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

Optimal control of ankle joint moment: Toward unsupported standing in paraplegia

This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set (PDS), is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.Comment: 1 Figures, 6 page

New results in feedback control of unsupported standing in paraplegia

The aim of this study was to implement a new approach to feedback control of unsupported standing and to evaluate it in tests with an intact and a paraplegic subject. In our setup, all joints above the ankles are braced and stabilizing torque at the ankle is generated by electrical stimulation of the plantarflexor muscles. A previous study showed that short periods of unsupported standing with a paraplegic subject could be achieved. In order to improve consistency and reliability and to prolong the duration of standing, we have implemented several modifications to the control strategy. These include a simplified control structure and a different controller design method. While the reliability of standing is mainly limited by the muscle characteristics such as reduced strength and progressive fatigue, the results presented here show that the new strategy allows much longer periods (up to several minutes) of unsupported standing in paraplegia

Design of a vibration isolation system for a cycle ergometer to be used onboard the Space Shuttle

Low frequency vibrations generated during exercise using the cycle ergometer onboard the Space Shuttle are disrupting sensitive microgravity experiments. The design team is asked by NASA/USRA to generate alternatives for the design of a vibration isolation system for the cycle ergometer. It is the design team's objective to present alternative designs and a problem solution for a vibration isolation system for an exercise cycle ergometer to be used onboard the Space Shuttle. In the development of alternative designs, the design team emphasizes passive systems as opposed to active control systems. This decision is made because the team feels that passive systems are less complex than active control systems, external energy sources are not required, and mass is reduced due to the lack of machinery such as servomotors or compressors typical of active control systems. Eleven alternative designs are developed by the design team. From these alternatives, three active control systems are included to compare the benefits of active and passive systems. Also included in the alternatives is an isolation system designed by an independent engineer that was acquired late in the project. The eight alternatives using passive isolation systems are narrowed down by selection criteria to four considered to be the most promising by the design team. A feasibility analysis is performed on these four passive isolation systems. Based on the feasibility analysis, a final design solution is chosen and further developed. From the development of the design, the design team has concluded that passive systems are not effective at isolating vibrations for the low frequencies considered for this project. Recommendations are made for guidelines of passive isolation design and application of such systems

On the modelling of spur and helical gear dynamic behaviour

This chapter is aimed at introducing the fundamentals of spur and helical gear dynamics. Using three-dimensional lumped models and a thin-slice approach for mesh elasticity, the general equations of motion for single-stage spur or helical gears are presented. Some particular cases including the classic one degree-of-freedom model are examined in order to introduce and illustrate the basic phenomena. The interest of the concept of transmission errors is analysed and a number of practical considerations are deduced. Emphasis is deliberately placed on analytical results which, although approximate, allow a clearer understanding of gear dynamics than that provided by extensive numerical simulations. Some extensions towards continuous models are presented

Noise and vibration from building-mounted micro wind turbines Part 2: Results of measurements and analysis

Description To research the quantification of vibration from a micro turbine, and to develop a method of prediction of vibration and structure borne noise in a wide variety of installations in the UK. Objective The objectives of the study are as follows: 1) Develop a methodology to quantify the amount of source vibration from a building mounted micro wind turbine installation, and to predict the level of vibration and structure-borne noise impact within such buildings in the UK. 2) Test and validate the hypothesis on a statically robust sample size 3) Report the developed methodology in a form suitable for widespread adoption by industry and regulators, and report back on the suitability of the method on which to base policy decisions for a future inclusion for building mounted turbines in the GPDO