DYNAMIC ANALYSIS OF HETEROGENEOUS ANISOTROPIC PLATES RESTING ON THE PASTERNAK ELASTIC FOUNDATION

Abstract

   In this study, the effects of elastic foundation on the frequencies of the heterogeneous orthotropic plates using shear deformation plate theory are investigated. Pasternak elastic foundation model is used to define the reaction of two-parameter elastic media on the plate. The formulation of the problem is based on the Donnell type plate theory. The Young's moduli of heterogeneous orthotropic material change as exponential function, Poisson's ratio and density are considered constant. The basic partial differential equations are reduced to ordinary differential equations using Galerkin method and closed-form solution is obtained for the frequency of heterogeneous orthotropic plates. The obtained values are compared with those in the current literature and the results were confirmed. Finally, a parametric study is performed to show the effects of heterogeneity, shear stresses and elastic foundations on the frequency parameters.

Keywords

• Heterogeneous anisotropic materials,Pasternak elastic foundation,Plates,Vibration,Frequency parameter

PASTERNAK ELASTİK ZEMİNE OTURAN HETEROJEN ANİZOTROPİK PLAKLARIN DİNAMİK ANALİZİ

Öz

   Bu makalede, elastik zeminin heterojen ortotropik plakların (HTOP) titreşim frekansları üzerindeki etkileri kayma deformasyon teorisi (KDT) kullanılarak incelenmektedir. İki parametreli elastik ortamın plak üzerindeki reaksiyonunu tanımlamak için Pasternak elastik zemin (PEZ) modeli kullanılmaktadır. Problemin formülasyonu Donnell tipi teoriye dayanır. Heterojen ortotropik malzemenin Young modüllerinin üstel fonksiyon olarak değiştiği, Poisson oranı ve yoğunluğu sabit kabul edilmektedir. Temel denklemler, Galerkin yöntemi kullanılarak zamana bağlı geometrik kısmi türevli diferansiyel denklemler adi diferansiyel denklemlere indirgenmektedir. Türetilen denklemden heterojen ortotropik plakların frekansı için kapalı çözüm elde edilmektedir. Elde edilen değerler literatürdeki benzer çalışmalar ile karşılaştırılarak sonuçlar doğrulanmıştır. Son olarak, heterojenliğin, kayma gerilmelerinin ve PEZ’in frekans parametrelerine etkilerini göstermek için parametrik çalışma gerçekleştirilmiştir.

Anahtar Kelimeler

• Heterojen anizotrop malzemeler,Pasternak elastik zemini,Plaklar,Titreşim,Frekans parametresi

Kaynakça

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