Search

International audience; We report on the mechanical excitation of a 220 μm thick thermoplastic film in its amorphous state by the radiation pressure of light. By modulating a low power visible laser (from 100 to 600 mW) at low frequencies (below 100 Hz), we observe a deformation of the film interfaces. The phenomenon, that is independent of the laser wavelength, is amplified at a resonant frequency and reaches 0.68 μm. The deformation is reversible and varies linearly with the optical power. Using the damped oscillator model, we show that the resonant frequency depends on the surface tension of the film. The associated free energy is then compared with the energy lost, taking into account the contribution of the damping corresponding to the imaginary part of the Young's modulus.

Nonlinear oscillators subjected to colored Gaussian/non-Gaussian excitations are modelled through a set of three coupled first-order stochastic differential equations by representing the excitation as a first-order filtered white noise. A 3-D finite element (FE) formulation is developed to solve the corresponding 3-D Fokker Planck (FP) equations. The joint probability density functions of the state variables, obtained as a solution of the FP equation, are typically non-Gaussian and are used for computing the crossing statistics of the response - an essential metric for time variant reliability analysis. The method is illustrated through a noisy Lorenz attractor and a Duffing oscillator subjected to additive colored noise. The increase in state-space dimension when the Duffing oscillator is additionally excited with a parametric Gaussian noise is effectively handled by using stochastic averaging to reduce the state-space dimension. Investigations are carried out to examine the accuracy of the FE method vis-a-vis Monte Carlo simulations. The proposed method is observed to be computationally significantly cheaper for these three problems. � 2014 Elsevier Ltd. All rights reserved.

We study the dynamical response of an asymmetric forced, damped Helmholtz-Duffing oscillator by using Jacobi elliptic functions, the method of elliptic balance, and Fourier series. By assuming that the modulus of the elliptic functions is slowly varying as a function of time and by considering the primary resonance response of the Helmholtz-Duffing oscillator, we derived an approximate solution that provides the time-dependent amplitude-frequency response curves. The accuracy of the derived approximate solution is evaluated by studying the evolution of the response curves of an asymmetric Duffing oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes. © 2013 Alex Elías-Zúñiga and Oscar Martínez-Romero.

We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion. © 2013 Alex Elías- Zúñiga and Oscar Martínez-Romero.

The enhanced cubication method is applied to develop approximate solutions for the most common nonlinear oscillators found in the literature. It is shown that this procedure leads to amplitude-time response curves and angular frequency values with maximum relative errors lower than those found by previously developed approximate solutions. © 2013 Alex Elías-Zúñiga and Oscar Martínez-Romero.

The cubication and the equivalent nonlinearization methods are used to replace the original Duffing-harmonic oscillator by an approximate Duffing equation in which the coefficients for the linear and cubic terms depend on the initial oscillation amplitude. It is shown that this procedure leads to angular frequency values with a maximum relative error of 0.055. This value is 21 lower than the relative errors attained by previously developed approximate solutions. © 2012 Alex Elías-Zúiga et al.

Recently, necessary and sufficient conditions for output synchronization of linear systems via diffusive couplings have been reported. In this paper, we study the case when such conditions are not satisfied and exact synchronization is impossible. In particular, we study two kinds of heterogeneous linear networks: (i) non-identical harmonic oscillators and (ii) double-integrators. We show that static diffusive couplings render heterogeneous networks of harmonic oscillators asymptotically stable. Networks of non-identical double-integrators, in contrast, are not asymptotically stable but synchronize with bounded synchronization error depending on the network topology and the heterogeneity in the agent dynamics. Numerical examples illustrate the results. QC 20130215

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DOI: 10.1061/(ASCE)EM.1943-7889.0000255. (C) 2011 American Society of Civil Engineers.

