Abstract
In this chapter, an approximate analytical technique for computing the damped backbone curves resulting from the inclusion of viscous damping is presented. Traditionally, the analysis of nonlinear systems involves studying the relation between the nonlinear frequency and the resulting vibration amplitudes. One approach is to compute the conservative (undamped-unforced) backbone curves of the system and compare them to the numerically computed forced-damped frequency responses. Although this technique can have acceptable accuracy in the case of very lightly damped systems, increasing the damping reduces the matching between the conservative backbone curves and the forced-damped frequency response curves. The new method presented in this chapter is related to the previous methods of Wentzel, Kramers and Brillouin and Burton. It is combined with a normal form transformation to obtain the damped backbone curves. Two examples are shown demonstrating how it can be directly applied to single-degree-of-freedom nonlinear oscillators with polynomial nonlinear terms.
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Acknowledgement
A. Nasir is fully funded by AIZaytoonah University of Jordan to obtain his PhD at the University of Sheffield.
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Nasir, A., Sims, N., Wagg, D.J. (2022). Exploring the Dynamics of Viscously Damped Nonlinear Oscillators via Damped Backbone Curves: A Normal Form Approach. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81162-4_14
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