Ultrasonic Generators for Energy Harvesting Applications: Self-Excitation and Mechanical Frequency Transformation

The main objective in the field of vibration-based energy harvesting is to convert the kinetic energy from an ambient energy source into an useable electrical form in the most efficient way. The intention is to provide power for low-powered electronic devices, such as intelligent sensors for structural health monitoring, in order to make an external power source or periodic battery replacement redundant and thus lower the costs. Applications of this technology can be found in the automotive and aerospace industry as well as in civil and mechanical engineering. One of the main challenges in the area of vibration-based energy harvesting is to design an energy harvesting device generating a significant amount of electrical power across varying vibration inputs. Due to the design, most energy harvesters are subject to forced excitation and have therefore the drawback that the performance strongly depends on the uncertain excitation parameters. Furthermore, to achieve a high power density of the piezoceramics used for the energy conversion, it is required to generate a high-frequency operation of the piezoceramics from a low-frequency vibration source. Such frequency transformation is, for example, exploited in ultrasonic motors, but has never been examined in the inverse direction for ultrasonic generators. In this thesis, a new concept of piezoelectric generators is studied in detail with respect to its applicability for energy harvesting systems. To this end, electromechanical models of two different ultrasonic motors are derived in order to study their convertibility of the operating direction. Based on the analytical models, the influence of the main parameters on the dynamic behavior as well as the characteristic steady-state operation are determined. Experiments are carried out to validate this concept

Dynamics of a milkshaker - Passage through resonance and frequency transformation

Rotor dynamics is a fascinating subject both from an experimental and a theoretical point of view. Most often experiments on various phenomena require more or less sophisticated test rigs, either because the experiments are dangerous or because the effects are difficult to reproduce. In teaching it is, however, beneficial to have experiments that are simple and can be performed by the students themselves. One of these examples is a standard milkshaker, which at a closer look, exhibits rich dynamical phenomena. The first phenomenon that can be observed and studied is the passage through resonance. Depending on the eccentricity of the rotor, the driving torque of the motor is strong enough or not to reach supercritical speeds. If for a given torque the eccentricity is too large, the system gets stuck in the resonance with a rather large amplitude. A second phenomenon that can be observed is the following: When the milkshaker is placed on an even surface it starts to move on the surface. The movement is caused by a wobbling motion of the system due to the eccentricity. Although the angular velocity of the rotor is high, the motion on the surface is quite slow in comparison. This is an interesting phenomenon that can be related to mechanical frequency transformation which occurs in the contact between the milkshaker and the ground. Depending on whether the rotor is running in a supercritical range or stuck below the resonance frequency, different motions can be observed. The system can be analyzed with a relatively simple nonlinear rigid body model. In this paper we study both phenomena mentioned above from a theoretical point of view. The equations of motion are derived in analytical form and their nonlinear behavior is investigated. Due to its relatively simple nature, the system has been used in lectures as a demonstrator and for student tutorial projects

Some Recent Results on MDGKN-Systems

The linearized equations of motion of finite dimensional autonomous mechanical systems are normally written as a second order system and are of the MDGKN type, where the different n × n matrices have certain characteristic properties. These matrix properties have consequences for the underlying eigenvalue problem. Engineers have developed a good intuitive understanding of such systems, particularly for systems without gyroscopic terms (G-matrix) and circulatory terms (N-matrix, which may lead to self-excited vibrations). A number of important engineering problems in the linearized form are described by this type of equations. It has been known for a long time, that damping (D-matrix) in such systems may either stabilize or destabilize the system depending on the structure of the matrices. Here we present some new results (using a variety of methods of proof) on the influence of the damping terms, which are quite general. Starting from a number of conjectures, they were jointly developed by the authors during recent months

Analysis of an oscillatory Painlevé-Klein apparatus with a nonholonomic constraint

In dynamics, both the concepts of rigid body and Coulomb’s law of friction are well established, although it is known at least since Painlevé’s time that they may lead to irregularities and contradictions, such as loss of uniqueness or existence of the solution of the equations of motion. The problem is still of very actual interest, since it can be of practical significance also for the industrially used rigid body codes. One of the simplest mechanical systems in which these difficulties can be well described is the Painlevé–Klein apparatus. As most other systems discussed in this context in the literature, this is a holonomic system. In the present note, we briefly examine a nonholonomic oscillatory system which is an extension of the classical Painlevé–Klein apparatus and we study its dynamics with respect to the Painlevé paradox. Both the borders of paradoxical regions and their reachability are addressed

Construction of Lyapunov functions for the estimation of basins of attraction

Technical systems are often modeled through systems of differential equations in which the parameters and initial conditions are subject to uncertainties. Usually, special solutions of the differential equations like equilibrium positions and periodic orbits are of importance and frequently the corresponding equations are only set up with the intent to describe the behavior in the vicinity of a limit cycle or an equilibrium position. For the validity of the analysis it must therefore be assumed that the initial conditions lie indeed in the basins of attraction of the corresponding attractors. In order to estimate basins of attraction, Lyapunov functions can be used. However, there are no systematic approaches available for the construction of Lyapunov functions with the goal to achieve a good approximation of the basin of attraction. The present paper suggests a method for defining appropriate Lyapunov functions using insight from center manifold theory. With this approach, not only variations in the initial conditions, but also in the parameters can be studied. The results are used to calculate the likelihood for the system to reach a certain attractor assuming different random distributions for the initial conditions