M. Ghandchi Tehrani

Nonlinear damping and quasi-linear modelling.

The mechanism of energy dissipation in mechanical systems is often nonlinear. Even though there may be other forms of nonlinearity in the dynamics, nonlinear damping is the dominant source of nonlinearity in a number of practical systems. The analysis of such systems is simplified by the fact that they show no jump or bifurcation behaviour, and indeed can often be well represented by an equivalent linear system, whose damping parameters depend on the form and amplitude of the excitation, in a ‘quasi-linear’ model. The diverse sources of nonlinear damping are first reviewed in this paper, before some example systems are analysed, initially for sinusoidal and then for random excitation. For simplicity, it is assumed that the system is stable and that the nonlinear damping force depends on the nth power of the velocity. For sinusoidal excitation, it is shown that the response is often also almost sinusoidal, and methods for calculating the amplitude are described based on the harmonic balance method, which is closely related to the describing function method used in control engineering. For random excitation, several methods of analysis are shown to be equivalent. In general, iterative methods need to be used to calculate the equivalent linear damper, since its value depends on the system’s response, which itself depends on the value of the equivalent linear damper. The power dissipation of the equivalent linear damper, for both sinusoidal and random cases, matches that dissipated by the nonlinear damper, providing both a firm theoretical basis for this modelling approach and clear physical insight. Finally, practical examples of nonlinear damping are discussed: in microspeakers, vibration isolation, energy harvesting and the mechanical response of the cochlea.

An Overview of the Receptance Method in Active Vibration Control

Abstract This paper describes the practical application of the receptance method for active vibration control of real structures. The method uses in general the measured transfer function between the input/output data including the dynamics of the actuators and sensors. Therefore, it does not require knowledge or evaluation of the system matrices M, C, K, which usually contain modeling errors. This would be the main advantage over conventional matrix methods. The method is developed for partial pole placement and robust pole placement. The receptance method is applied to a modular test structure, which can have different configurations, in which one of these configurations in the form of ‘an ‘H’ is presented in this paper. The vibration modes including the torsional modes were controlled using the single-input state feedback control. The method is also applied to an Agusta-Westland W30 helicopter airframe in the vibrations test house at Yeovil.

Periodic and chaotic response of a macro-scale tuning fork gyroscope

In this paper, the dynamic behaviour of a macro-scale tuning fork gyroscope is presented. The gyroscope consists of two inverted pendulums on a suspension mass. The suspension mass is subjected to force excitation generated by an electromagnetic shaker. The dynamics of the shaker are included in the analysis. It is shown that the system is a parametrically excited system. Parametric excitation can lead to vibration in the horizontal motion of the suspension mass, when the two pendulums are in phase. The problem is particularly interesting for energy harvesting. Due to the interaction between the system’s degrees of freedom, the energy is transferred from vertical (base excitation) to horizontal direction. Initial parametric studies are carried out to analyse the dynamic behaviour of the system by varying the initial conditions, base excitation frequency and amplitude. It is demonstrated that under certain parameters the system can exhibit complex dynamic behaviour such as chaotic motion.

Experimental Implementation of a Nonlinear Feedback Controller for a Stroke Limited Inertial Actuator

This research consists of theoretical and experimental studies of a stroke limited inertial, or proof mass, actuator used in active vibration control. Traditionally, inertial actuators are used with velocity feedback controllers to reduce structural vibrations. However, physical limits, such as stroke saturation, can affect the behaviour and the stability of the control system. In fact, stroke saturation results in impulse like excitations, which are transmitted to the structure that is liable to damage. Moreover, the shocks produced by the impacts are in phase with the velocity of the structure. This produces an input force, which reduces the overall damping and eventually leads to limit cycle oscillations and the instability of the system. This paper examines the experimental implementation of a nonlinear feedback controller to avoid collisions of the proof mass with the actuator’s end stops, hence preventing the instability of the system due to stroke saturation. Firstly, the nonlinear behaviour of the stroke limited inertial actuator is reported. This allows identifying the stroke length of the proof mass. Secondly, the nonlinear feedback controller is presented, which acts as a second loop alongside the velocity feedback control loop. The main purpose of the nonlinear feedback controller is to increase the damping of the actuator when the poof mass gets close to the end stops. Finally, the experimental implementation of the nonlinear controller is investigated and a comparison in terms of performance and stability of the control system is made when both the feedback loops or only the velocity feedback loop are present.

Design of an electromagnetic-transducer energy harvester

This paper presents the design and the manufacturing of an electromagnetic-transducer energy harvester. The design considers the coupling between the mechanical vibrating behaviour, generated by a base excitation, and the electromagnetic conversion of energy, which is aimed to produce the voltage across a load resistance. The design is based on some constraints, which are related to the characteristics of the shaker and aimed to obtain the best performance of the device. Current tests show the presence friction at low input levels, which is associated with the gearbox. The output voltage and the harvested power of the device are studied experimentally for different values of load. By increasing the value of the load from zero (short circuit) to high values (open circuit) the swing angle increases, while the harvested power presents a peak associated with the electrical damping. Also, harmonic tests are run at resonance for different levels of excitation to demonstrate the effect of the nonlinearity on the voltage and the harvested power. A nonlinear load resistance, is then introduced as part of future work. The aim is to try to increase the harvested power with respect to the linear load, at low level of excitation.

Dynamic analysis of nonlinear behaviour in inertial actuators

Inertial actuators are devices typically used to generate the control force on a vibrating structure. Generally, an inertial actuator comprises a proof-mass suspended in a magnetic field. The inertial force due to the moving mass is used to produce the secondary force needed to control the vibration of the primary structure. Inertial actuators can show nonlinear behaviour, such as stroke saturation when driven at high input voltages. If the input voltage is beyond their limit, they can hit the end stop of the actuator casing and saturate. In this paper, the force generated by an inertial actuator is measured experimentally and numerical simulations of a linear piecewise stiffness model are carried out and compared with the results of analytical methods. First, a numerical model for a symmetric bilinear stiffness is derived and a parametric study is carried out to investigate the change of the end stop stiffness. In addition, the variation of the amplitude of the excitation is considered and a comparison is made with the analytical solution using the harmonic balance method. Finally, experimental measurements are carried out and the results are compared with simulated data to establish the accuracy of the model.