# Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach
## 1 Introduction  
Aerial ropeways are transportation systems which are becoming increasingly popular in recent years, not only in mountain regions with ski resorts and in sightseeing areas, but also in urban environments [1]. Two criteria can be used to classify ropeway systems, namely, the number of cables, and the operating mode. In this work, attention is focused on monocable ropeways, in which the vehicles are fixed on a single propelling cable. The cable travels continuously in a loop at a uniform speed and passes across the supporting towers, equipped with an ensemble of rollers, which facilitate a smooth cable transit across the tower where a change of slope occurs. Investigating the static and dynamic response of these multibody systems is challenging, and the literature on this topic is limited and mainly focused on the dynamic response of the vehicles under the ropeway operating condition [2; 3]. Some works [4; 5; 6] investigated the dynamic behavior of carrying hauling ropes, dealing with the study of the effects of moving loads in an existing ropeway system, while [7] investigated the nonlinear coupling between the motion of the hauling cable and the swaying dynamics of the cabins in bi-cable circulating gondola ropeway systems. They show that these systems depend on the track inclination. A recent work [8] presented a computational approach for determining the initial tension of the carrying cable of a bi-cable ropeway under an in-service moving load, and to investigate the influence of nonlinear effects on the displacement state and axial forces. Furthermore, a theoretical model that solves the minimization of aerial ropeway vehicle oscillations, induced as the vehicle passes over a support, was proposed in [9], and then experimentally validated by the same authors in [10]. On the other hand, little attention was paid to the study of the local dynamic interactions taking place between the vehicle, the cable, the roller battery, and the supportingtower; few works have investigated these aspects [11]. A nonlinear model of compression roller batteries, used as a starting point for the studies proposed in the present work, was first developed in [12; 13]. In such works, experimental tests were also carried out on an operating ropeway, so as to identify the modal characteristics of the system by adopting the Enhanced Frequency Domain Decomposition method, and to validate the analytical model by comparing the experimental dynamic responses with the numerical simulations. The model was further extended in [14; 15] to include a passive vibration control system made by a group of linear or hysteretic vibration absorbers to mitigate the accelerations of roller batteries in cableways caused by vehicle transit. To the best of the author's knowledge, there are no publications dealing with the characterization of the nonlinear dynamic behavior of the ropeways roller batteries or aimed at investigating their dynamic response to periodic excitations. The present work aims at filling the lack of knowledge regarding the characterization of the nonlinear dynamic features of roller battery systems and to investigate the effects of the periodic excitations induced by the moving cable that may give rise to resonance phenomena and nonlinear modal interactions. These phenomena were studied in the past in different mechanical systems, such as cranes [16; 17; 18; 19], tethering [20], pendulum systems [21; 22], piezoelectric beams [23; 24], and plates [25; 26], or, more generally, in slender structures possessing strong geometric nonlinearities [27; 28; 29]. Such nonlinearities can affect the dynamic response of highly deformable structural elements and can be suitably exploited for practical applications, as it was largely demonstrated in the literature [30; 31; 32; 33]. Within this context, the asymptotic approach proved to be a suitable method to investigate the dynamics of nonlinear mechanical systems.