关键词: 双层梁, 分层, 受迫振动, 半光滑牛顿法, 非线性动力学

Abstract: Forced vibration analysis of delaminated bilayer beams considering interface contact is conducted based on the semi-smooth Newton method. Beam elements with only translational degrees of freedom are employed to model the upper and lower sub-beams. The contact complementarity conditions at the delamination interface are transformed into non-smooth equations using the Fischer-Burmeister complementarity function. By incorporating a generalized Jacobian matrix formulation and an adaptive regularization strategy, the Newmark-β time-domain stepwise integration method is utilized for the solution, enabling robust capture of the dynamic opening and closing states of the delamination interface. To validate the effectiveness and accuracy of the model, a delaminated bilayer beam with both ends clamped is taken as an example. The results indicate that, even with a relatively small number of elements, the natural frequencies and time-displacement curves obtained are in good agreement with the finite element solutions from ANSYS. Even without considering geometric nonlinear factors, changes in contact conditions can still induce complex nonlinear dynamic behaviors in bilayer beams with delamination. As the excitation frequency varies, the system may undergo nonlinear dynamic behaviors such as periodic motion, period-doubling motion, and chaotic motion.

Key words: bilayer beam, delamination, forced vibration, semi-smooth Newton method, nonlinear dynamics