Thermal radiation analysis for small satellites with single-node model using techniques of equivalent linearization

Abstract In this paper, the method of equivalent linearization is extended to the thermal analysis of satellite using both conventional and dual criteria of linearization. These criteria are applied to a differential nonlinear equation of single-node model of the heat transfer of a small satellite in the Low Earth Orbit. A system of nonlinear algebraic equations for linearization coefficients is obtained in the closed form and then solved by the iteration method. The temperature evolution, average values and amplitudes versus the heat capacity obtained by various approaches including Runge–Kutta algorithm, conventional and dual criteria of equivalent linearization, and Grande's approach are compared together. Numerical results reveal that temperature responses obtained from the method of linearization and Grande's approach are quite close to those obtained from the Runge–Kutta method. The dual criterion yields smaller errors than those of the remaining methods when the nonlinearity of the system increases, namely, when the heat capacity varies in the range [1.0, 3.0] × 10 4  J K −1 .

[1]  Stephen H. Crandall.  A half-century of stochastic equivalent linearization , 2006 .

[2]  P. Spanos,et al.  Random vibration and statistical linearization , 1990 .

[3]  Jinfang Wang,et al.  Numerical Methods for Nonlinear Estimating Equations , 2003 .

[4]  Thomas K. Caughey,et al.  Response of Van Der Pol's oscillator to random excitation , 1959 .

[5]  I. Pérez-Grande,et al.  Analytical study of the thermal behaviour and stability of a small satellite , 2009 .

[6]  An improved criterion of Gaussian equivalent linearization for analysis of non-linear stochastic systems , 2003 .

[7]  Adrian Tatnall,et al.  Spacecraft system engineering , 2011 .

[8]  Y. Oshima,et al.  An Analytical Approach to the Thermal Design of Spacecrafts , 1968 .

[9]  Linearized techniques for solving the inverse problem in the satellite thermal control 1 1 Paper IAF , 1998 .

[10]  John P. W. Stark,et al.  Spacecraft systems engineering , 1995 .

[11]  T. Caughey.  Equivalent Linearization Techniques , 1962 .

[12]  Jose Gaite,et al.  Linear approach to the orbiting spacecraft thermal problem , 2012, ArXiv.

[13]  Jih-Run Tsai,et al.  Overview of satellite thermal analytical model , 2004 .

[14]  José Gaite,et al.  Nonlinear analysis of spacecraft thermal models , 2010, 1010.4707.

[15]  A dual criterion of equivalent linearization method for nonlinear systems subjected to random excitation , 2012 .

[16]  Jr. R. Booton.  The Measurement and Representation of Nonlinear Systems , 1954 .

[17]  Isabel Pérez-Grande,et al.  Nonlinear analysis of a simple model of temperature evolution in a satellite , 2007, 0707.3399.

[18]  N. D. Anh,et al.  A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation , 2012 .

[19]  P. Spanos,et al.  Stochastic Linearization in Structural Dynamics , 1988 .