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

Year 2019, Volume: 8 Issue: 1, 226 - 236, 28.01.2019

Zihni Zerin

https://doi.org/10.28948/ngumuh.516884

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

Abstract

   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.

Keywords

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

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