply supported beam is widely used in many areas like bridges and double-beam structures. Excessive vibration in such structures especially at the resonance can cause the structural failure. There are two techniques for suppressing the vibration in the beam-structures that have been studied previously; conventional and continuous vibration absorbers. A beam-type vibration absorber is one of the continuous vibration absorber applications and it is used to suppress the vibration of the main beam. Solving the vibration problem of such kind of structure is difficult and complicated, because the motion equations of the system are coupled. The equations cannot be analytically solved before decoupling them. Therefore, some mathematical transformation and variables variation methods were considered to solve this problem, but it is still under the limitation of identical beams. This means that the analytical method is valid just for identical beams. The main objective of this research study is to propose an easy and efficient method to solve the problem of the beam absorber system. In addition, there are sub-objectives have been achieved in this thesis; to study the effect elasticity ration of the main and absorber beams, to study the effect of the moving mass inertia on the main beam response, and finally to find the optimum design for the absorber system. The objectives have been achieved by developing the damping factor formulation of dynamic vibration absorber, and by using Time integration method in aided MATLAB. That was in the theoretical study. An experimental test has been performed by using LMS software to observe the performance of the absorber beam in suppressing the main beam vibration. The numerical results showed good agreement with the literature. That means the proposed method has been successfully developed. The experimental results showed good agreement with the numerical results. In other hand, it was found from the results that the effect of the moving mass inertia on the main beam response can be reduced by increasing the layer stiffness. Also, it has been noted that the elasticity ratio can be improved to find the optimum design of the absorber beam system by increasing its value and decreasing the mass ratio of the main and absorber beams. Finally, the numerical results proved that the proposed method is more effective than the methods used in previous works, because it valid for identical and non-identical beams.

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