This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.
In this study, a laminated cantilever composite beam is studied in frequency domain by using some popular model order reduction techniques. In the analyses, component mode synthesis (CMS) and quasi-static mode synthesis (QSM1, QSM2) methods are applied to semi-discrete finite element equations to obtain reduced order models for structural analyses. The performance of the model order reduction methods is compared. In addition, fiber orientation, stacking sequence, ply thickness, and its location effects on the number of modes of the methods and on the natural frequencies are investigated. Results reveal that the performance of the QSM2 method is found to be better than the others. It is observed that the fiber orientation, stacking sequence, ply thickness, and its location parameters affect the natural frequency values and the number of modes of the methods.
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