Quenching Vibration on a Harmonically Excited Symmetric Laminated Composite Plate

In this paper a simple and efficient method is developed to quench the steady state vibration of a harmonically excited, damped and symmetric laminated composite rectangular plate. This is achieved by enforcing points of zero displacement, or nodes, at some specified locations on the laminated composite plate using properly tuned damped oscillators. Using the assumed-modes method, the governing equations of the laminated composite plate carrying the damped oscillators are first formulated. A set of constraint equations is established by enforcing nodes at user-specified locations on the plate. Two attachment scenarios are considered: when the attachment and node locations coincide, and when they are distinct. Numerical experiments show that for both cases, the damped oscillator parameters can be readily determined and the desired node locations can be successfully imposed. More importantly, enforcing nodes can suppress vibration in the vicinity of the node locations, thereby keeping that region of the laminated composite plate nearly stationary.

Novel Impedance Sensor based on the Chaotic Van der Pol and Damped Duffing Circuits Coupled

The signature of chaotic systems can be characterized either by the sensitivity of the initial conditions or by the change of its parameters. This feature can be used for manufacturing high sensitivity sensors. Sensors based on chaotic circuits have already been used for measuring water salinity, inductive effects, and both noise and weak signals. This article investigates an impedance sensor based on the Van der Pol and Duffing damped oscillators. The calibration process is a key point and therefore the folding behavior of signal periods was also explored. A sensitivity of 0.15 kΩ/Period was estimated over a range from 89.5 to 91.6 kΩ. This range can be adjusted according to the application by varying the gain of the operational amplifier used in this implementation. The development of this type of sensor might be used in medical and biological engineering for skin impedance measurements, for example. This type of chaotic sensor has the advantage of sensing small disturbances and then detect small impedance changes within biological materials which, in turn, may not be possible with other detectors.

Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data

Modern large telescopes are built based on the effectiveness of adaptive optics systems in mitigating the detrimental effects of wavefront distortions on astronomical images. In astronomical adaptive optics systems, the main sources of wavefront distortions are atmospheric turbulence and mechanical vibrations that are induced by the wind or the instrumentation systems, such as fans and cooling pumps. The mitigation of wavefront distortions is typically attained via a control law that is based on an adequate and accurate model. In this paper, we develop a modelling technique based on continuous-time damped-oscillators and on the Whittle’s likelihood method to estimate the parameters of disturbance models from wavefront sensor time-domain sampled-data. On the other hand, when the model is not accurate, the performance of the minimum variance controller is affected. We show that our modelling and identification techniques not only allow for more accurate estimates, but also for better minimum variance control performance. We illustrate the benefits of our proposal via numerical simulations.

Herglotz’s Variational Problem for Non-Conservative System with Delayed Arguments under Lagrangian Framework and Its Noether’s Theorem

Because Herglotz’s variational problem achieves the variational representation of non-conservative dynamic processes, its research has attracted wide attention. The aim of this paper is to explore Herglotz’s variational problem for a non-conservative system with delayed arguments under Lagrangian framework and its Noether’s theorem. Firstly, we derive the non-isochronous variation formulas of Hamilton–Herglotz action containing delayed arguments. Secondly, for the Hamilton–Herglotz action case, we define the Noether symmetry and give the criterion of symmetry. Thirdly, we prove Herglotz type Noether’s theorem for non-conservative system with delayed arguments. As a generalization, Birkhoff’s version and Hamilton’s version for Herglotz type Noether’s theorems are presented. To illustrate the application of our Noether’s theorems, we give two examples of damped oscillators.

Super Damping of Mechanical Vibrations

We report the phenomenon of coherent super decay (CSD), where a linear sum of the displacement of several damped oscillators can collectively decay much faster than the individual ones in the first stage, followed by stagnating ones after more than 97% of the energy has been dissipated. The parameters of the damped oscillators for CSD are determined by the process of response function decomposition, which is to use several slow decay response functions to approximate the response function of a fast decay resonator. Evidence established in experiments and in finite element numerical simulations not only strongly supported the numerical investigations, but also uncovered an unexplored region of the tuned mass damper (TMD) parameter space where TMD’s with total mass less than 0.2% of a stainless steel plate can damp its first resonance at 100 Hz up to a damping ratio of 4.6%. Our findings also shed light onto the intriguing underline relationships between complex functions with different singular points.