The sensitivity of laser interferometers can be pushed into regimes that enable the direct observation of the quantum behaviour of mechanical oscillators. In the past, membranes with subwavelength thickness (thin films) have been proposed to be high-mechanical-quality, low-thermal-noise oscillators. Thin films from a homogeneous material, however, generally show considerable light transmission accompanied by heating due to light absorption, which potentially limits quantum opto-mechanical experiments, in particular at low temperatures. In this paper, we experimentally analyse a Michelson-Sagnac interferometer including a translucent silicon nitride (SiN) membrane with subwavelength thickness. We found that such an interferometer provides an operational point that is optimally suited for quantum opto-mechanical experiments with translucent oscillators. In the case of a balanced beam splitter of the interferometer, the membrane can be placed at a node of the electromagnetic field, which simultaneously provides lowest absorption and optimum laser noise rejection at the signal port. We compare the optical and mechanical models of our interferometer with experimental data and confirm that the SiN membrane can be coupled to a laser power of the order of 1Wat 1064 nm without significantly degrading the membrane's quality factor of the order of 106, at room temperature. DFG/EXC/QUEST IMPRS Alexander von Humboldt Foundation

The response of a non-linear mechanical oscillator, depending on the type of non-linearity, to an excitation of particular harmonic might contain sub- and super-harmonics, transients and chaotic components. The conventional frequency response function, used to completely characterise the input-output behaviour of a linear mechanical oscillator, not only does not capture the above characteristics but also, in case of broadband excitation, fails to attribute them to individual frequencies. In this paper we apply the Choi-Williams time frequency distribution to simulated data of a single and three degree of freedom Duffing oscillator in order to assess its input-output relationship. © (2006) by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved. 5 2863 2872 2863-2872

Date of Conference: 27-29 Aug. 1997 Conference name: 1st International Conference, Control of Oscillations and Chaos Proceedings, 1997 In this work we consider the control of forced chaotic oscillators. To obtain any desirable behavior, the system parameters are effectively modified using state feedback. The system states used in the feedback are estimated through a nonlinear observer. The application of the proposed method is illustrated for Duffing and Van der Pol oscillators.

Chaotic motion of a harmonically excited square prism modelled as a Duffing oscillator and kept in fluid flow is considered. The fluid dynamic forces contribute additional non-linear terms to the inherent non-linearity of the system. The harmonically excited oscillator without the fluid flow exhibits three types of steady state periodic motions, dual period 1 motions and period 3 motion without dual. The flow changes the nature of motion of the oscillator. With the flow velocity as bifurcation parameter, the system exhibits period 1 motion without dual, bifurcating into dual period 1 motions which period double into dual period 2, 4, 8 motions, etc., leading to chaos as the flow velocity is increased. Lyapunov exponents for different flow velocities are computed which show the bifurcation points. The harmonic balance method is used to obtain approximate solutions for the periodic motions and to predict the period doubling bifurcations by a stability analysis.

The active control of flow-induced oscillations, specifically, vortex-induced oscillations of circular cylinders and galloping oscillations of circular cylinders and galloping oscillations of a square prism, are considered. In the case of vortex-induced oscillations, the vibrating cylinder is modeled as a single-degree-of-freedom (sdof) linear damped oscillator and the fluid motion as a Rayleigh oscillator. Galloping oscillations are modeled as a sdof limit-cycle system with cubic and higher order non-linearities in the velocity term. In formulating the control method it is assumed that the fluid interaction is an external excitation/disturbance on the structure. A suitable disturbance model is chosen based on the spectral content of the disturbance. For the problems considered here, the disturbance model assumes the form of a harmonic oscillator the frequency of which, in the case of vortex-induced oscillations, is equal to the natural frequency of the structure or the "lock-in" frequency, and in the case of galloping oscillations, is equal to the limit-cycle frequency. A disturbance counteracting control law is synthesized by using a Luenberger observer incorporating the structure and disturbance dynamics. It is shown that using this approach one is able to completely suppress the fluid-induced oscillations of the structure. ? 1993 Academic Press. All rights reserved.