Guilhem Michon

Duffing Oscillator With Parametric Excitation: Analytical and Experimental Investigation on a Belt-Pulley System

This paper is devoted to the theoretical and experimental investigation of a sample automotive belt-pulley system subjected to tension fluctuations. The equation of motion for transverse vibrations leads to a Duffing oscillator parametrically excited. The analysis is performed via the multiple scales approach for predicting the nonlinear response, considering longitudinal viscous damping. An experimental setup gives rise to nonlinear parametric instabilities and also exhibits more complex phenomena. The experimental investigation validates the assumptions made and the proposed model.

Experimental Investigation and Design Optimization of Targeted Energy Transfer Under Periodic Forcing

In this paper, the dynamic response of a harmonically forced Linear Oscillator (LO) strongly coupled to a Nonlinear Energy Sink (NES) is investigated both theoretically and experimentally. The system studied comprises a LO with an embedded, purely cubic NES. The behavior of the system is analyzed in the vicinity of 1 : 1 resonance. The complexification-averaging technique is used to obtain modulation equations and the associated fixed points. These modulation equations are analyzed using asymptotic expansion to study the regimes related to relaxation oscillation of the slow flow called Strongly Modulated Response (SMR). The zones where SMR occurs are computed using a mapping procedure. The Slow Invariant Manifolds (SIM) is used to derive a proper optimization procedure. It is shown that there is an optimal zone in the forcing amplitude-nonlinear stiffness parameter plane, where SMR occurs without having a high amplitude detached resonance tongue. Two experimental setups are presented. One is not optimized and has a relatively high mass ratio (≈ 13%) and the other one is optimized and exhibits strong mass asymmetry (mass ratio ≈ 1%). Different frequency response curves and associated zones of SMR are obtained for various forcing amplitudes. The reported experimental results confirm the design procedure, and the possible application of NES for vibration mitigation under periodic forcing.

Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments

Recently, it has been demonstrated that a vibro-impact type nonlinear energy sink (VI-NES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of a LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equation of motion are analyzed using the method of multiple scales in the case of 1 : 1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR response regimes. A good agreement between theoretical and experimental results is observed.

Parametric Instability of an Axially Moving Belt Subjected to Multifrequency Excitations: Experiments and Analytical Validation

This paper experimentally investigates the parametric instability of an industrial axially moving belt subjected to multifrequency excitation. Based on the equations of motion, an analytical perturbation analysis is achieved to identify instabilities. The second part deals with an experimental setup that subjects a moving belt to multifrequency parametric excitation. A data acquisition technique using optical encoders and based on the angular sampling method is used with success for the first time on a nonsynchronous belt transmission. Transmission error between pulleys, pulley/belt slip, and tension fluctuation are deduced from pulley rotation angle measurements. Experimental results validate the theoretical analysis. Of particular note is that the instability regions are shifted to lower frequencies than the classical ones due to the multifrequency excitation. This experiment also demonstrates nonuniform belt characteristics (longitudinal stiffness and friction coefficient) along the belt length that are unexpected sources of excitation. These variations are shown to be sources of parametric instability.

Chatter Control in Turning Process with a Nonlinear Energy Sink

This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.

Virtual Vibration Measurement Using KLT Motion Tracking Algorithm

This paper presents a practical framework and its applications of motion tracking algorithms applied to structural dynamics. Tracking points (“features”) across multiple images is a fundamental operation in many computer vision applications. The aim of this work is to show the capability of computer vision (CV) for estimating the dynamic characteristics of two mechanical systems using a non contact, marker less and simultaneous Single Input Multiple Output (SIMO) analysis. KLT (Kanade-Lucas-Tomasi) trackers are used as virtual sensors on mechanical systems video from high speed camera. First we introduce the paradigm of virtual sensors in the field of modal analysis using video processing. To validate our method, a simple experiment is proposed: an Oberst beam test with harmonic excitation (mode 1). Then with the example of helicopter blade, Frequency Response Functions (FRFs) reconstruction is carried out by introducing several signal processing enhancements (filtering, smoothing). The CV experimental results (frequencies, mode shapes) are compared with classical modal approach and FEM model showing high correlation. The main interest of this method is that displacements are simply measured using only video at FPS (Frame Per Second) respecting the Nyquist frequency.

