Parametric Vibration of Three-Layered Cylindrical Shells with Functionally Graded Core

Abstract

In this study, the parametric vibration of three-layered cylindrical shells with functionally graded (FG) core is investigated. Firstly, analytical models of an FG core, which uses the intermediate member and outer sheath layers of the cylindrical shell formed from metal-rich and ceramic-rich represented as ternary systems. The governing equations of three-layered cylindrical shells with an FG core are derived and are reduced Mathieu-Hill equation by using Galerkin method. The expressions for non-dimensional frequency, critical axial load and boundaries of instability regions of three-layered cylindrical shell with an FG core are found. The expressions for non-dimensional frequency parameter, critical axial load and boundaries of instability regions are obtained for the monolayer FGM, pure metal and pure ceramic cylindrical shells, as a special case. Finally, the effects of variations of volume fractions, shell characteristics and variations of the thickness of a core on the values of critical parameters of three-layered cylindrical shells made of different types of FG core are studied numerically. Comparisons are made with the available studies in the open literature to validate this study

Keywords

• FGM core
• Three-layered cylindrical
• shell
• Parametric vibration
• Critical axial load

Fonksiyonel Değişimli Çekirdeğe Sahip Üç Tabakalı Silindirik Kabukların Parametrik Titreşimi

Abstract

Bu çalışmasında, çekirdeği fonksiyonel değişimli malzemelerden (FDM'ler) ve dış katmanları zenginleştirilmiş seramik ve metalden oluşan üç tabakalı silindirik kabukların statik ve zamana bağlı periyodik değişen yükler etkisi altında parametrik titreşimi incelenmektedir. Ara eleman olarak kullanılan fonksiyonel değişimli (FD) çekirdek ve zenginleştirilmiş metal ve seramikten oluşturulan dış tabakalardan oluşan üçlü sistemin analitik modeli sunulmaktadır. Fonksiyonel değişimli çekirdeğe (FDÇ'e) sahip sandviç silindirik kabukların statik ve zamana bağlı periyodik değişen eksenel basınç yükleri altında dinamik stabilite ve deformasyon uygunluk denklemleri türetilmektedir. Temel denklemler, Galerkin Yöntemi uygulanarak Mathieu-Hill denklemine dönüştürülmekte ve çözülerek FDÇ üç tabakalı silindirik kabukların kararsızlık bölgeleri, frekans parametresi ve kritik statik yük için ifadeler elde edilmektedir. Bu ifadelerden pür seramik, pür metal ve pür FD silindirik kabuklar için uygun ifadeler özel olarak elde edilmektedir. Son olarak kararsızlık bölgelerinin sınarlarına, FD çekirdek çeşitlerinin ve hacim kesir bileşenleri değişiminin, kabuk karakteristikleri ve çekirdek-kabuk kalınlıkları oranı değişiminin etkileri kapsamlı bir şekilde incelenmektedir. Elde edilen sonuçlar açık literatürde bulunan sonuçlarla karşılaştırılarak doğruluğu teyit edilmektedir.

Keywords

• FDÇ
• Üç tabakalı silindirik kabuk
• Parametrik titreşim
• Kritik eksenel yük

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