The nonlinear characteristic of vibration control systems has attracted increasing attention for its advantage in improving structural performance. In this paper, a new type of viscoelastic damping limb-like-structure (VE-LLS) device is proposed by combing the viscoelastic (VE) damper and limb-like-structure (LLS) together, which possesses coupling nonlinearity characteristic caused by geometric and material factors, as well as a remarkable advantage in improving the control performance. First, to explore the nonlinear geometrical effects on the static stiffness of the VE-LLS device, a formula is derived from static stiffness, and the results are discussed. Second, dynamic analysis is performed of the proposed device considering the coupling geometrical and material nonlinearities in frequency domain, with the real-time effect of frequency and temperature on the mechanical properties of the viscoelastic damper considered in solving the nonlinear vibration equation. The harmonic balance method (HBM) is used to solve the nonlinear dynamic equation. Then, the displacement transmissibility of the VE-LLS device is calculated and assessed. The results indicate that the proposed device possesses excellent vibration isolation performance, and the geometric parameters of the viscoelastic damper have significant nonlinear effect on the performance. Finally, an experiment is carried out of the VE-LLS device to verify the accuracy of the static stiffness analysis. The results show that the theoretical results agree well the experimental ones, and that the theoretical results have high accuracy and reliability.
A new stability result for a thermoelastic Bresse system with viscoelastic damping