Maryam Ghandchi Tehrani

Active control of parametrically excited systems

This article discusses active control of parametrically excited systems. Parametric resonance is observed in a wide range of applications and can lead to high levels of unwanted motion. For example, in cable-stayed bridges, the vibration of the deck excites the cables axially, inducing a periodically time-varying tension. If the frequency of deck vibration is about twice the natural frequency of the cable, a parametric resonance occurs and leads to a large-amplitude swinging motion of the cable. To tackle the consequences of parametric instability, active vibration control employing a piezoelectric actuator is proposed in this article. We consider a beam subjected to an axial harmonic load that represents a parametrically excited system with a periodically varying stiffness. Using both analytical and experimental methods, we assess the stability of the beam and propose active control aimed at relocating the transition curves and hence stabilising the system via velocity feedback and pole placement. Analytical relationship between the transition curves and the poles of the system is derived. Transition curves can be assigned to a prescribed location using appropriate velocity and displacement control gains. Finally, we demonstrate the proposed approach with experiments on a beam equipped with a macro fibre composite patch.

Nonlinear damping in an energy harvesting device

Energy harvesting from ambient vibration has attracted significant attention in recent years. Some interesting applications include low-power wireless sensors, harvesting power from human motion and large-scale energy harvesters. In order to increase the frequency range of the excitation amplitude over which the vibration energy harvester operates, various nonlinear arrangements have been suggested, particularly using nonlinear springs [1-5]. In contrast, it has recently been shown that the dynamic range of a vibration energy harvester can be increased using a nonlinear damper [5]. Nonlinear damping, particularly stiction, can, however, also be an unwanted problem in practical power harvesters. However, this paper considers the effect of stiction, as Coulomb damping, on the performance of such a vibration power harvester. A mechanical single degree-of-freedom nonlinear oscillator is considered, subjected to a harmonic base excitation. The relative displacement and the average harvested power are obtained for different sinusoidal base excitation amplitudes and frequencies, both analytically and numerically. The performance of the nonlinear harvester at different excitation levels is compared with a linear harvester, which has the same maximum relative displacement at resonance when driven at maximum amplitude. It is demonstrated that the nonlinear harvester can harvest much more energy, compared to the linear one, when driven below its amplitude threshold [5]. The effect of Coulomb damping, as a source of loss, is also investigated, for the harvesters with a linear damping and a cubic damping. It is shown that the Coulomb damping can reduce the amount of the harvested energy, particularly at low excitation amplitudes.

An experimentally validated parametrically excited vibration energy harvester with time-varying stiffness

Vibration energy harvesting is the transformation of vibration energy to electrical energy. The motivation of this work is to use vibration energy harvesting to power wireless sensors that could be used in inaccessible or hostile environments to transmit information for condition health monitoring. Although considerable work has been done in the area of energy harvesting, there is still a demand for making a robust and small vibration energy harvesters from random excitations in a real environment that can produce a reliable amount of energy. Parametrically excited harvesters can have time-varying stiffness. Parametric amplification is used to tune vibration energy harvesters to maximize energy gains at system superharmonics, often at twice the first natural frequency. In this paper the parametrically excited harvester with cubic and cubic parametric nonlinearity is introduced as a novel work. The advantages of having cubic and cubic nonlinearity are explained theoretically and experimentally.

Adaptive control of tonal disturbance in mechanical systems with nonlinear damping

This paper describes an adaptive system for controlling the tonal vibration of a single-degree-of-freedom system with nonlinear damping. The adaptive control system consists of a force actuator in parallel with the suspension, which includes the nonlinear damper, and a velocity sensor mounted on the mass. The adaptation of the controller is done once every period of the excitation. Because the response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a linear model of the plant, can be slow to converge and may not achieve the desired performance. An on-line observer is used to obtain a describing function model of the plant, which can vary with the excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.

Vibration control using nonlinear damped coupling

In this paper, a dynamical system, which consists of two linear mechanical oscillators, coupled with a nonlinear damping device is considered. First, the dynamic equations are derived, then, an analytical method such as harmonic balance method, is applied to obtain the response to a harmonic base excitation. The response of the system depends on the excitation characteristics. A parametric study is carried out based on different base excitation amplitudes, frequencies, and different nonlinear damping values and the response of the system is fully described. For validation, time domain simulations are carried out to obtain the nonlinear response of the coupled system.

Phase dependent nonlinear parametrically excited systems

Nonlinear parametrically excited (NPE) systems govern the dynamics of many engineering applications, from cable-stayed bridges where vibrations need to be suppressed, to energy harvesters, transducers and acoustic amplifiers where vibrations need to be amplified. This work investigates the effect of different system parameters on the dynamics of a prototype NPE system. The NPE system in this work is a cantilever beam with an electromagnetic subsystem excited at its base. This system allows cubic stiffness, parametric stiffness, cubic parametric stiffness, and the phase difference between different sources of excitation to be varied independently to achieve different dynamic behaviors. A mathematical model is also derived, which provides theoretical understanding of the effects of these parameters and allows the analysis to be extended to other applications.

Extending the dynamic range of an energy harvester with a variable load resistance

In some energy harvesters, the maximum throw of the seismic mass is limited due to the physical constraints of the device. The shunt load resistance of such a harvester is generally selected based on the allowable throw of the mass when the device is subjected to the maximum level of excitation. However, the energy harvester with this value of shunt resistance does not perform well at lower levels of excitation. In this article, a variable load resistance, scheduled on the excitation level, is introduced to extend the dynamic range of an energy harvester in applications where excitation level varies. This method is applied to the design of an energy harvester, which comprises a sprung mass coupled to an electric motor through a lead screw. The dynamic equation and parameters of the system are introduced and the device is experimentally characterized, by conducting random vibration tests. The harvested power and the relative displacement are then obtained for different sinusoidal base excitation amplitudes when the system is excited at a frequency close to its natural frequency. It is demonstrated that the use of a variable load resistance mechanism can significantly improve the dynamic range and output power of the energy harvester.

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.

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.