Copyright by the AIP Publishing. Arrieta, A. F.; Hagedorn, P.; Erturk, A.; et al., "A piezoelectric bistable plate for nonlinear broadband energy harvesting," Appl. Phys. Lett. 97, 104102 (2010); http://dx
Considerable effort is spent in the design and testing of disk brake systems installed in modern passenger cars. This effort can be reduced if appropriate mathematical–mechanical models are used for studying the dynamics of these brakes. In this context, the mechanism generating brake squeal in particular deserves closer attention. The present paper is devoted to the modeling of self-excited vibrations of moving continua generated by frictional forces. Special regard is given to an accurate formulation of the kinematics of the frictional contact in two and three dimensions. On the basis of a travelling Euler–Bernoulli beam and a rotating annular Kirchhoff plate with frictional point contact the essential properties of the contact kinematics leading to self-excited vibrations are worked out. A Ritz discretization is applied and the obtained approximate solution is compared to the exact one of the traveling beam. A minimal disk brake model consisting of the discretized rotating Kirchhoff plate and idealized brake pads is analyzed with respect to its stability behavior resulting in traceable design proposals for a disk brake.
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 (Nmatrix, 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.
Adaptive structures have been the focus of much research due to performance gains not possible to achieve using conventional designs. Within this context, the idea of morphing promises augmented capabilities in terms of manoeuvrability, fuel efficiency and the ability to perform dissimilar tasks in an optimal manner. To achieve morphing, materials capable of changing shape requiring minimum actuation are necessary. Bi-stable composites are a type of composite structures which have two statically stable configurations. This bi-stability property, resulting from locked in-plane residual stresses, has attracted considerable attention from the adaptive structure community for morphing structures as actuation is no required to hold each stable configuration. The change between stable states is physically realised as a jump phenomenon or snap-through, which is strongly non-linear in nature. Morphing strategies exploiting snap-through have been studied showing encouraging preliminary results. This article exploits the dynamic response of bi-stable composites as a means of augmenting the actuation for morphing control. A morphing strategy targeting modal frequencies leading to snap-through of the structure is successfully developed. This results in a full-state configuration control by inducing and reversing snap-through as desired. The strategy is tested on a specimen using Macro Fiber Composites as smart actuators validating the proposed concept.
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