Abstract

In this study, free vibration behavior of a multilayered symmetric sandwich beam made of Functionally Graded Material (FGM) with variable cross-section is investigated. The elasticity and density of the Functionally Graded (FG) sandwich beam vary through the thickness according to the power and exponential laws by using mixture rules and laminate theory. In order to provide this, fifty layered beam is considered. Each layer is isotropic and homogeneous although the volume fractions of the constituents of the layers are different. Furthermore, the width of the beam varies exponentially along the length of the beam with rectangular cross-section. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using theoretical procedure. The effects of material index, geometric index and slenderness ratio are also discussed. Finally, the obtained results are compared with those in literature and a finite element based commercial program ANSYS® and found to be consistent with each other.

Highlights

  • The Functionally Graded Materials (FGMs) are obtained by changing the volume fractions of constituents from one surface to the other gradually

  • Pradhan and Murmu [7] presented thermomechanical vibration analysis of beams and sandwich beams made of FGM under different conditions

  • Bedjilili et al [8] coped with the free vibration of composite beams with a variable fiber volume fraction using the first-order shear deformation theory

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Summary

INTRODUCTION

The Functionally Graded Materials (FGMs) are obtained by changing the volume fractions of constituents from one surface to the other gradually. Aydogdu and Taskin [5] investigated free vibration of supported FG beam by using parabolic, first order and exponential shear deformation beam theories. There are some studies related to free vibration behaviors of beams with variable cross section. Atmane et al [12] presented a theoretical investigation for free vibration of a functionally graded beam with variable cross-section. Their theory is based on Kirchhoff-Love hypothesis and they only changed the material properties exponentially. Free vibration behavior of a symmetric FG sandwich beam with variable cross-section is analyzed. The effects of material and geometrical indexes and slenderness ratio on the vibration behaviors of the sandwich beam with variable cross-section are discussed

DETERMINATION OF THE EFFECTIVE MATERIAL AND GEOMETRY PROPERTIES
THEORETICAL FORMULATION AND SOLUTION
RESULTS AND DISCUSSION
Effect of the slenderness r5atio
CONCLUSIONS
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