Hysteretic Behavior of a Belt Tensioner: Modeling and Experimental Investigation:

In this paper we describe the modeling of the hysteretic behavior of belt tensioners. An initial experimental device is composed only of the tensioner by using forcing frequencies, preloads and deflection amplitudes. It permits the identification of the parameters of the restoring force model used. Comparison of the measured and predicted force-deflection loops of the tensioner subjected to large deflections permits preliminary validation of the model. The second experimental device consists of a belt-tensioner system. Its non-linear modeling includes the above hysteretic model and the belt’s longitudinal characteristics. Validation of the belt-tensioner model is completed by comparing the measured and predicted belt tension. Finally, it is shown by using a parametric investigation and phase-plane portrait that the response of the belt-tensioner system increases with the frequency and the amplitude of the excitation.

Robustness Analysis of Helicopter Ground Resonance with Parametric Uncertainties in Blade Properties

This paper presents a stability robustness analysis of the helicopter ground-resonance phenomenon. By using the lifting procedure the uncertain linear-time-periodic model of the helicopter is transformed into an augmented uncertain linear-time-invariant model that allows the application of μ-analysis tools. The lifting procedure involves a periodic switching linear-time-invariant piecewise model computed using oversampling of the system period. The representativeness of the lifted model for various oversampling period values and methods is discussed and compared with a Floquet analysis for several parametric discretization configurations. A μ-analysis is then applied to find the worst-case parametric configuration for a given rotor angular rate. The parametric uncertainties taken into account are the dynamic characteristics (stiffness and damping) of each blade hinge. A significant advantage of the proposed approach is that it enables performing ground-resonance analysis for a rotor with dissimilar blade properties due to aging effects. Considering uncertainties on the four blade hinge stiffnesses and damping factors, the μ-analysis performed on the lifted model leads to the conclusion that the worst case for degraded rotor stability corresponds to the symmetric perturbation of all the blades.

Experimental Investigation and Theoretical Analysis of a Nonlinear Energy Sink Under Harmonic Forcing

In the present works, we examine experimentally and theoretically the dynamic behavior of linear oscillator strongly coupled to a nonlinear energy sink under external periodic forcing. The nonlinear oscillator has a nonlinear restoring force realized geometrically with two linear springs that extend axially and are free to rotate. Hence, the force-displacement relationship is cubic. The linear oscillator is directly excited via an electrodynamic shaker. Experiments realized on the test bench consist of measuring the displacement of the oscillators while increasing and decreasing frequencies around the fundamental resonance of the linear oscillator. Many nonlinear dynamical phenomena are observed on the experimental setup such as jumps, bifurcation, and quasiperiodic regimes. The retained nonlinear model is a two degree of freedom system. The behavior of the system is then explained analytically and numerically. The complexification averaging technique is used to derive a set of modulation equation governing the evolution of the complex amplitude at the frequency of excitation, and a stability analysis is performed.Copyright

Theoretical and Experimental Study of an Harmonically Forced Vibro-Impact Nonlinear Energy Sink

Recently, it has been demonstrated that a Vibro-Impact type Nonlinear Energy Sink (VI-NES) can be used efficiently to mitigate vibration of a Linear Oscillator (LO) under transient loading. In this paper, the dynamic response of an harmonically forced LO, strongly coupled to a VI-NES is investigated theoretically and experimentally. Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equation of motion are analyzed using the method of multiple scales in the case of 1 : 1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit Strongly Modulated Response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR response regimes. A good agreement between theoretical and experimental results is observed.Copyright