Inverse design of nonlinearity in energy harvesters for optimum damping

This paper presents the inverse design method for the nonlinearity in an energy harvester in order to achieve an optimum damping. A single degree-of-freedom electro-mechanical oscillator is considered as an energy harvester, which is subjected to a harmonic base excitation. The harvester has a limited throw due to the physical constraint of the device, which means that the amplitude of the relative displacement between the mass of the harvester and the base cannot exceed a threshold when the device is driven at resonance and beyond a particular amplitude. This physical constraint requires the damping of the harvester to be adjusted for different excitation amplitudes, such that the relative displacement is controlled and maintained below the limit. For example, the damping can be increased to reduce the amplitude of the relative displacement. For high excitation amplitudes, the optimum damping is, therefore, dependent on the amplitude of the base excitation, and can be synthesised by a nonlinear function. In this paper, a nonlinear function in the form of a bilinear is considered to represent the damping model of the device. A numerical optimisation using Matlab is carried out to fit a curve to the amplitude-dependent damping in order to determine the optimum bilinear model. The nonlinear damping is then used in the time-domain simulations and the relative displacement and the average harvested power are obtained. It is demonstrated that the proposed nonlinear damping can maintain the relative displacement of the harvester at its maximum level for a wide range of excitation, therefore providing the optimum condition for power harvesting

Impulsive parametric damping in energy harvesting

In this paper, an electro-mechanical system with a time-varying damper, which is capable of changing the damping coefficient impulsively, is considered. The effect of the impulsive parametric damping to the modal energy content of the mechanical system is investigated analytically as well as numerically. First, the governing differential equation is presented and then the solution of the system’s response is obtained through numerical integration. The energy dissipated by the damper is then calculated to investigate the amount of the energy that can be harvested, and the results are compared with the results from a system without parametric impulses. It is shown, that the amount of the harvested energy can be increased by introducing parametric impulses. Then, an analytical formulation is derived for the system using Dirac-Delta impulses and the analytical results are validated with numerical simulations. The device is subjected to an initial condition and therefore is vibrating freely without any base excitation. This could be used for applications such as harvesting energy from the passage of a train, where the train vibration can introduce an initial velocity to the harvester and the energy can then be extracted from the free vibration of the harvester

Adaptive feedforward control design for gust loads alleviation and LCO suppression

An adaptive feedforward controller is designed for gust loads alleviation and limit cycle oscillations suppression. Two sets of basis functions, based on the finite impulse response and modified finite impulse response approaches, are investigated to design the controller for gust loads alleviation. Limit cycle oscillations suppression is shown by using the modified finite impulse response controller. Worst case gust search is performed by using a nonlinear technique of model reduction to speed up the costs of calculations. Both the “one–minus–cosine” and Von Kármán continuous turbulence gusts of different intensities were generated to examine the performance of controllers. The responses of these two types of gust can be reduced effectively by finite impulse response controller in the whole process, while the modified finite impulse response controller is found to increase the loads during the initial transient response. The above two types of gust induced limit cycle oscillations were used to test the modified finite impulse response controller. Results show that it can suppress limit cycle oscillations to some exten

Adaptive feedforward control design for gust loads alleviation and LCO suppression

An adaptive feedforward controller is designed for gust loads alleviation and limit cycle oscillations suppression. Two sets of basis functions, based on the finite impulse response and modified finite impulse response approaches, are investigated to design the controller for gust loads alleviation. Limit cycle oscillations suppression is shown by using the modified finite impulse response controller. Worst case gust search is performed by using a nonlinear technique of model reduction to speed up the costs of calculations. Both the “one–minus–cosine” and Von Kármán continuous turbulence gusts of different intensities were generated to examine the performance of controllers. The responses of these two types of gust can be reduced effectively by finite impulse response controller in the whole process, while the modified finite impulse response controller is found to increase the loads during the initial transient response. The above two types of gust induced limit cycle oscillations were used to test the modified finite impulse response controller. Results show that it can suppress limit cycle oscillations to some exten

Dynamic response of a nonlinear parametrically excited system subject to harmonic base excitation

A Nonlinear Parametrically Excited (NPE) system subjected to a harmonic base excitation is presented. Parametric amplification, which is the process of amplifying the system’s response with a parametric excitation, has been observed in mechanical and electrical systems. This paper includes an introduction to the equation of motion of interest, a brief analysis of the equations nonlinear response, and numerical results. The present work describes the effect of cubic stiffness nonlinearity, cubic parametric nonlinearity, and the relative phase between the base excitation and parametric excitation under parametric amplification. The nonlinearities investigated in this paper are generated by an electromagnetic system. These nonlinearities were found both experimentally and analytically in previous work [1]; however, their effect on a base excited NPE is demonstrated in the scope of this paper. This work has application in parametric amplification for systems, which are affected by strong stiffness nonlinearities and excited by harmonic motion. A careful selection of system parameters, such as relative phase and cubic parametric nonlinearity can result in significant parametric amplification, and prevent the jump from upper stable solutions to the lower stable solutions

An optimum design of a double pendulum in autoparametric resonance for energy harvesting applications

In this paper energy harvesting from vibrating surfaces through electromagnetic induction is addressed. A double pendulum subject to base excitations generates electrical energy through energy harvesting coils mounted on the pendulum masses. Optimum double pendulum generates energy at a rate of 9 mW for excitation parameters characteristic of bridge vibration, frequency of 2 Hz and amplitude of 1 mm

Electromechanical pendulum for vibration control and energy harvesting

This paper presents the design of an experimental electromechanical device for vibration control and energy harvesting. Traditionally, when the broadband resonant response due to a selected mode of a lightly damped structure needs to be controlled a vibration absorber is used. The resonance frequency of the absorber can be chosen to minimise the response of the structure under control. Optimising the damping ratio to achieve this aim also dissipates the most power in the damper, but care must be taken not to exceed the maximum throw of the device at high excitation levels. The absorber may also be mistuned by changes in operation condition and thus underperform. It is thus important to be able to design tuneable vibration absorbers, able to adapt their resonance frequency and their damping ratio depending on the operation condition.In this paper an electromechanical device consisting of a pendulum connected to an electrical motor is proposed. It is shown that by shunting the terminal of the device with an appropriate electrical circuit it is possible to control both its resonance frequency and its damping ratio. The power dissipated in the resistive part of the shunt circuit could also be harvested and used to implement the tuning mechanism, or for other purposes