This paper uses the methodology developed in Part I of this work to study the longitudinal, transverse, and their coupled vibrations of moving elevator cable-car systems. A suspension cable is a one-dimensional length-variant distributed-parameter component. When there is only one suspension cable connected to the car, the car is modeled as a point mass. When there are multiple suspension cables, the car is modeled as a rigid body, and the rotation of the car is considered. There are complicated matching conditions between the cable and car, which cannot be satisfied in the classical assumed modes method but can be satisfied in the current method. Hence, not only the longitudinal and transverse displacements but also the internal forces/moment, such as the axial force, the bending moment, and the shear force, which are related to the spatial derivatives of the longitudinal and transverse displacements, are accurately calculated. The results from different choices of boundary motions and trial functions are essentially the same, and the convergence is much faster than that of the assumed modes method. The longitudinal-transverse coupled vibrations of a moving cable-car system are also studied using the current method, and the results are compared with those from the linear models. While the result from the linear model for the transverse vibration agrees well with that from the nonlinear coupled model, the axial force from the linear model can significantly differ from that from the nonlinear model when the car approaches the top of the hoistway.

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