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Title: Analysis of Multi-Sectioned Beam Vibrations
Authors: Abdullah A. Al Ajeel 
Supervisor: Prof. Khaled Al Hazza
Keywords: Vibrations
Issue Date: 2018
Publisher:  Kuwait university - college of graduate studies
Abstract: Beams are widely used in the industrial sectors where they usually have an uneven shape, multi-sections, different densities, and varying widths and thicknesses. Many re-searchers tend to simplify the system by assuming even shapes or by using Finite Element Methods (FEM) to predict the dynamic behavior or to control such systems. It is well known that, these methods might find a solution but it is either inaccurate or mathematically chal-lenging. Finding reduced order equations greatly simplifies the prediction of the dynamic be-havior and the choice of proper control scheme. In this work, a mathematical method to reduce the partial differential equation of mul-ti-sectioned beams to ordinary differential equation is proposed. The beam nonlinear equation of motion is derived by utilizing Hamilton’s principle. This equation is linearized and then reduced by adopting Galerkin’s Method. The linear natural frequenciesarecalculated analyti-cally by using Maple and validated numerically using FEM.The generated analytical solution isdesigned to solve complex models fora multi-thicknesses cantilever beam which is separat-ed into multiple segments. Each segment can have different thickness, density, or shape but with common width. The change in density has been utilized to determine the effect of piezo-electric actuator dimensions and locations on a beam’s natural frequencies. Finally In order to study the effect of beam segmentsonthe natural frequencies,multi-sectioned examples are cal-culated analytically using the proposed method and validated numerically using FEM. The results show that the analytical and FEM natural frequencies are almost identical for both uniform and non-uniformed cantilever beams with a minor percentage error. The same results are found as per changing the segment density. In fact, the percentage error is found to be less than 10%. The results confirm that the proposed analytical technique is suc-cessfully predicted the linear natural frequencies and can be used to predict the dynamical behavior of multi-sectioned beams with different used materials
Appears in Programs:0630 Mechanical Engineering

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