Abstract

In this paper, a modified Fourier series method is presented for the free vibration of moderately thick orthotropic functionally graded plates with general boundary restraints based on the first-order shear deformation theory. Regardless of boundary restraints, displacements and rotations of each plate are described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate all the boundary discontinuities and jumps. Exact solutions are obtained by the energy functions of the plates based on Rayleigh-Ritz method. The convergence and reliability of the current method and the corresponding theoretical formulations are verified by comparing the present results with those available in the literature, and numerous new results for orthotropic functionally graded (OFG) plates with general boundary restraints are presented. In addition, the effects of gradient index, volume fraction and geometric parameters on frequencies with general boundary restraints are illustrated.

Highlights

  • As a kind of novel composite materials, functionally graded materials (FGMs) can be characterized by the variation in composition and structure gradually over volume, resulting in continuous changes along the desired directions

  • The convergence and reliability of the proposed modified Fourier series method is validated by comparing the current solutions with those results published in the literature under the distribution of P-orthotropic functionally graded (OFG)

  • A modified Fourier series method has been applied to solve the free vibrations of moderately thick OFG plates with general boundary restraints

Read more

Summary

Introduction

As a kind of novel composite materials, functionally graded materials (FGMs) can be characterized by the variation in composition and structure gradually over volume, resulting in continuous changes along the desired directions. From the review of the literature, most of the previous variety of possible volume distributions in practical engineering applications, and these distributions studies on influence the OFG on plates are defined in a single volume distribution type.to are a have great the vibration properties of the OFG plates. IndexTherefore, on the volume fractionofinthe different the material properties changemethod continuously the objective presentdistributions, work is to provide an accurate and reliable for the through the thickness of the free vibration analysis of moderately thick OFG plates in various volume distribution types with. Rotations ofiseach plate, regardless of boundary restraints, the free vibration analysis of moderately thick plates in various volume distribution types described as an improved form of double Fourier cosine series and several closed-form auxiliary with general restraints. Studies focused on free vibration properties of OFG plates are presented, which may serve as a supplement of the material performance of OFG plates

Theoretical Formulation
Material Properties
Stress–Strain Relations and Stress Resultants
Energy Functions
Admissible Displacement Functions
Numerical Results and Discussion
OFG Plates with General Boundary Restraints
Fundamental Frequencies Analysis
Variation
Conclusions
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call