Abstract Vibrating Systems

Statistical energy analysis of nonlinear vibrating systems.

Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy bein...

From Abstract Rewriting Systems to Abstract Proof Systems

Some personal recollections on the introduction of ‘abstract proof systems’ as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel de Vrijer: the analogy with abstract

An Approximation Method for Exact Controls of Vibrating Systems

We propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator. The algorithm combines Russell’s “stabilizability implies controllability” principle with the Galerkin’s method. The main new feature brought in by this work consists in giving precise error estimates. In order to test the efficiency of the method, we consid...

Observation of vibrating systems at different time instants

In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of Szijártó and Hegedűs in which the authors ask the question of determining the initial data by only knowing the position of the string at two distinct time instants. The choice of the observation instants is crucial and the estimations rely on the Fourier series expansio...

Dynamic Analysis of Linear Structural Systems with Nonlinear Vibrating Isolators Using Mode Superposition Method