Passive targeted energy transfers and strong modal interactions in the dynamics of a thin plate with strongly nonlinear attachments

We study Targeted Energy Transfers (TETs) and nonlinear modal interactions attachments occurring in the dynamics of a thin cantilever plate on an elastic foundation with strongly nonlinear lightweight attachments of different configurations in a more complicated system towards industrial applications. We examine two types of shock excitations that excite a subset of plate modes, and systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena occurring between the plate and the attachments. The following attachment configurations are considered: (i) a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) attachment – termed nonlinear energy sink (NES); (ii) a set of two SDOF NESs attached at different points of the plate; and (iii) a single multi-degree-of-freedom (MDOF) NES with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and locations of the NESs, in order to optimize passive TETs from the plate modes to the attachments, and we showed that the optimal position for the NES attachments are at the antinodes of the linear modes of the plate. The parametric study of the damping coefficient of the SDOF NES showed that TETs decreasing with lower values of the coefficient and moreover we showed that the threshold of maximum energy level of the system with strong TETs occured in discrete models is by far beyond the limits of the engineering design of the continua. We examine in detail the underlying dynamical mechanisms influencing TETs by means of Empirical Mode Decomposition (EMD) in combination with Wavelet Transforms. This integrated approach enables us to systematically study the strong modal interactions occurring between the essentially nonlinear NESs and different plate modes, and to detect the dominant resonance captures between the plate modes and the NESs that cause the observed TETs. Moreover, we perform comparative studies of the performance of different types of NESs and of the linear Tuned-Mass-Dampers (TMDs) attached to the plate instead of the NESs. Finally, the efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed

Passive targeted energy transfers and strong modal interactions in the dynamics of a thin plate with strongly nonlinear attachments

We study Targeted Energy Transfers (TETs) and nonlinear modal interactions attachments occurring in the dynamics of a thin cantilever plate on an elastic foundation with strongly nonlinear lightweight attachments of different configurations in a more complicated system towards industrial applications. We examine two types of shock excitations that excite a subset of plate modes, and systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena occurring between the plate and the attachments. The following attachment configurations are considered: (i) a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) attachment – termed nonlinear energy sink (NES); (ii) a set of two SDOF NESs attached at different points of the plate; and (iii) a single multi-degree-of-freedom (MDOF) NES with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and locations of the NESs, in order to optimize passive TETs from the plate modes to the attachments, and we showed that the optimal position for the NES attachments are at the antinodes of the linear modes of the plate. The parametric study of the damping coefficient of the SDOF NES showed that TETs decreasing with lower values of the coefficient and moreover we showed that the threshold of maximum energy level of the system with strong TETs occured in discrete models is by far beyond the limits of the engineering design of the continua. We examine in detail the underlying dynamical mechanisms influencing TETs by means of Empirical Mode Decomposition (EMD) in combination with Wavelet Transforms. This integrated approach enables us to systematically study the strong modal interactions occurring between the essentially nonlinear NESs and different plate modes, and to detect the dominant resonance captures between the plate modes and the NESs that cause the observed TETs. Moreover, we perform comparative studies of the performance of different types of NESs and of the linear Tuned-Mass-Dampers (TMDs) attached to the plate instead of the NESs. Finally, the efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed

Robust and Adaptive Nonlinear Control of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators

Limit cycle oscillations (LCO), also known as utter, cause significant challenges in fight control of unmanned aerial vehicles (UAVs), and could potentially lead to structural damage and catastrophic failures. LCO can be described as vibrational motions in the pitching and plunging displacements of an aircraft wing. Even in low Reynolds number (low-Re) fight regimes, LCO can exceed the limiting boundary for safe UAV fight. Further, as practical considerations motivate the design of smaller, lighter weight UAVs, there is a growing need for UAV systems that do not require heavy mechanical actuators (e.g., ailerons). To address this, the use of synthetic jet actuators (SJAs) in UAV fight control systems is becoming popular as a practical alternative to mechanical deflection surfaces. SJAs are promising tools for LCO suppression systems in small UAVs due to their small size, ease of operation, and low cost. Uncertainties inherent in the dynamics of SJAs present significant challenges in SJA-based control design. Specifically, the input-output characteristic of SJAs is nonlinear and contains parametric uncertainty. Further control design challenges exist in situations where multiple actuators lose effectiveness. In the event of loss of effectiveness in multiple actuators, control challenges arise due to the fact that the resulting system contains fewer actuators than degrees of freedom (DOF) to be controlled (i.e., an underactuated system). Still further difficulties exist in control design for dual parallel underatuated systems, where standard backstepping-based control approaches cannot be applied. In this thesis, three nonlinear SJA-based control methods are presented, which are capable of complete (i.e., asymptotic) suppression of LCO in UAV systems containing uncertainty. An adaptive control method is presented first, which is shown to achieve asymptotic regulation of LCO for UAVs in the presence of model uncertainty and unmodelled external disturbances. Motivated by the desire to reduce the computational complexity of the closed-loop system, a structurally simplistic robust (single feedback loop) control design is presented next, which is shown to achieve asymptotic LCO regulation without the need for adaptive parameter estimation. Finally, to address the control challenges encountered in the event of actuator faults, a robust control method is presented, which achieves simultaneous suppression of the pitching and plunging displacements using only a single scalar control input. The control design presented for this underactuated scenario is also proven to completely compensate for the inherent SJA nonlinearity. Rigorous Lyapunov-based stability analyses are provided to prove the theoretical results, and numerical simulation results are provided to complement the theoretical development