^{1}

^{2}

^{1}

^{2}

This paper attempts to investigate the flutter characteristic of sandwich panel composed of laminated facesheets and a functionally graded foam core. The macroscopic properties of the foam core change continuously along this direction parallel to the facesheet lamina. The model used in the study is a simple sandwich panel-wing clamped at the root, with three simple types of grading strategies for FGM core:

Aeroelastic phenomena are the result of the mutual interaction of elastic and aerodynamic forces, the occurrence of which during the flight can be destructive and lead to the loss of the aircraft [

Based on author’s previous research [

In a cantilevered composite sandwich panel (1.2 m × 0.4 m) with one end fixed, thicknesses of facesheet and foam core are 0.0005 m and 0.01 m. The material properties of T300/QY8911 used for composite facesheet are listed in Table

Material property of T300/QY891.

| | | | ^{3}) | |
---|---|---|---|---|---|

127.56 | 13.03 | 0.3 | 6.41 | 1577.76 | 0.125 |

The sandwich stiffness matrices can be written in terms of the facesheet and core stiffness as follows [

For composite facesheet, the membrane stiffness matrix can be expressed in terms of lamination parameters and material stiffness invariants:

The material stiffness invariants are calculated as follows:

The membrane lamination parameters are given by the following integrals:

The lamination parameters cannot be chosen arbitrarily. For a laminate of 0, 90, 45, and −45 degree fiber angles,

For the density gradient foam material, to calculate Young’s modulus of the closed-cell foam material, Xiao et al. [^{3}.

The flutter speed is always affected by the span-wise bending stiffness and chord-wise torsional stiffness for a wing panel. In order to research the flutter speed with grading bending and torsional stiffness, three types of grading strategies [

Submitting for

PK-method method is adopted for flutter speed calculation [

Keeping the total mass of the foam core constant and varying the densities of

Gradient factor.

Gradient factor (GF) | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Density variation range [ | | | | |

^{3} (nongradient).

Orthotropic sandwich panel (

Figure

Average increases of the flutter speeds for various GS and GF compared with the sandwich panel with no gradient change.

GF1 | GF2 | GF3 | |
---|---|---|---|

GS1 | 2.33% | 4.07% | 26.58% |

GS2 | 1.94% | 3.69% | 5.32% |

GS3 | −0.10% | −0.58% | −1.45% |

When

Figure

Figure

Minimum weight design of cantilevered sandwich panel as shown in Figure

Cantilevered sandwich panel.

Material grading across the sandwich panel [

Density grading in the chord-wise direction

Density grading in the span-wise direction

Density diagonal grading across the

Flutter velocity contours for orthotropic sandwich panel with no gradient change (

Flutter velocity contours for orthotropic sandwich panel (

GF = 1 (GS1)

GF = 2 (GS1)

GF = 3 (GS1)

GF = 1 (GS2)

GF = 2 (GS2)

GF = 3 (GS2)

GF = 1 (GS3)

GF = 2 (GS3)

GF = 3 (GS3)

Flutter velocity contours for nonorthotropic sandwich panel with no gradient change (

Point B

Point C

Flutter speed of the two sets with various GS and GF.

Point B

Point C

The optimization problem can be stated as follows:

Because of the ability to deal with the continuous global optimization problem with a nonlinear objective function, particle swarm optimization (PSO) is an evolutionary global algorithm and has become more and more popular. PSO was first proposed by Kennedy and Eberhart [

The basic steps in the PSO algorithm are as follows.

Initialize the swarm with random position values and random initial velocities.

Determine the velocity vector for each particle in the swarm using the knowledge of the best position obtained by each particle and the swarm as a whole and also the previous position of each particle in the swarm.

Modify the current position of each particle using the velocity vector and the previous position of each particle.

Repeat from Step

The velocity vector of each particle is calculated as follows:

The position of each particle at iteration

According to (9-11) of [^{3}. So the optimum sandwich configuration is obtained as

Optimum design variables and laminate configuration.

| | ^{3}) | ^{3}) | | | | Sandwich |
---|---|---|---|---|---|---|---|

10 | 0.125 | 20 | 37.64 | 0 | −1 | −0.076 | |

In this paper, the flutter speed of a cantilevered sandwich panel is studied using lamination parameters of composite facesheet, with influence of density gradient on sandwich panel considered. The results show that the flutter speed of the sandwich panel has the potential to increase when the proper gradient changes of the foam cores (GF) increase for chord-wise strategy and span-wise strategy with the total mass of the core constant. A minimum weight design of composite sandwich panel with lamination parameters of facesheet and density distribution of foam core as design variables was conducted using PSO. The results show that the PSO algorithm can be effective for the lamination parameters-based optimizaiton problem.

The paper conducts a series of flutter analysis for a range of functionally graded core of composite sandwich. The previous studies in this area have already shown that the flutter characteristics are sensitive to the wing geometry (e.g., aspect ratio and sweep) as well as material properties and that the conclusion drawn in this paper is a little simplistic. Further research will be focused on careful analysis considering other key parameters based on the existing literature and offer a more comprehensive discussion.

The authors declare that they have no competing interests.

The support for this work by the National Natural Science Foundation of China (11402204) is gratefully acknowledged.