## What is/are Graded Circular?

Graded Circular - Herein, an ultra-thin meta-absorber is proposed to achieve broadband low-frequency underwater SA via inserting thin and thickness-graded circular-elastic-plate scatterers (CPSs) into an elastomer matrix.^{[1]}

## classical plate theory

In this study, the free axisymmetric vibrations of functionally graded circular plate of linearly varying thickness controlled by a taper parameter in radial direction and non-linear temperature rise along the thickness have been investigated on the basis of classical plate theory.^{[1]}The Neumann series method has been used for the first time to solve the boundary value problem of free axisymmetric and nonaxisymmetric vibrations of continuous and discrete-continuous functionally graded circular plate on the basis of the classical plate theory.

^{[2]}Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory.

^{[3]}

## non linear temperature

In this article, axisymmetric vibrations of a non-uniform functionally graded circular plate subjected to uniform in-plane peripheral loading and non-linear temperature rise across the thickness have been analyzed on the basis of classical theory of plates.^{[1]}

## Functionally Graded Circular

The functionally graded circular nanoplate is a commonly seen component in the nano-electromechanical system.^{[1]}Exact solution of axisymmetric wave propagation problem in radially and functionally graded circular cylinder made from combination of isotropic and transversely isotropic materials is obtained.

^{[2]}The three-dimensional free flexural vibrations of functionally graded circular cylindrical shell with curvilinear radius variation fully or partially filled with incompressible and inviscid fluid are investigated for the first time using a coupled axisymmetric solid-fluid hierarchical finite element method based on curved elements.

^{[3]}The FGCPS can be regard as the coupling of multiple functionally graded circular arc shell elements in the form of share node by coordinate transformation.

^{[4]}Based on this general solution, we next study an axisymmetric bending problem of functionally graded circular plates subjected to a transverse loading $$q_0 r^n$$ (n is an even number) and give explicitly analytical elastic solutions to the case of uniform loadings under simply supported and two types of clamped supported conditions.

^{[5]}This paper deals with the vibration characteristics of rotating functionally graded circular cylindrical shells (FG-CS).

^{[6]}A rotating functionally graded circular disk undergoing a contact load is taken into account to investigate the thermoelastic characteristics.

^{[7]}In this article, axisymmetric vibrations of a non-uniform functionally graded circular plate subjected to uniform in-plane peripheral loading and non-linear temperature rise across the thickness have been analyzed on the basis of classical theory of plates.

^{[8]}The present work proposes a semi-analytical technique for solution of mixed boundary value problem in functionally graded circular annulus wherein shear modulus varies radially in power-law form while Poisson’s ratio is constant.

^{[9]}In this study, the free axisymmetric vibrations of functionally graded circular plate of linearly varying thickness controlled by a taper parameter in radial direction and non-linear temperature rise along the thickness have been investigated on the basis of classical plate theory.

^{[10]}The thermoelastic characteristics of a functionally graded circular disk are sensitive to the variations of angular speed and the ratio between the top coat and the substrate, of the disk.

^{[11]}The vibration of functionally graded circular plates of variable thickness under a thermal environment is analyzed when the nodal lines are concentric circles by using the generalized differential quadrature method for the nonlinear temperature distribution in the thickness direction.

^{[12]}This paper is concerned with the nonlinear dynamic buckling of sandwich functionally graded circular cylinder shells filled with fluid.

^{[13]}An analysis is presented for the study of thermal environment on free axisymmetric vibrations of functionally graded circular plates subjected to uniform in-plane peripheral loading and non-linear temperature distribution along the thickness direction.

^{[14]}The Neumann series method has been used for the first time to solve the boundary value problem of free axisymmetric and nonaxisymmetric vibrations of continuous and discrete-continuous functionally graded circular plate on the basis of the classical plate theory.

^{[15]}Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory.

^{[16]}Noda, Ootao and Tanigawa (2012) presented the solutions of transient thermoelastic problems for a functionally graded circular disk with piecewise power law.

^{[17]}In this paper, the complex variable method is applied to study three-dimensional problems of transversely isotropic functionally graded circular plates subjected to concentrated edge forces and couples.

^{[18]}This paper deals with free vibration problem of ceramic and metal functionally graded circular cylindrical shells embedded in a Pasternak elastic foundation and partially/completely in contact with a fluid within the framework of the first-order shear deformation theory.

^{[19]}In this work, a theoretical model is built to characterize the functionally graded circular flexoelectric energy harvesters based on the Kirchhoff thin plate hypothesis.

^{[20]}A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners.

^{[21]}

## graded circular plate

Based on this general solution, we next study an axisymmetric bending problem of functionally graded circular plates subjected to a transverse loading $$q_0 r^n$$ (n is an even number) and give explicitly analytical elastic solutions to the case of uniform loadings under simply supported and two types of clamped supported conditions.^{[1]}In this article, axisymmetric vibrations of a non-uniform functionally graded circular plate subjected to uniform in-plane peripheral loading and non-linear temperature rise across the thickness have been analyzed on the basis of classical theory of plates.

^{[2]}In this study, the free axisymmetric vibrations of functionally graded circular plate of linearly varying thickness controlled by a taper parameter in radial direction and non-linear temperature rise along the thickness have been investigated on the basis of classical plate theory.

^{[3]}The vibration of functionally graded circular plates of variable thickness under a thermal environment is analyzed when the nodal lines are concentric circles by using the generalized differential quadrature method for the nonlinear temperature distribution in the thickness direction.

^{[4]}An analysis is presented for the study of thermal environment on free axisymmetric vibrations of functionally graded circular plates subjected to uniform in-plane peripheral loading and non-linear temperature distribution along the thickness direction.

^{[5]}The Neumann series method has been used for the first time to solve the boundary value problem of free axisymmetric and nonaxisymmetric vibrations of continuous and discrete-continuous functionally graded circular plate on the basis of the classical plate theory.

^{[6]}Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory.

^{[7]}In this paper, the complex variable method is applied to study three-dimensional problems of transversely isotropic functionally graded circular plates subjected to concentrated edge forces and couples.

^{[8]}

## graded circular cylindrical

The three-dimensional free flexural vibrations of functionally graded circular cylindrical shell with curvilinear radius variation fully or partially filled with incompressible and inviscid fluid are investigated for the first time using a coupled axisymmetric solid-fluid hierarchical finite element method based on curved elements.^{[1]}This paper deals with the vibration characteristics of rotating functionally graded circular cylindrical shells (FG-CS).

^{[2]}This paper deals with free vibration problem of ceramic and metal functionally graded circular cylindrical shells embedded in a Pasternak elastic foundation and partially/completely in contact with a fluid within the framework of the first-order shear deformation theory.

^{[3]}A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners.

^{[4]}

## graded circular disk

A rotating functionally graded circular disk undergoing a contact load is taken into account to investigate the thermoelastic characteristics.^{[1]}The thermoelastic characteristics of a functionally graded circular disk are sensitive to the variations of angular speed and the ratio between the top coat and the substrate, of the disk.

^{[2]}Noda, Ootao and Tanigawa (2012) presented the solutions of transient thermoelastic problems for a functionally graded circular disk with piecewise power law.

^{[3]}

## graded circular cylinder

Exact solution of axisymmetric wave propagation problem in radially and functionally graded circular cylinder made from combination of isotropic and transversely isotropic materials is obtained.^{[1]}This paper is concerned with the nonlinear dynamic buckling of sandwich functionally graded circular cylinder shells filled with fluid.

^{[2]}