In this study, the effects of stacking sequences of composite laminated beams on natural frequencies are investigated using the differential quadrature method (DQM). DQM is an efficient discretization technique for obtaining accurate numerical solutions to initial and/or boundary value problems using a considerably small number of grid points. In this way, a theoretical DQM model for the laminated composite beam has been developed. Some of the results obtained from DQM are compared with the results obtained experimentally. Then, these results are compared with the numerical and experimental results available in the literature. It has been seen that all of the results considered are very close to each other. It has also been concluded that the effective stiffness of the laminated composite beam can be altered through a change in the stacking sequence. This allows tailoring of the material to achieve desired natural frequencies and respective mode shapes without changing its geometry drastically or without increasing its weight.

The Differential Quadrature Method (DQM) was first proposed by Bellman and his associates [1, 2]. Since 1970s, DQM has been applied many areas in engineering problems. Bert and Malik [3] have mentioned examples to deal with the high order differential equations of Euler beam, whose governing equation is a forth order one with double boundary conditions at each boundary. The main difficulty for such forth order problems as Euler beams is that there are multiple boundary conditions but only one variable at each boundary. Applying multiple boundary condition at the same location is a big problem that to be dealt with in DQM. For this reason, Jang et al. [4] have proposed a-point approximation. A point very adjacent to the real boundary has been inserted to impose the second condition on there. Bert and Malik [3] have applied the-technique in the solution of linear structural problems. For differential equations involving more than one boundary condition at one point, the DQM has no generally effective technique to solve them without use to the current δ-point technique.

In this study, vibration analysis of layered composite beams with variable cross sections and delaminations was investigated analytically and numerically. In the analytical part, Bernoulli beam theory was used and the effect of shear force on the beam was neglected. The layered composite beam consists of eight layers and contains delaminations with various sizes. In the numerical part of the study, ansys program package was used for finite element analysis. Layered composite beams with the same geometry were created in the finite element model. In the numerical part, the contact element was also defined between the delaminated parts. Furthermore, it has been shown numerically and analytically that the slope angle of the beam influences the vibration of the layered composite beam. Moreover, as the delamination between the beams increases, the vibration of the beam is observed to decrease. The layered composite beam is shown in graphical form in which the vibration can be changed without changing the geometry of the beam, showing that the vibration can be changed by changing the fiber orientation angle.

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Bu çalışmada, otomotiv sanayisinde kullanılabilecek PLA (Poli-Laktik Asit) malzemesinin yapısı hücresel hibrit malzeme olan bal petekli yapılardan üretilmiş kirişlerin doğal frekans değerleri üzerindeki etkisi incelenmiştir. Yapılan çalışmada dörtgen, beşgen, altıgen ve yuvarlak gibi farklı çekirdek yapısındaki petekler ile bunların kombinasyonu olan altıgen-dörtgen(kare)-daire ve beşgenaltıgen-daire gibi çeşitli bal petekli kirişlerin tasarımı ve üretimi gerçekleştirilmiştir. Üretimi gerçekleştirilen kirişin nümerik (Ansys) ve deneysel titreşim analizleri yapılıp oluşan doğal frekans değerleri karşılaştırılması yapılarak titreşim mod değerlerinin birbirine yakın olduğu görülmüştür. Oluşturulan ankastre mesnetli kirişlerde, bal peteği yapılarının şekillerine göre aynı hacim ve yapıda olanların doğal frekans değerlerinin değiştirilebileceği gösterilmiştir.