Publications

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Authors: Paul Mucchielli, Ankush Gogoi, Budhaditya Hazra, Vikram Pakrashi

Abstract: This work proposes an Itō calculus-based mathematical framework for the optimal design of a nonlinear passive control arrangement. Traditional numerical methods make use of ordinary differential integration schemes to study such nonlinear systems, thereby failing to account for the stochastic nature of the input excitation. Furthermore, such integration schemes require finer time steps for accurate analysis of stochastically excited nonlinear systems, therefore, rendering these schemes to be computationally expensive. Towards this, the present work proposes a new approach employing stochastic differential calculus for the optimal design of a stochastically excited three-dimensional nonlinear pendulum tuned mass damper (PTMD) system. The proposed approach comprises of Itō-Taylor expansion-based framework for deriving the displacement mean-square response of the primary structure. Three different approaches for the determination of the mean-square response are shown. The first approach is based on numerical simulation by employing Itō-Taylor 1.5 integration scheme and the other two premises on the formulation of Itō-Taylor-based mean-square differential equations. The accurate mean-square response obtained from different approaches is then utilised for the optimal design of the PTMD system. The optimal parameters resulted in amplitude reduction of around 75 % in terms of displacement mean-square response and about 85 % at peak frequency. Further, the optimal parameters were utilised to carry out stability analysis of the nonlinear PTMD system.