Dynamic Characteristics Analysis On The Simplified Model Of The Shape-Memory Polymer Solar Array

Permitting the large recoverable deformation subjected to an external stimulus is the unique property of the shape-memory polymer(SMP),which determines its potential application in solar array to implement the autonomous deployment of the spatial structure.The vibrations on the solar array will affect the normal operation of the satellite.Due to the particularity of the SMP,its constitutive model is complex,which makes it difficult to analyze the dynamic response of the solar array based on the SMP.To solve this problem,the dynamic response of the shapememory polymer solar array(SMPSA)is analyzed by the generalized multi-symplectic method in this thesis.Firstly,based on viscoelastic theory and Boltzmann superposition principle,the integral stress-strain relationship of the SMP is derived.Then,the SMPSA is simplified as a hubviscoelastic beam model.And the dynamic equations of the model are derived by the integral stress-strain relationship and the Hamiltonian principle.After that,the generalized multisymplectic formulations of the dynamic model are deduced.The symplectic Runge-Kutta method is employed to discrete the decomposed form of the generalized multi-symplectic formulations to construct the structure-preserving numerical scheme.At last,the shape-memory effect of the SMPSA and the dynamic response of its simplified model are simulated numerically.The validity of the constitutive relationship,which can describe the shape-memory effect of the SMPSA,is verified by the numerical result of the shape-memory effect.From the numerical results of the dynamic response,it can be found that the vibration of the SMPSA will dissipate spontaneously,which is different from the non-dissipative vibration of the traditional solar array.Besides,the relationships between the dynamic response of the SMPSA and the amplitude/frequency of the external torque are explored.When the stable angle of the SMPSA is small with certain torque conditions,little differences in the vibrational amplitude and the vibrational damping time between the two cases,changing the amplitude or frequency of the torque,are found.When the stable angle is large with certain torque conditions,the vibrational amplitude of the SMPSA obtained with a changing amplitude of the external torque is larger than that with a changing frequency.While the opposite is true for the vibrational damping time.In addition,based on the relationship between temperature and the SMP properties,the dynamic response of the SMPSA at the high temperature,the low temperature and the glass transition temperature is simulated.The numerical result shows that with the increase of the ambient temperature,both the vibrational amplitude and vibrational dissipative velocity show an increasing trend.The above conclusions give some guidance in the expansion and control of the SMPSA.