Free Vibration Analysis of Moderately Thick Orthotropic Functionally Graded Plates with General Boundary Restraints

The material considered in this study not only has a functionally graded characteristic but also exhibits different tensile and compressive moduli of elasticity. One-dimensional and two-dimensional mechanical models for a functionally graded beam with a bimodular effect were established first. By taking the grade function as an exponential expression, the analytical solutions of a bimodular functionally graded beam under pure bending and lateral-force bending were obtained. The regression from a two-dimensional solution to a one-dimensional solution is verified. The physical quantities in a bimodular functionally graded beam are compared with their counterparts in a classical problem and a functionally graded beam without a bimodular effect. The validity of the plane section assumption under pure bending and lateral-force bending is analyzed. Three typical cases that the tensile modulus is greater than, equal to, or less than the compressive modulus are discussed. The result indicates that due to the introduction of the bimodular functionally graded effect of the materials, the maximum tensile and compressive bending stresses may not take place at the bottom and top of the beam. The real location at which the maximum bending stress takes place is determined via the extreme condition for the analytical solution.

Section: Discussionmentioning

confidence: 99%

One-Dimensional and Two-Dimensional Analytical Solutions for Functionally Graded Beams with Different Moduli in Tension and Compression

Sun

Dong

et al. 2018

“…According to the first-order shear deformation plate theory, Zhao et al [ 10 ] applied the element-free kp-Ritz method to analyze the vibrations of square and skew plates under different combinations of boundary conditions. Fu et al [ 11 ] employed the Ritz method with admissible functions consisting of double Fourier cosine and several closed-form auxiliary functions to study the vibrations of orthotropic FGM plates with general boundary restraints. Ferreira et al [ 12 ] investigated the vibrations of square plates employing the first-order and third-order shear deformation plate theories and the collocation method with multiquadric radial basis functions.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions Based on Fourier Cosine Series for the Free Vibrations of Functionally Graded Material Rectangular Mindlin Plates

Huang

2020

This study aimed to develop series analytical solutions based on the Mindlin plate theory for the free vibrations of functionally graded material (FGM) rectangular plates. The material properties of FGM rectangular plates are assumed to vary along their thickness, and the volume fractions of the plate constituents are defined by a simple power-law function. The series solutions consist of the Fourier cosine series and auxiliary functions of polynomials. The series solutions were established by satisfying governing equations and boundary conditions in the expanded space of the Fourier cosine series. The proposed solutions were validated through comprehensive convergence studies on the first six vibration frequencies of square plates under four combinations of boundary conditions and through comparison of the obtained convergent results with those in the literature. The convergence studies indicated that the solutions obtained for different modes could converge from the upper or lower bounds to the exact values or in an oscillatory manner. The present solutions were further employed to determine the first six vibration frequencies of FGM rectangular plates with various aspect ratios, thickness-to-width ratios, distributions of material properties and combinations of boundary conditions.

“…Moreover, FGMs possess many new properties that most traditional laminated materials do not have, which gives the use of FGMs many advantages in aerospace, automotive, and biomedical applications. During the past decades, FGMs have received a significant amount of attention from the academic community and engineering field, and many scholars have carried out research on functionally graded materials and structures [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ].…”

Section: Introductionmentioning

confidence: 99%

An Electroelastic Solution for Functionally Graded Piezoelectric Circular Plates under the Action of Combined Mechanical Loads

Yang

et al. 2018

In this study, we obtained an electroelastic solution for functionally graded piezoelectric circular plates under the action of combined mechanical loads which include the uniformly distributed loads on the upper surface of the plate and the radial force and bending moment at the periphery of the plate. All electroelastic materials parameters are assumed to vary according to the same gradient function along the thickness direction. The influence of different functionally graded parameters on the elastic displacement and elastic stress, as well as the electric displacement and electric potential, was discussed by a numerical example. The solution presented in this study is not only applicable to the case of combined loads, but also to the case of a single mechanical load. In addition, this solution reflects the influence of the function gradient on the pure piezoelectric plate, which is helpful to the refined analysis and optimization design of similar structures.