Multi-harmonic equivalent dynamic model of the gyroelastic repetitive truss with nonlinear joints

This work is concerned with the theoretical development of an equivalent nonlinear continuum beam element for the repetitive truss with nonlinear joints and discrete control moment gyroscopes. Firstly, using the dynamic condensation method and the multi-harmonic constitutive matrix of nonlinear joint, the hybrid beam-joint element is derived by eliminating the degree of freedom of the nonlinear joints. Then, the eccentric installation of control moment gyroscope is considered to obtain the hybrid gyroelastic beam element, where the internal degree of freedom of control moment gyroscope is eliminated. Afterward, the equivalent nonlinear continuum beam element is obtained by assembling both the hybrid beam-joint elements and hybrid gyroelastic beam elements and using the displacement equivalence method. The degree of freedom of the truss is greatly reduced. Finally, an experiment is conducted with a specially designed suspension system on the granite platform. The correctness of modeling is validated by comparing the experimental data and simulation results. The experiment shows that the rotation of truss leads to the nonlinear bending vibration when the control moment gyroscopes are installed in the transverse direction, which indicates the bending-torsional coupling effect of the equivalent nonlinear continuum beam element.