Dynamical analysis of a time-varying length rope-driven system with boundary displacement excitation based on time-varying length finite element method

This paper developed a finite element method for the time-varying length rope-driven system under the Eulerian description since the transient responses of the time-varying length rope-driven system induced by boundary displacement excitation cannot be considered accurately in the prior work. The displacement excitation can be considered directly by substituting the boundary conditions after preprocessing that matches the subsequent time discrete method-Newmark-Beta method in this paper-into the numerical calculation. Meanwhile, the treatment of the mixed boundary conditions with a concentrated mass is introduced under the Eulerian description. The proposed method is validated by a basic model with an analytical solution and compared with the Galerkin method and by a sophisticated model derived from an actual elevator from the perspectives of complex mode analysis and linear-nonlinear time domain calculation, respectively. The results show that the proposed method can effectively deal with complex boundary conditions and accurately capture the transient wave response caused by displacement boundary excitation. Compared with the Galerkin method, whose accuracy depends on the forms and orders of the selected trial functions, the proposed method has better adaptability and accuracy in dynamical analysis of a time-varying length rope-driven system.