# Recently studied topics

The following topics were studied by the Dynamics and Vibrations Group in the recent past:

# Piezoceramics & Ultrasonic Wave Motors

Ultrasonic motors are actuators that use the high-frequency (ultrasonic) mechanical vibration of a stator to move a rotor. The mechanical force is generated mostly by piezoelectric ceramics. In contrast to the well-known electrodynamic motor based on the Lorentz effect, USM exhibit a large torque at low speed.

Active research in the field of USM technology began approximately 30 years ago, when new working and design principles were studied and prototypes were invented. Over the past ten years, the focus has shifted towards reliability, cost and design optimization, efficiency and mass production of USMs.

Today's research considers, amongst others

- Motor and Material Performance Optimization

It is aimed to explore best the properties of the active material, i.e. the piezoelectric ceramic. This includes study of the material properties including nonlinearities where usually a simplified linear model is adopted, as well as research of the interaction of the active material with structural members, thus forming an actuator and power optimization of actuators - Motor Design and Modeling

To achieve high reliability and performance, experience with prototypes and mathematical modeling of motors or parts thereof have to accompany each other. In the dynamics group, both methods are used for different types of ultrasonic motors - Motor Control

Due to the special characteristics of USM, new control strategies are studied including effects of e.g. temperature, hysteresis behavior or saturation.

# Paradoxical States for Rigid Body Systems with Friction

The assumption of the existence of rigid bodies is widely used in the field of mechanical engineering in order to simplify he mathematical equation describing the problem and to reduce computational effort. If some bilateral constraints of system are non-smooth and the friction force is determined by Coulomb's law, analytical solutions might not exist or might not be unique depending on the initial conditions, the friction force magnitude and the system geometry. This paradox was first discovered by the French scientist and prime minister Paul Painlevé in the late 19th century and is today known as Painlevé's Paradox. System like the shown Painlevé-Klein-System behave in such a paradoxical way for a certain set of parameters.

The main task of this research project is to find an explicit description and indicator for the appearance of such paradoxical situations in order to avoid misleading results. The indicator must work fro holonomic as well as non-holonomic bilateral constraints. As such problems are especially dangerous for “black box” multibody algorithms, the description must include a formalism used by such tools. In a second stage, a physical explanation for the real system behavior must be given under relaxation of either the classical Coulomb law (von Mises's Approach) or under relaxation of the assumption of rigidity (Prandtl's approach).

# Semiactive Control by Friction

Semiactive control operates on a mechanical system by changing stiffness or viscosity. Another possibility is a controlled force, that works normal to a pair of surfaces in rough contact. In this case the friction forces lead to an additional dissipation, controlled depending on the system state.

In contrary to semiactive design active control requires an external energy source. Here, questions of stability rise, furthermore the system becomes more complex. Passive concepts, on the other hand, are often not efficiently enough. Semiactive control uses the advantages of control without the drawback of active systems. It is a promising approach with applications in mechanical and civil engineering and also space structures.

The control of a mechanical system with rough contacts presupposes an understanding of the dynamics. Leaving aside the question of control, these dynamics are still a topic of actual research, especially questions concerning the theoretical background and numerical problems. Some of these results are used in the actual work.

There is a construction in the laboratory of the Dynamics Group for applying this concepts. It goes back to Prof. Gaul, who investigated the influence of normal forces on the vibrations of two layered beams in rough contact. The system at hand consists of a thick beam, clamped between two thinner beams. The pressure between these beams can be adjusted by help of a piezostack, leading to a semiactive design.