Search

This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter. When the control parameter is varied, the clarinet model undergoes a dynamic bifurcation. A consequence of this is the phenomenon of bifurcation delay: the bifurcation point is shifted from the static oscillation threshold to a higher value, called dynamic oscillation threshold. In a previous work Bergeot et al. in Nonlinear Dyn. doi:, (), the dynamic oscillation threshold is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. These dynamic thresholds are found to depend on the increase rate and are independent on the initial value of the parameter, both in simulations and in theory. [ABSTRACT FROM AUTHOR]

Reed instruments are modeled as self-sustained oscillators driven by the pressure inside the mouth of the musician. A set of nonlinear equations connects the control parameters (mouth pressure, lip force) to the system output, hereby considered as the mouthpiece pressure. Clarinets can then be studied as dynamical systems; their steady behavior being dictated uniquely by the values of the control parameters. Considering the resonator as a lossless straight cylinder is a dramatic yet common simplification that allows for simulations using nonlinear iterative maps. This paper investigates analytically the effect of a linearly increasing blowing pressure on the behavior of this simplified clarinet model. When the control parameter varies, results from the so-called dynamic bifurcation theory are required to properly analyze the system. This study highlights the phenomenon of bifurcation delay and defines a new quantity, the dynamic oscillation threshold. A theoretical estimation of the dynamic oscillation threshold is proposed and compared with numerical simulations. [ABSTRACT FROM AUTHOR]

An investigation of structural intensity control associated with flexural vibration in beams using strain sensing is presented in this paper. The instantaneous intensity is completely taken into account in the control algorithm, i.e., all the terms are considered in the real-time control process and, in particular, the evanescent waves are considered in this approach. Previous work has shown the validity of the approach using an array of accelerometers to measure structural intensity. It is the purpose of this paper to present results on the use of strain sensing in the control of structural intensity. A finite difference approach using discrete PVDF strain sensors provides the structural intensity sensing scheme. A feed forward filtered-X LMS algorithm is adapted to this energy-based control problem, involving a nonpositive definite quadratic form in general. In this respect, the approach is limited to cases where the geometry is such that the intensity component will have the same sign for the control source and the primary disturbance. Experimental validation of the approach is conducted on a free-free beam covered with viscoelastic material and excited harmonically by a shaker. A comparison is made between classical acceleration control and structural intensity control and the performance of both approaches is presented. These results tend to indicate that intensity control allows the error sensors to be placed closer to the control source and the primary disturbance, while preserving a good control performance. [ABSTRACT FROM AUTHOR]