Tunable nonlinear modal bandwidth and time-bandwidth product for MDOF nonlinear systems

Bandwidth is a key quantity that characterizes the energy dissipation capability of damped dynamical systems. Understanding the system’s bandwidth and breaking the time-bandwidth (T-B) product limit is useful for developing new devices and applications for vibration isolation/absorption and energy harvesting. While they are well-defined for linear systems based on normal modes and have recently been extended to single-degree-of-freedom (SDOF) nonlinear systems, their extensions to multi-DOF (MDOF) nonlinear systems remain a critical challenge because there exists no such a general framework as modal transformation for nonlinear MDOF systems due to their inherent modal coupling and nonlinear interactions. In this study, we present a new unified framework for the definition of nonlinear modal bandwidth on the generalization of spectral submanifolds (SSMs) of MDOF nonlinear systems, allowing characterizing nonlinear modal dissipative capability of each generalized nonlinear modes of MDOF nonlinear systems. On this basis, numerical experiments for principle explanation about nonlinear modal bandwidth and T-B product properties on different single-mode SSMs of MDOF nonlinear systems are conducted. It is found that both the nonlinear modal bandwidth and T-B product properties on single-mode SSMs of MDOF nonlinear stiffness and damping systems exhibit strong tunable characteristics with systematic dependence on input energy levels and specific single-mode SSMs. Particularly, the introduction of additional damping in nonlinear damping system is found to lead to a significant expansion in the nonlinear modal bandwidth of nonlinear modes, with the bandwidth of low-order nonlinear mode potentially surpassing that of high-order nonlinear mode under high-energy scenarios. Finally, the limitations of this work and the required future research are discussed.