Nonlinear Dynamics Of Rigid-Flexible Coupled Structures Composed Of One Dimensional Continum

This dissertation studies the nonlinear dynamics of the large space antenna structures based on the simplied dynamic models.The main contents of the dissertation are as follows:(1)For a simplied space antenna structure,the numerical simulttions show that the model with the first cantilever beam mode in the floating frame is accurate enough to describe the dynamic characteristics of the space antenna in small deformation.(2)Two simplified rigid-flexible models,L-and T-shaped beams,are presented respectively,with the consideration of the coupling between the rigid arm and the deformation of flexible beam.The method of multiple scales in matrix form is developed for the rigid-flexible system,in which the interaction of two modes is considered.The analytical solutions of the nonlinear vibration of the antenna system are obtained via the method of multiple scales.Further,the primary resonance response of the T-shaped model with four DOFs is investigated.The influence of the system parameters such as the excitation frequency on the frequency-amplitude response is analyzed.(3)The internal resonances of the systems with two,three and four DOFs are analyzed,respectively.The resonance conditions for 2:1 and 3:1 internal resonances are determined in terms of the structure parameters such as the length ration of arms and the stiffness of the torsional spring.The method of multiple scales is used to obtain the alytical solution of the antenna system under 2:1 or 3:1 internal resonance.Moreover,the frequency-amplitude equations are obtained and their bifurcation and stabilities are analyzed.(4)According to the theory of singularity,the universal unfolding for the frequency-amplitude equation of the rigid-flexible system is given,and the unfolding parameters are obtained.The transition sets and bifurcation diagrams for different unfolding parameters regions are discussed,which can establish the relationship between the unfolding parameters and the system parameters.(5)A ground-based experimental scheme is proposed to verify the nonlinear response of the space antenna system.At first,the experimental structures are established according to the equivalence principle between the rotation of the free tip of a cantilever beam under an external moment and the rotation of the torsional spring.Then,the equivalent stiffness of the torsional spring is regulated to meet the requirement of the internal resonance by adjusting the length of the cantilever beam.The steady-state vibration responses of the beam are measured by using the laser displacement sensor.The experimental results verify the analytical analysis and indicate that the experiment scheme is feasible.