A nonlinear dynamic modeling method for a spacecraft body composed of a laminated composite beam undergoing large rotation is proposed in this paper. To study the characteristics of a laminated composite beam attached to a spacecraft body for the dynamic systems, the deformation description of a laminated beam is established with the consideration of laying angles and laying layers, and the displacement-strain relations is acquired based on the global-local higher-order shear deformation theory. Accordingly, a nonlinear dynamic model of the spacecraft body composed of a laminated composite beam is deduced using Hamilton variational principle. And the complete coupling terms for the laminated material properties are considered unlike any other singular or unidirectional materials. Then, the dynamic behavior of the spacecraft system is analyzed by comparison of an orthogonal-symmetric, singular, and unidirectional laminated beam. The results show that the laminated composite structures have significant influences on the dynamics properties of spacecraft compared with conventional equivalent singular or unidirectional materials. Hence, the nonlinear model is well suitable for approaching the problem of coupling relationship between geometric nonlinearity and large rotation motions. These conclusions will have significant theory and engineering practice values for coupling dynamics properties of laminated beams.

Laminated composite materials are formed by combining layers of different materials or the same material by using different laying angles, laying sequence, and laying layers [

Flexible beams undergoing large-scale motions have their own unique theoretical and practical values in many applications. Many slender structures in aerospace engineering, such as space manipulators, solar wings, and satellite antenna, can be idealized to beam structures, and the dynamics properties of those structures are critical to system performance, integrity, and reliability [

In order to study dynamic behavior characteristics of a spacecraft beam with laminated composite structures and a large-scale motion, the aim of the present investigation is to develop a dynamic model. Also, the rigid-flexible coupling dynamics modeling are performed with the consideration of laying angles and laying layers of laminated composite beams. Then, the complete expressions of nonlinear terms, coupled deformation terms, and nonlinear elastic forces are developed in this study.

The laminated composite beam can be illustrated in Figure

Laminated beam with a large-scale motion.

Let

Deformation of the

The laying angles are denoted as

Laying angles of the

The transformation relations between Euler parameters and Euler angles can be written as

We introduce a

Substituting (

Using the finite element discretization method, the laminated composite beam can be divided into

Element division of a laminated composite beam.

The node displacement vector

A simple way to obtain the derivatives of the director field is to use interpolation. So, being

The parameters of

The node deformation displacement vector

We introduce a

Then, the displacement vector of any point in

The coupled shape function matrix

According to the deformation displacement of point

Using the displacement-strain relations of (

We introduce the stress

Then, (

The coupling dynamics equations of a laminated composite beam undergoing a large-scale motion can be obtained by using the Hamilton variational principle. The Hamilton variational principle can be given by [

The kinetic energy of the laminated composite beam undergoing a large-scale motion can be written as

According to (

Substituting (

The potential energy of the laminated composite beam undergoing a large-scale motion can be written as

Further, we introduce a

Then, substituting (

The virtual work

Let the external force

Given the generalized inertial force

Substituting (

Substituting (

In this section, numerical simulations of a laminated composite beam rotating around the fixed axis are conducted as shown in Figure

A spacecraft body with a laminated beam rotating around a fixed axis.

The numerical examples can be governed and verified by a generally large-scale motion. The equation of angular displacement curve can be defined by

Boron/aluminum composite materials are used in both the orthogonal-symmetric laminated beam

Material characteristic of boron/aluminum composite [

Parameters | Value | Note |
---|---|---|

215.3 | Modulus of elasticity along fiber direction 1 | |

144.1 | Modulus of elasticity perpendicular to fiber direction 2 | |

144.1 | Modulus of elasticity perpendicular to fiber direction 3 | |

54.39 | Shear modulus along fiber directions 1 and 2 | |

54.39 | Shear modulus along fiber directions 2 and 3 | |

45.92 | Shear modulus along fiber directions 1 and 3 | |

0.195 | Poisson’s ratio along directions 1 and 2 | |

0.255 | Poisson’s ratio along directions 2 and 3 | |

0.255 | Poisson’s ratio along directions 1 and 3 |

The initial parameters are the following: the displacement and velocity of the spacecraft body is zero, namely,

To reveal the dynamics characteristics of the spacecraft beam with a large-scale motion as shown in Figure

Transversal deformation of point

Longitudinal deformation of point

The angular deformation velocity and acceleration curves of point

Angular deformation velocity of point

Angular deformation acceleration of point

Furthermore, we study the influences of different laying layers of laminated structure on the system dynamics characteristics. The structural dimensions and material parameters of the beam are defined by Figure

Figures

Transversal deformation of point

Longitudinal deformation of point

Figures

Angular deformation velocity of point

Angular deformation acceleration of point

The transverse and longitudinal deformation of point

Transverse deformation of point

Longitudinal deformation of point

Through the above analysis, the dynamics characteristics of the rectangle beam considering laminated composite material structures and simplification of isotropic material (singular material) from the conventional equivalence have been verified preliminarily by using numerical methods. And, the complete expressions of the coupling stiffness matrix and the nonlinear elastic force are considered in the dynamic modeling of the spacecraft system. The results show that the laminated structure has significant influences on the exact calculation of the dynamic model. This also reveals the importance and correctness of considering laminated composite structures. Meanwhile, the influence of the laminated composite beam with various lamination parameters on the system dynamic behavior is further carefully considered in this section. The results also show that the number of layers and the laying angles have more significant influences on system dynamics properties.

When the spacecraft with laminated beam appendages undergoes large-scale motions, such as attitude adjustment and orbital maneuver, the elastic deformation of laminated composite appendages can be induced, which can influence the dynamics properties of the spacecraft system. From these reasons, the rigid-flexible coupling dynamic model for a spacecraft body with laminated composite beam-shape appendages have been presented in this paper by considering constitutive relationships of anisotropic laminated structures. Accordingly, the important influences of the coupling stiffness matrix and the nonlinear elastic force are considered in this model. Furthermore, the numerical simulations of laminated composite beams with a large rotation motion are conducted by considering the influences of the laminated structures and equivalent laminated beams of a singular material, different laying angles, and layers on the dynamics properties of the spacecraft system. The numerical results indicate that characteristics of material properties, the number of layers, and laying angles cannot be ignored for the dynamic analysis of large-scale rigid-flexible multibody systems with laminated composite structures.

The authors declare that they have no conflicts of interest.

This material is based on Projects 51575126 and 51675118 supported by the National Natural Science Foundation of China and Project 2015T80358 supported by the China Postdoctoral Science Foundation.