scholarly journals Lamb Waves in Anisotropic Functionally Graded Plates: A Closed Form Dispersion Solution

2019 ◽  
Vol 36 (1) ◽  
pp. 1-6
Author(s):  
S. V. Kuznetsov
Keyword(s):  
Closed Form ◽  
Dispersion Equation ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Stratified Media ◽  
Exponential Mapping ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Transverse Inhomogeneity ◽  
Dispersion Solution

ABSTRACTPropagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.

Cauchy formalism for Lamb waves in functionally graded plates

2018 ◽  
Vol 25 (6) ◽  
pp. 1227-1232 ◽  
Author(s):  
Sergey V. Kuznetsov
Keyword(s):  
Wave Propagation ◽  
Functionally Graded Materials ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Anisotropic Plates ◽  
Transverse Inhomogeneity ◽  
Lamb Wave Propagation

Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is analyzed by applying Cauchy six-dimensional formalism previously developed for the study of Lamb wave propagation in homogeneous or stratified anisotropic plates. For anisotropic plates with arbitrary transverse inhomogeneity a closed form implicit solution for the dispersion equation is derived and analyzed.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

scholarly journals Porous Functionally Graded Plates: An Assessment of the Influence of Shear Correction Factor on Static Behavior

2020 ◽  
Vol 25 (2) ◽  
pp. 25 ◽  
Author(s):  
Ana F. Mota ◽  
Maria Amélia R. Loja ◽  
Joaquim I. Barbosa ◽  
José A. Rodrigues
Keyword(s):  
Correction Factor ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Static Behavior ◽  
Graded Materials ◽  
Shear Correction Factor ◽  
Quadrilateral Plate ◽  
Bending Behavior ◽  
Application Fields

The known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and the corresponding estimations of their material properties—in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure’s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates.

scholarly journals Finite Element Analysis of the Deformation of Functionally Graded Plates under Thermomechanical Loads

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
A. E. Alshorbagy ◽  
S. S. Alieldin ◽  
M. Shaat ◽  
F. F. Mahmoud
Keyword(s):  
Volume Fraction ◽  
Thermomechanical Behavior ◽  
Functionally Graded ◽  
Neutral Plane ◽  
Functionally Graded Plates ◽  
Element Analysis ◽  
Graded Materials ◽  
First Order ◽  
Fg Plates ◽  
Continuous Power

The first-order shear deformation plate model, accounting for the exact neutral plane position, is exploited to investigate the uncoupled thermomechanical behavior of functionally graded (FG) plates. Functionally graded materials are mainly constructed to operate in high temperature environments. Also, FG plates are used in many applications (such as mechanical, electrical, and magnetic), where an amount of heat may be generated into the FG plate whenever other forms of energy (electrical, magnetic, etc.) are converted into thermal energy. Several simulations are performed to study the behavior of FG plates, subjected to thermomechanical loadings, and focus the attention on the effect of the heat source intensity. Most of the previous studies have considered the midplane neutral one, while the actual position of neutral plane for functionally graded plates is shifted and should be firstly determined. A comparative study is performed to illustrate the effect of considering the neutral plane position. The volume fraction of the two constituent materials of the FG plate is varied smoothly and continuously, as a continuous power function of the material position, along the thickness of the plate.

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