Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

Abstract

With extending the Rayleigh-Ritz procedure to study the hub-plate system, the characteristics of global analytical modes are addressed for a typical rigid-flexible coupling dynamic system, i.e., a threeaxis attitude stabilized spacecraft installed with a pair of solar arrays. The displacement field of the solar arrays is expressed as a series of admissible functions which is a set of characteristic orthogonal polynomials generated directly by employing Gram-Schmidt process. The rigid body motion of spacecraft is represented by the product of constant and generalized coordinate. Then, through Rayleigh-Ritz procedure, the eigenvalue equation of the three-axis attitude stabilized spacecraft installed with a pair of solar arrays is derived. Solving this eigenvalue equation, the frequencies and analytical expressions of global modes for the flexible spacecraft are obtained. To validate the present analysis, comparisons between the results of the present method and ANSYS software are performed and very good agreement is achieved. The convergence studies demonstrate the high accuracy, excellent convergence and high efficiency of the present approach. Finally, the method is applied to study the characteristics of global modes of the flexible spacecraft.

Natural Characteristics Analysis for the Spacecraft Equipped with Constructed Cantilever Solar Panels

“…The comparison between this method and the finite element calculation results verifies the effectiveness of this method [13]. Liu et al conducted dynamic modeling of flexible spacecraft based on global modal method [14,15]. Chen et al modeled a general nonlinear rectangular cantilever plate considering large deflection and angle based on Hamiltonian principle.…”

“…As the dynamical model is similar to that of Ref. [14], the total kinetic energy and strain energy has the same expression. By neglecting the same process of the derivation, the expressions of the kinetic and strain energy are given as follows The transformation matrix of the coordinate system from o − xyz to o 0 − x 0 y 0 z 0 is expressed as follows…”

“…According to the concept of rigid-flexible coupled modes in Ref. [14], the rigid body motion of the spacecraft can be expressed as the product of a constant and a time term…”

“…where S o and θ (q) 0 are unknown coefficients. The solar panel vibration displacement Expression (1) and the spacecraft rigid body displacement Expression (14) are substituted into the flexible spacecraft kinetic energy Expression (10) and potential energy Expression (11). Through the Rayleigh-Ritz method, the system Rayleigh quotient with respect to the coefficients…”

Nonlinear dynamic modeling and decoupling for rigid–flexible coupled system of spacecraft with rapid maneuver

“…21 Under the concept of the GMM, Liu et al. 22 studied the hub-plates model and obtained the rigid–flexible coupled modes using the Rayleigh–Ritz method. The GMM overcomes the shortcomings of poor precision in the improper selection of the assumed modal functions, and has a lower dimension than FEM.…”