Free vibration and buckling analysis of FGM sandwich beams Trigonometric series functions Navier's method In this study, free vibration and buckling analyses of functionally graded (FGM) sandwich beams is investigated by Navier's method. Two cases of functionally graded sandwich beams are considered: a) Homogeneous ceramic core and FGM faces (Type A), and b) FGM core and homogeneous faces (Type B). Figure A. Geometric properties of FGM beams considered Purpose: The aim of this study is to perform free vibration and buckling analysis of functionally graded sandwich beams with different boundary conditions, power-law indices and slenderness using trigonometric series functions. Theory and Methods: Displacement field is defined according to the first order shear deformation theory, and the equations of motion are derived by the Lagrange's principle. Volumetric ceramic ratio is defined by a power-law rule. In the analytical solution, different trigonometric series functions are used for each end conditions considered. Results: Natural frequencies and buckling loads are obtained for different boundary conditions, power-law indices and slenderness. Numerical results are compared with the available literature, and a good agreement are obtained between the results. Conclusion: To make a generalization, it is seen that natural frequencies and buckling loads decrease when the metallic feature is dominant in FDM sandwich beams, and increase when the ceramic feature is dominant.
Bu çalışmada, birinci mertebe kayma deformasyonu teorisine dayalı olarak fonksiyonel derecelendirilmiş kirişlerin serbest titreşim analizi Navier tipi çözüm yöntemi kullanılarak yapılmıştır. Hareket denklemleri Lagrange eşitlikleri ile türetilmiş, problemin çözümünde ise trigonometrik fonksiyonlar kullanılmıştır. Farklı sınır şartlarına, hacimsel oran fonksiyonunun farklı k değerlerine ve kirişin açıklığının yüksekliğine oranına bağlı olarak doğal frekanslar sayısal olarak hesaplanmıştır. Sayısal sonuçlar literatürle kıyaslanmış ve oldukça uyumlu oldukları görülmüştür. Anahtar Kelimeler: Fonksiyonel derecelendirilmiş malzeme, Navier metodu, Birinci mertebe kayma deformasyonu teorisi.
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