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This paper presents a vertical vibration model for 2:1-roping traction elevator system. In this model, masses of suspension ropes are considered and their kinetic energy is calculated by applying Rayleigh method. Equations of motion for free vibration are derived. To verify the improvement of the model, an output dependent only modal test scheme using eigenvalue realization algorithm is conducted to obtain natural frequencies from a real elevator installation. The comparison of experimental results and numerical results of proposed model and previous similar models is presented on calculation of natural frequencies. The results show that proposed model is able to reflect the 5th natural frequencies more exactly under 0 % and 100 % load conditions.

Particle damping is a kind of passive and strongly nonlinear damping for energy dissipation. Many researchers have expended huge amounts of effort and time to study internal mechanism of particle damping. However, there is not a systematic and feasible approach for estimating damping performance of non-obstructive particle damping (NOPD). In this paper, we performed studies to mathematically evaluate the damping effect of particle damping based on principles of gas-solid flows. In consideration of the structural characteristics of NOPD which granular materials should be filled into sealed cavity of vibrating structure and the damping act on lateral and bottom of holes in NOPD technology, the gross damping is divided into lateral damping and bottom damping by Janson's theory of stress change direction. And the damping coefficients are compiled into a plug-in by MATLAB and are invoked in FEM software by enterprise integration kits of COMSOL. Meanwhile the frequency domain and time domain analysis of the experiment are used to verify the prediction accuracy of dynamic vibration response of an aluminium cantilever beam which ONPD is imposed at the free end with different packing rate and granular material, the result indicate that the mathematical model has excellent performance to predict the dynamic vibration response of NOPD. Then, the relationship damping effect with the particle filling ratio, particle density and length-diameter ratio of the hole is also researched using co-simulation, it should be noted that larger packing rate and particle density, smaller length-diameter ratio of the hole can play excellent damping effects in NOPD.