INVESTIGATION OF THE FREE VIBRATION OF AN ALUMINUM BEAM COATED WITH FGM CONTAINING POROSITIES

Abstract

In this study, the free vibration analysis of an aluminum beam coated with functionally graded material (FGM) containing porosities was investigated. The modulus of elasticity and density of the functionally graded material is assumed to vary with a polynomial function along the layer thickness of the beam. In order to represent the FGM in a realistic way, the coating thickness consists of 25 layers and each layer is modeled as homogeneous isotropic in itself. The effective density and modulus of elasticity of the FGM is determined using classical lamination theory. In this study, the solution of the problem was realized by using the finite element method using Timoshenko beam theory which includes first order shear deformation. The FEM code is written in MATLAB and the natural frequencies of the beam are calculated. A parametric study is conducted to show the influences of porosity (a), core thickness to FGM thickness ratio (h/H), beam span to height ratio (L/H) and power law index (n) on the natural beam frequencies. It was observed that the studied parameters had a significant effect on the natural frequencies.

Keywords

• Free vibration
• Functionally graded material
• Porosity
• Finite element method

POROSİTELİ FDM İLE KAPLI ALÜMİNYUM KİRİŞİN SERBEST TİTREŞİMİNİN İNCELENMESİ

Öz

Bu çalışmada çekirdek tabakası alüminyum ve yüzeyleri porosite ihtiva eden fonksiyonel derecelendirilmiş malzeme (FDM) ile kaplı simetrik yapıda ankastre sandviç bir kirişin serbest titreşim analizi incelenmiştir. Fonksiyonel derecelendirilmiş malzemenin elastisite modülü ve yoğunluğu kirişin tabaka kalınlığı boyunca bir polinom fonksiyonla değiştiği kabul edilmiştir. FDM’yi gerçeğe yakın bir şekilde temsil etmek için kaplama kalınlığının 25 tabakadan oluştuğu ve her bir tabaka kendi içinde homojen izotrop olarak modellenmiştir. Bu yapılara ait efektif yoğunluk ve elastisite modülü tabakalı kompozit kiriş teorisi kullanılarak belirlenmiştir. Çalışmada birinci mertebe kayma deformasyonu içeren Timoshenko kiriş teorisi kullanılarak problemin çözümü sonlu elemanlar metoduyla gerçekleştirilmiştir. Kirişin doğal frekanslarının hesaplanması için MATLAB’ta sonlu elemanlar kodu yazılmıştır. Çalışmada porosite hacim oranının (a), çekirdek tabaka kalınlığının FDM kalınlık oranına (h/H), kiriş açıklığının yüksekliğine oranının (L/H) ve FDM’nin mekanik özelliklerini belirleyen polinom parametresinin (n) doğal frekansların üzerindeki etkisi incelenmiştir. İncelenen parametrelerin kirişin doğal frekanslarını önemli ölçüde etkilediği gözlemlenmiştir.

Anahtar Kelimeler

• Serbest titreşim
• Fonksiyonel derecelendirilmiş malzeme
• Porosite
• Sonlu elemanlar metodu

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