RESEARCH ARTICLE A. GESUALDO, A. IANNUZZO, F. PENTA, M. MONACO Nonlinear dynamics of a wind turbine tower © Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract The recent proliferation of wind turbines has revealed problems in their vulnerability under different site conditions, as evidenced by recent collapses of wind towers after severe actions. Analyses of structures subjected to variable actions can be conducted through several methods with different accuracy levels. Nonlinear dynamics is the most reliable among such methods. This study develops a numerical procedure to obtain approx- imate solutions for rigid-plastic responses of structures subjected to base harmonic pulses. The procedure’s model is applied to a wind turbine tower subjected to inertial forces generated by harmonic ground acceleration, and failure is assumed to depend on the formation of shear hinges. The proposed approach provides an efficient representation of the post-elastic behavior of the structure, has a low computational cost and high effectiveness, and uses a limited number of mechanical parameters. Keywords nonlinear dynamics, plastic shear failure, modal approximation, time history 1 Introduction The need for sustainable energy production has led to several innovative technological solutions. A new genera- tion of windmills has emerged from these solutions. Aeolian parks, which are sets of modern wind turbines, are crucial in clear energy production [1]. Several of these parks have been built in seismic areas, and many have been established in Irpinia, a region in Southern Italy that was devastated by a strong earthquake in 1980. Nonlinear dynamics is a reliable tool to examine the effects of earthquakes on these structures. A high level of expertise, high costs, and large amounts of calculation time are required to model the steel towers of these modern windmills [2]. Constitutive and structural models with sufficient accuracy and low numerical complexity are generally adopted when elastic responses can be dis- regarded and micromechanical behavior involves complex experimental tests [3]. Rigid-plastic approximations, which are extensively utilized in earthquake engineering, produce simplified procedures [4,5]. The implementation of rigid-plastic models is limited to conventional stiffness- based computer methods because these models consider the instantaneous jump of stiffness between zero and infinity. The model presented in the following sections and those developed for rigid-plastic bending frames overcome this limitation. Several constitutive models have been presented for rigid-plastic bending frames in the last 50 years, whereas shear constitutive ones are scarce. Despite the limited use of these procedures in dynamic problems, they exhibit low computational complexity and reduced number of mechanical parameters (i.e., yield character- istics) [6,7]. These advantages are the starting point of the present study because simple relationships between structure strength and parameters that are useful for design purposes can be established [8]. Many studies have examined the dynamic plastic bending responses of structural elements in steel and reinforced-concrete structures. Bending hinges represent the general response characteristics of several structural elements under trans- verse loads [9,10]. A few studies have performed dynamic analyses of plastic shear failure. An important issue in bending and shear problems is related to the localization and extension of plastic hinges [11,12]. A closed solution of the problem has been developed with classical tools of numerical analysis, such as linear complementarity [13,14]. Moreover, different approaches that involve vector-form intrinsic finite elements have recently been implemented; in these approaches, the definition of the Received January 19, 2018; accepted July 1, 2018 A. GESUALDO, A. IANNUZZO Department of Structures for Engineering and Architecture, University of Naples “Federico II”, 80125 Naples, Italy F. PENTA Department of Industrial Engineering, University of Naples “Federico II”, 80125 Naples, Italy M. MONACO (✉) Department of Architecture and Industrial Design, University of Campania “Luigi Vanvitelli”, 81031 Aversa (Ce), Italy E-mail: michela.monaco@unicampania.it Front. Mech. Eng. https://doi.org/10.1007/s11465-019-0524-3